11. What are energy and power signals? (April/may 2011, Nov/Dec 2012) Energy signal: The energy of a discrete time signal x(n) is defined as

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1 DHAALAKSHMI COLLEGE OF EGIEERIG, CHEAI DEPARTMET OF COMPUTER SCIECE AD EGIEERIG IT650 DIGITAL SIGAL PROCESSIG UIT - I : SIGALS AD SYSTEMS PART A MARKS. Defie Sigal ad Sigal Processig. A sigal is defied as ay physical quatity that varies with time, space, or ay other idepedet variable. Sigal processig is ay operatio that chages the characteristics of a sigal. These characteristics iclude the amplitude, shape, phase ad frequecy cotet of a sigal.. What are the classificatios of sigals? ov/dec 00 There are five methods of classifyig sigals based o differet features: a Based o idepedet variable. i Cotiuous time sigal. ii Discrete time sigal. b Depedig upo the umber of idepedet variable. i Oe dimesioal sigal, ii Two dimesioal sigal. iii Multi dimesioal sigal. c Depedig upo the certaity by which the sigal ca be uiquely described as i Determiistic sigal. ii Radom sigal. d Based o repetitio ature. i Periodic sigal. ii o Periodic sigal. e Based o reflectio i Eve sigal. ii Odd sigal 3. Defie discrete system. A discrete time system is defied as a device or algorithm that operates o a discrete time iput sigal, accordig to some well defied rule, to produce aother discrete time sigal y called the output sigal.

2 4. What are the classificatios of discrete time systems? The classificatios of discrete time systems are. Static ad Dyamic system.. Time variat ad time ivariat system. 3. Liear ad o liear system. 4. Stable ad U-stable system. 5. Causal ad o-causal system. 6. IIR ad FIR system. 5. Differetiate Cotiuous time ad discrete time sigal. Cotiuous time sigal: It is also referred as aalog sigal i.e., the sigal is represeted cotiuously i time. Discrete time sigal : Sigals are represeted as sequece at discrete time itervals. 6. Defie digital sigal. A discrete time sigal or digital is defied as which discrete valued represeted by a fiite umber of digits is referred to as a digital sigal. 7. What is Determiistic sigal? Give eample. A sigal that ca be uiquely determied by a well - defied process such as a mathematical epressio or rule, or look-up table is called a determiistic sigal. Eample : A siusoidal sigal v t Vm sit 8. What is radom sigal? Give eample. A sigal that is geerated i a radom fashio ad caot be predicted ahead of time is called a radom sigal. Eample : Speech sigal, ECG sigal ad EEG sigal. 9. Defie a Periodic sigal b o periodic sigal. Periodic sigal: A periodic sigal is defied as the sigal is periodic with period if ad oly if += for all. o periodic sigal: A o periodic sigal is defied as if there is o value of that satisfies the equatio What are the symmetric ad at symmetric sigals? Symmetric sigal: A real valued sigal is called symmetric if - =. Atisymmetric sigal: A sigal is called atisymmetric if - = -.

3 . What are eergy ad power sigals? April/may 0, ov/dec 0 Eergy sigal: The eergy of a discrete time sigal is defied as E A sigal is called a eergy sigal if ad oly if the eergy obeys the relatio 0 E. For a eergy sigal P=0. Power sigal: The average power of a discrete time sigal is defied as P lim A sigal is called power sigal if ad oly if the average power P satisfies the coditio 0 P.. What are the differet types of sigal represetatio? The differet types of sigal represetatio are. Graphical represetatio. Fuctioal represetatio 3. Tabular represetatio 4. Sequece represetatio 3. What are the differet types of operatios performed o discrete time sigals? The differet types of operatios performed o discrete time sigals are. Delay of a sigal. Advace of a sigal 3. Foldig or Reflectio of a sigal 4. Time scalig 5. Amplitude scalig 6. Additio of sigals 7. Multiplicatio of sigals 4. Represet the followig duratio sequece ={, 3, -, -4} as a sum of weighted impulse sequeces. Give ={, 3, -, -4} We ca write k k 3 4

4 5. What is a static ad dyamic system? A discrete time system is called static or memory less if its output at ay istats depeds o the iput samples at the same time, but ot a past or future samples of the iput. E., y = a, Y=a I ay other case, the system is said to be dyamic or to have memory. E., y = a-+-, y=+- 6. What is a liear time ivariat system? ov/dec 00 A system is called time ivariat if its iput output characteristics do ot chage with time. E., y=+- 7. What is a causal system? A system is said to be causal if the output of the system at ay time depeds oly o preset ad past iputs, but does ot deped o future iputs. This ca be epressed mathematically as, y=f[, -, - 8. Defie a stable system. Ay relaed system is said to be bouded iput-bouded output BIBO stable if ad oly if every bouded iput yields a bouded output. Mathematically, their eist some fiite umbers, M ad My such that, M ad y My 9. What is a liear system? A system that satisfies the superpositio priciple is said to be a liear system. Superpositio priciple states that, the respose of the system to a weighted sum of sigals be equal to the correspodig weighted sum of the outputs of the system to each of the idividuals iput sigals. 0. Defie uit sample respose impulse respose of a system ad what is its sigificace? The uit sample respose is defied as the output sigal desigated as h, obtaied from a discrete time system whe the iput sigal is a uit sample sequece uit impulse. The output y of a LTI system for a iput sigal ca be obtaied by covolvig the impulse respose h ad the iput sigal. y h k k h k. What is the causality coditio for a LTI system? The ecessary ad sufficiet coditio for causality of a LTI system is, its uit sample respose h=0 for egative values of i.e., h= 0 for <0. What is the ecessary ad sufficiet coditio o the impulse respose for stability?

5 The ecessary ad sufficiet coditio guarateeig the stability of a liear time-ivariat system is that its impulse respose is absolutely summable. h k. 3. What is meat by discrete or liear covolutio? The covolutio of discrete time sigal is kow as discrete covolutio. Let be the iput to a LTI system ad y be the output of the system. Let h be the respose of the system to a impulse. The output y ca be obtaied by covolvig the impulse respose h ad the iput sigal. y y k k k h k OR h k k 4. What are the steps ivolved i the covolutio process? The steps ivolved i the covolutio process are a Epress both sequece i terms of the ide k. b Foldig: Fold the hk about the origi ad obtai h-k. c Time shiftig : Shift the hk by uits to right if is positive or left if is egative to obtai hk. d Multiplicatio: Multiply k by h-k to obtai wk=kh-k e Summatio: Sum all the values of the product wk to obtai the value of output y. f Icremet the ide, shift the sequece h-k to right by oe sample ad do step4. 5. What do you meat by samplig process? Samplig is the coversio of a cotiuous time sigal or aalog sigal ito a discrete time sigal obtaied by takig samples of the cotiuous time sigal or aalog sigal at discrete time istats. 6. State samplig theorem. April/May 0, ov/dec 0 A samplig theorem states that the bad limited cotiuous time sigal with highest frequecy bad width fm hert, ca be uiquely recovered from its samples provided that the samplig rate fs is greater tha or equal to fm samples per secod. 7. Defie yquist rate. ov/dec 008 The yquist rate is defied as the frequecy fm, which, uder samplig theorem, must be eceeded by the samplig frequecy. 8. What is meat by Quatiatio process?

6 The process of covertig a discrete time cotiuous valued sigal ito discrete time discrete valued sigal is called Quatiatio. 9. What is aliasig effect? April/May 008 The superimpositio of high frequecy compoet o the low frequecy is kow as frequecy aliasig or aliasig effect. 30. How ca aliasig be avoided? To avoid aliasig the samplig frequecy must be greater tha twice the highest frequecy preset i the sigal. 3. What is a ati aliasig filter? ov/dec 008 A filter used to reject frequecy sigals before it is sampled to reduce the aliasig is called a ati aliasig filter. 3. What is meat by critical samplig? If the samplig frequecy is eactly equal to the yquist rate is kow as critical samplig. 33. What are the steps ivolved i the A/D coversio? The steps ivolved i the A/D coversio are. Samplig. Quatiatio 3. Codig Each discrete value is represeted by a biary sequece 34. What is meat by Quatiatio error? It is the differece betwee the quatied value ad actual sample value. eq=q- 35. What is a quatiatio level? The value of error that allows i a digital sigal is called the quatiatio level. 36. Defie resolutio or quatiatio step sie. ov/dec 006 The resolutio is defied as the distace betwee two successive levels. 37. What is SQR? The quality of the output of the A/D coverter is usually measured by the sigal to quatiatio oise ratio SQR, which is ratio of the sigal power to oise power. Pav SQR P q

7 38. What is the use of a Sample ad Hold circuit? The sample ad hold circuit is used to hold the sample the aalog sigal ad hold the sampled value costat as log as the A/D coverter takes time for accurate coversio. 39. Defie coversio time. Coversio time may be defied as the time take by a ADC for covertig a give amplitude, epressed i decimal value, of a quatied aalog sigal applied across its iput termials ito correspodig biary equivalet value. 40. Defie voltage resolutio. The voltage resolutio is defied as VFS Votageresolutio where V FS - full scale voltage ad umber of bits. 4. Defie percetage resolutio. Percetage resolutio is defied as % resolutio Defie Z trasform. The Z trasform of a discrete time sigal or sequece is defied as the power series. X 43. What is meat by regio of covergece? April/May 008 The regio of covergece ROC of X is the set of all values of for which X attais a fiite value. 44. What are the properties of regio of covergece? The properties of regio of covergece are. The ROC is a rig or disk i the Z plae cetered at the origi.. The ROC caot cotais ay poles. 3. The ROC of a LTI stable system cotais the uit circle. 4. The ROC must be a coected regio.

8 45. What are the properties of - trasform? ov/dec 008. Liearity: X a X a a a. Shiftig: a 0 m i i m m i X m b X m m 3. Multiplicatio: X d d m m 4. Scalig i - domai: a X a 5. Time reversal : X 6. Cojugatio: X 7. Covolutio: 0 R H m m r h m 8. Iitial value: 0 X Lt 9. Fial value: X Lt 46. State Parseval s relatio i -trasform. April/May 0 Parseval s relatio i -trasform state that If ad are comple valued sequeces, the dv v v X v X j c 47. What is the relatioship betwee -trasform ad DTFT? ov/dec 00 The -trasform of is give by X. Where j re Substitutig value i eq we get, j j e r re X.. The Fourier trasform of is give by j j e e X.3 Eq ad Eq3 are idetical, whe r=. I the -plae this correspods to the locus of poits o the uit circle. Hece j e X is equal to X evaluated alog uit circle

9 48. What are the differet methods of evaluatig iverse trasform?. Log divisio method.. Partial fractio method. 3. Residue method. 4. Covolutio method. 49. Fid the covolutio of the followig usig - trasform. h,, ;,, Solutio: Z h X H X H X H h,3,4,3, 50. Defie system fuctio. Let ad y is the iput ad output sequeces of a LTI system with impulse respose h. The the system fuctio of the LTI system is defied as the ratio of Y ad X, i.e., Y H X where, Y is the trasform of the output sigal y X is the trasform of the iput sigal

10 PART B 6 Marks. Check whether the systems described by the followig equatios are. 6 [/D 4]. Static or dyamic Liear or o-liear Shift variat or shift ivariat Causal or o-causal Stable or ustable. Compute the liear covolutio of the followig sequece usig mathematical equatio, multiplicatio ad tabulatio methods. ad, 0. 6 [/D 4] 3. Compute the covolutio of the sigals ad usig tabulatio method. 4. Check whether the followig systems are static or dyamic, liear or o-liear, time variat or time ivariat, Causal or o-causal, stable or ustable. a 6 [/D 3] 0 [/D 3] b c d e 5. Describe the differet types of digital sigal represetatio. 8 [/D 3] 6. What is yquist rate? Eplai its sigificace while samplig the aalog sigals. 8 [/D 3]

11 7. A causal system is represeted by the followig differetial equatio. Compute the system fuctio ad fid the uit sample respose of the system i aalytical form. 8. Determie the causal sigal for the followig -trasform: a 6 [/D ] 6 [/D ] b 9. Fid the iverse -trasform of, ROC: 8 [/D ] Usig a Residue method b Covolutio method c 0. State ad prove circular covolutio. 8 [/D ]. LTI system is described by the differece equatio Fid the impulse respose, magitude fuctio ad phase fuctio. Solve b, if. Sketch the magitude ad phase respose for a = [/D ]. Fid the covolutio where ad 8 [/D 0] 3. Fid the -trasform of the followig discrete time sigals ad fid ROC. a b c 4. a State ad eplai samplig theorems. b Fid the Z-trasform of auto correlatio fuctio 5. Fid the -trasform of the followig discrete time sigals ad fid ROC. a b 6. Fid whether the followig systems are Liear ad Time ivariat a 8 [/D 0] 6 [/D 0] 6 [M/J 4] 6 [M/J 4] b

12 7. Cosider the aalog sigal. What is the yquist rate for this sigal? Assume that we sample this sigal usig a samplig rate what is the discrete time sigal obtaied after samplig? 8. Derive the equatio for covolutio sum ad summarie the steps ivolved i computig covolutio. 8 [M/J 3] 8 [M/J 3] 9. Determie the trasform ad ROC of the sigal 6 [M/J 3] 0. Check whether the discrete time system is static or dyamic, liear or oliear, time variat or time ivariat, Causal or o causal, stable or ustable 0 [M/J 3]. State samplig theorem ad eplai aliasig graphically. 8 [M/J ]. Fid the circular covolutio of h give that 4 [M/J ] 3. Fid the -Trasform of the give sequece 4 [M/J ] 4. Fid the liear covolutio of h through circular covolutio. Assume the suitable legth, M. 8 [M/J ] 5. List all the properties of aalog ad digital frequecies. 4 [M/J ] 6. Fid the -Trasform of auto correlatio of sigal. 4 [M/J ] 7. Suppose a LTI system with iput ad output y is characteried by its uit sample respose h=. Fid the respose y of such a system to the iput sigal =u. 8. A causal system is represeted by the followig differetial equatio uit sample respose of the system i aalytical form.. Compute the system fuctio ad fid the 8 [M/J ] 8 [M/J ] 9. Compute the ormalied autocorrelatio of the sigal 8 [M/J ]

13 30. Determie the impulse respose for the cascade of two LTI system havig impulse resposes ad. 8 [M/J ]

14 UIT II : FREQUECY TRASFORMATIOS PART A MARKS. Defie Fourier trasform of a discrete time sigal. April/May 008 The Fourier trasform of a discrete time sigal is defied as F X e j. Why FFT of a discrete time sigal is called sigal spectrum? By takig Fourier trasform of a discrete time sigal, it is decomposed ito its frequecy compoets. Hece the Fourier trasform is called sigal spectrum. 3. List the differece betwee Fourier trasform of discrete time sigal ad aalog sigal? a The FT of aalog sigal cosists of a spectrum with a frequecy rage to. But the FT of discrete time sigal is uique i the rage to or 0to, ad also it is periodic with periodicity of. b The FT of aalog sigals ivolves itegratio but FT of discrete time sigals ivolves summatio. 4. Defie iverse Fourier trasform. The iverse Fourier trasform of X is defied as F j X X e d 5. Give some applicatios of Fourier trasform. ov/dec 00 The applicatio of Fourier trasform are. The frequecy respose of LTI system is give by the Fourier trasform of the impulse respose of the system.. The ratio of the Fourier trasform of output to Fourier trasform of iput is the trasfer fuctio of the system i frequecy domai. 3. The respose of a LTI system ca be easily computed usig covolutio property of Fourier trasform. 6. What is the frequecy respose of LTI system? The Fourier trasform of the impulse respose h of the system is called frequecy respose of the system. It is deoted by H.

15 7. Write the properties of frequecy respose of LTI system. The properties of frequecy respose of LTI system are i The frequecy respose is periodic fuctio with a period of. ii If h is real the H is symmetric ad H is atisymmetric. iii If h is comple the the real part of H is atisymmteric over the iterval 0. iv The frequecy respose is a cotiuous fuctio of. 8. Write short otes o the frequecy respose of first order system. A first order system is characteried by the differece equatio y ay The frequecy respose of first order system depeds o the co efficiet a i the differece equatio goverig the LTI system. Whe the value of a is i the rage of 0<a<, the first order system behave as a low pass filter. Whe the value of a is i the rage <a<0, the first order system behave as a high pass filter. 9. Write a short ote o the frequecy respose of secod order system. A secod order system is characteried by the differece equatio y r cos 0 y r y r cos 0 The frequecy respose of secod order system depeds o the parameters r ad 0 i the differece equatio the LTI system. Whe the value of r is i the rage of 0<r<, the secod order system behave as a resoat filter with ceter frequecy 0. Whe the value of r is varied from 0 to, the sharpess of resoat peak icreases. 0. Defie discrete Fourier series. Cosider a sequece p with a period of samples so that p=p/; The the discrete Fourier series of the sequece p is defied as X p k 0 p e jk /. What are the two basic differeces betwee the Fourier trasform of a discrete time sigal with the Fourier trasform of a cotiuous time sigal?. For a cotiuous sigal, the frequecy rage eteds from to. O the other had, the frequecy rage of a discrete time sigal eteds from to or 0to.. The Fourier trasform of a cotiuous sigal ivolves itegratio, whereas, the Fourier trasform of a discrete time sigal ivolves summatio process.

16 . Fid the Fourier trasform of a sequece = for = 0 otherwise. Solutio: X e j e e j e e e j j j j cos cos 3. Defie the Discrete Fourier trasformatio of a give sequece. The - poit DFT of a sequece is X k 0 e jk / k= 0,, Write the formula for - poit IDFT of a sequece Xk. The -poit IDFT of a sequece Xk is K 0 X k e jk / = 0,, List ay four properties of DFT. ov/dec 008 a Periodicity If Xk is - poit DFT of a fiite duratio sequece the for all X k X k for all k. b Liearity If Xk=DFT[] ad Xk=DFT[] The DFT[a+a]=aXk+ak c Time reversal of a sequece If DFT {}=Xk, The DFT{-}=DFT{-}=X-k=X-k d Circular time shiftig of a sequece If DFT {}=Xk, The DFT{-l}=Xk e jkl /

17 6. IF -poit sequece has - poit DFT Xk the what is the DFT of the followig? j e iv l iii ii i l/ Solutio: j kl j l k X e DFT iv e k X l DFT iii k X DFT ii k X DFT i } { } { } { } { l/ / 7. Calculate the DFT of the sequece = 6 4 for Solutio: 0 / k j e k X K=0,,..- 8 / / / k j k j k j k j e e e e 8. State the time shiftig property of DFT. The time shiftig properties of DFT states that If DFT[]=Xk, The DFT[-m]= / k X e j k

18 9. Fid the DFT of the sequece ={,,0,0 } Solutio: 3 0 e j k/4 k 0,,, 3. 3 X 0 { 0 0} 0 X k 0 e jk / k=0,,, j / { 0 0} X e j j 0 3 j X e { 0 0} j3 / 3 { 0 0} X e j j 0 X k {, j, 0, j } 0. Whe the DFT Xk of a sequece is imagiary? If the sequece is real ad odd or imagiary ad eve, the Xk is purely imagiary.. Whe the DFT Xk of a sequece is real? If the sequece is real ad eve or imagiary ad odd, the Xk is purely real.. State Circular frequecy shiftig property of DFT. The circular frequecy shiftig property of DFT states that If DFT[]=Xk, The j l/ DFT[ e ] X k l 3. What is ero paddig? What are its uses? May/Jue 009 The process of legtheig the sequece by addig ero valued samples is called appedig with eros or ero paddig. USES: i We ca get better display of the frequecy spectrum. ii With ero paddig, the DFT ca be used i liear filterig.

19 4. What do you uderstad by periodic covolutio? Let p ad p be two periodic sequeces each with period with If DFS DFS X p p 3 p X X k X p p p k k k X p k ad the the periodic sequece p with Fourier series coefficiets X p ca be obtaied by periodic covolutio, defied as 3 3 p p m p m 0 The covolutio i the form of eq is kow as periodic covolutio, as the sequeces i eq are all periodic with period, ad the summatio is over oe period. 5. Defie circular covolutio. May/Jue 009 The covolutio property of DFT is defied as the multiplicatio of the DFTs of the two sequece is equivalet to the DFT of the circular covolutio of the two sequeces. X k X k DFT{ } 3 m0 m m 6. How the circular covolutio is obtaied by usig Graphical method? Give two sequeces ad, the circular covolutio of these two sequeces ca be obtaied by usig the followig steps. 3. Graph samples of, as equally spaced poits aroud a outer circle i couter clockwise directio.. Start at the same poit as graph samples of as equally spaced poits aroud a ier circle i clock wise directio. 3. Multiply correspodig samples o the two circles ad sum the products to produce output. 4. Rotate the ier circle oe sample at a time i clock wise directio ad go to step3 to obtai the et value of output. 5. Repeat step4 util the ier circle first sample lies up with the first sample of the eterior circle oce agai. 3 k

20 7. Distiguish betwee liear ad circular covolutio of two sequeces. Sl.O Liear Covolutio Circular covolutio. If is a sequece of L umber of samples ad h with M umber of samples, after covolutio y will cotai =L+M- If is a sequece of L umber of samples ad h with M umber of samples, after covolutio y will cotai =MaL,M samples.. Liear covolutio ca be used to fid the respose of a liear filter. Circular covolutio caot be used to fid the respose of a filter. 3. Zero paddig is ot ecessary to fid the respose of a liear filter. Zero paddig is ecessary to fid the respose of a filter. 8. What are the steps ivolved i circular covolutio? The circular covolutios ivolve basically four steps as the ordiary liear covolutio. These are. Foldig the sequece. Circular time shiftig the folded sequece 3. Multiplyig the two sequeces to obtai the product sequece. 4. Summig the values of product sequece. 9. What are the differet methods performig circular covolutio?. Graphical method. Stockhma s method 3. Tabular array method 4. Matri method. 30. Obtai the circular covolutio the followig sequeces ={,, }; h={, -, } Solutio: The circular covolutio of the above sequeces ca be obtaied by usig matri method. h0 h h 0 y0 0 h h h y h h h0 y 3 y 3,,

21 3. How will you obtai liear covolutio from circular covolutio. Cosider two fiite duratio sequeces 9 ad h0 of duratio L samples ad samples respectively. The liear covolutio of these two sequeces produces a output sequece of duratio L+M- samples, whereas, the circular covolutio of ad h give samples where =MaL,M. I order to obtai the umber of samples i circular covolutio equal to L+M-, both ad h must be appeded with appropriate umber of ero valued samples. I other words, by icreasig the legth of the sequeces ad h to L+M- poits ad the circularly covolvig the resultig sequeces we obtai the same result as that of liear covolutio. 3. What is meat by sectioed covolutio? If the data sequece is of log duratio, it is very difficult to obtai the output sequece y due to limited memory of a digital computer. Therefore, the data sequece is divided up ito smaller sectio. These sectios are processed separately oe at a time ad combied later to get the output. 33. What are the differet methods used for the sectioed covolutio? The two methods used for the sectioed covolutio are i the overlap-add method iiover lapsave method. 34. Differetiate i overlap-add method ii overlap save method. Sl.o Overlap add method Overlap save method. I this method the sie of the iput data block is =L+M- I this method the sie of the iput data block is L.. Each data block cosists of the last M- data poits of the previous data followed by the L ew data poits. Each data block is L poits ad we appeded M- eros to compute -poit DFT. 3. I each output block M- poits are corrupted due to aliasig, as circular covolutio is employed. 4. To form the output sequece the first M- data poits are discarded i each output block ad the remaiig datas are fitted together. I this o corruptio due to aliasig as liear covolutio is performed usig circular covolutio. To form the output sequece, the last M- poits from each output block is added to the first M- poits of the succeedig block.

22 35. Distiguish betwee DFT ad DTFT. Sl.o DFT DTFT. Obtaied by performig samplig Samplig is performed oly i time domai. operatio i both the time ad frequecy domais.. Discrete frequecy spectrum Cotiuous fuctio of 36. What is FFT? The term Fast Fourier Trasform FFT usually refers to a class of algorithms for efficietly K computig the DFT.It makes use of the symmetry ad periodicity properties of twiddle factor W to effectively reduce the DFT computatio time. It is based o the fudametal priciple of decomposig the computatio of DFT of a sequece of legth ito successively smaller discrete Fourier trasforms. The FFT algorithm provides speed icrease factors, whe compared with direct computatio of the DFT, of approimately 64 ad 05 for 56 poits ad 04 poit trasforms respectively. 37. How may multiplicatios ad additios are required to compute -poit DFT usig radi- FFT? ov/dec 004 The umber of multiplicatios ad additios required to compute -poit DFT usig radi- FFT are log ad log respectively. 38. How may multiplicatios ad additios are required to compute -poit DFT directly? April/May 008 The umber of multiplicatios ad additios required to compute -poit DFT u are ad respectively. 39. What is the speed improvemet factor i calculatig 64 poit DFT of a sequece usig direct computatio ad FFT algorithms? OR 40. Calculate the umber of multiplicatios eeded i the calculatio of DFT ad FFT with 64-poit sequece. May/Jue 009 The umber of comple multiplicatios required usig direct computatio is The umber of comple multiplicatios required usig FFT is 64 log log 64 9

23 4096 Speed improvemet factor= What is meat by radi- FFT? The FFT algorithm is most efficiet i calculatig -poit DFT. If the umber of output poits ca be epressed as a power of, that is m, where M is a iteger, the this algorithm is kow as radi- FFT algorithm. 4. What is decimatio i time algorithm? The computatio of 8 poit DFT usig radi- FFT, ivolves three stages of computatios. Here =8= 3, therefore r= ad m=3. The give 8 poit sequece is decimated to - poit sequeces. For each poit sequece, the -popit DFT is computed. From the result of poit DFT the 4 poit DFT ca be computed. From the result of 4-poit DFT, the 8 poit DFT ca be computed. 43. What is decimatio i frequecy algorithm? It is the popular form of the FFT algorithm. I this the output sequece Xk is divided ito smaller ad smaller subsequeces, that is why the ame decimatio i frequecy. 44. What are the differece betwee ad similarities betwee DIT ad DIF algorithms? May/Jue 006 Differece betwee DIT ad DIF: I DIT, the iput is bit-reversed while the output is i atural order. For DIF, the reverse is true, i.e., iput is ormal order, while the output bit is reversed. However, both DIT ad DIF ca go from ormal to shuffled data or vice versa. Cosiderig the butterfly diagram, i DIF, the comple multiplicatio takes place after the add subtract operatio. Similarities betwee DIT ad DIF: Both algorithms require same umber of operatios to compute DFT. Both algorithms require bit reversal at some place durig computatio. 45. What are the applicatios of FFT algorithms? ov/dec 006 The applicatios of FFT algorithms icludes i Liear filterig ii Correlatio iii Spectrum aalysis

24 PART B 6 MARKS. State ad prove the periodicity ad time reversal properties of DFT. 8 [/D 4]. Obtai the 4-poit DFT of the followig sequeces... 8 [/D 4] 3. Compute the 8-poit DFT of the equatio =+ usig Radi- DIF-FFT algorithm. 6 [/D 4] 4. Discuss the properties of DFT. 8 [/D 3] 5. Discuss the use of FFT algorithm i liear filterig ad correlatio. 8 [/D 3] 6. Fid DFT for {,,,0,,,0,} usig FFT DIT butterfly algorithm ad plot the spectrum. 6 [/D 3] 7. State ad prove covolutio property of DFT. 6 [/D ] 8. Compute the FFT of the sequece for 0, where =8 usig DIT algorithm. 6 [/D ] 9. Evaluate the 8-poit for the followig sequeces usig DIT-FFT algorithm 8 [/D ] 0. Calculate the percetage of savig i calculatios i a 04-poit radi- FFT, whe compared to direct DFT. 0. Determie the respose of LTI system whe the iput sequece by radi- DIT FFT. The impulse respose of the system is. 8 [/D ] 6 [/D ]. Eplai, how liear covolutio of two fiite sequeces are obtaied via DFT. 8 [/D 0]. Compute the DFT of the followig sequeces: a b whe 8 [/D 0] 3. Draw the flow chart for = 8 usig radi-, DIF algorithm for fidig DFT coefficiets. 6 [/D 0]

25 4. Fid 8-poit DFT of the sequece usig radi- DIT algorithm. 6 [M/J 4] 5. Usig radi- DIT-FFT algorithm, determie DFT of the give sequece for = 8. 6 [M/J 4] 6. Fid eight poit DFT of the followig sequece usig direct method:. 0 [M/J 3] 7. State ay si properties of DFT. 6 [M/J 3] 8. Compute eight poit DFT of the followig sequece usig radi- decimatio i time FFT algorithm.. 0 [M/J 3] 9. Discuss the use of FFT i liear filterig. 6 [M/J 3] 0.Write short otes o filterig methods usig DFT. 8 [M/J ].Compute the DFT of the followig sequeces: a b, =0,,,.7..Let XK=DFT{} with ; K=0,,.,-. Determie the relatioship betwee XK ad the followig DFTs. a DFT {Re} b DFT {-} 3. By meas of the DFT ad IDFT, determie the respose at the FIR filter with the impulse respose h=[,,3] ad the iput sequece =[,,,] 4. Compute the DFT of the followig sequece usig decimatio i time FFT algorithm.. 8 [M/J ] 9 [M/J ] 6 [M/J ] 6 [M/J ]

26 UIT III : IIR FILTER DESIG PART A MARKS. What are the differet types of structures for realiatio of IIR systems? The differet types of structures for realiatio of IIR system are i Direct form I structure ii Direct form II structure iii Cascade form structure iv Parallel form structure v Lattice ladder form structure.. Distiguish betwee recursive realiatio ad o-recursive realiatio. For recursive realiatio the curret output y is a fuctio of past outputs, past ad preset iputs. This form correspods to a Ifiite Impulse respose IIR digital filter. For o-recursive realiatios curret output sample y is a fuctio of oly past ad preset iputs. This form correspods to a Fiite Impulse respose FIR digital filter. 3. How may umber of additios, multiplicatios ad memory locatios are required to realie a system H havig M eros ad poles i a Direct form I realiatio b Direct form II realiatio. a The Direct form I realiatio requires M++ multiplicatios, M+ additios ad M++ memory locatios. b The Direct form II realiatio requires M++ multiplicatios, M+ additios ad the maimum of M, memory locatios. 4. What is the mai advatage of Direct form- II realiatios whe compared to Direct form I realiatio? ov/dec 008 I Direct form II realiatio, the umber of memory locatios required is less tha that of Direct form I realiatio. 5. Defie sigal flow graph. A sigal flow graph is a graphical represetatio of the relatioship betwee the variables of a set of liear differece equatios.

27 6. What is trasposed theorem ad trasposed structure? The traspose of a structure is defied by the followig operatios. i Reverse the directios of all braches i the sigal flow graph. ii Iterchage the iput ad outputs. iiireverse the roles of all odes i the flow graph. iv Summig poits become brachig poits v Brachig poits become summig poits Accordig to traspositio theorem if we reverse the directios of all brach trasmittace ad iterchage the iput ad output i the flow graph, the system fuctio remais uchaged. 7. What is Caoic form structure? The Direct form II realiatio requires miimum umber of delays for the realiatio of the system. Hece it is called as Caoic form structure. 8. What is the mai disadvatage of direct form realiatio? The Direct form realiatio is etremely sesitive to parameter quatiatio. Whe the order of the system is large, a small chage i a filter coefficiet due to parameter quatiatio, results i a large chage i the locatio of the poles ad eros of the system. 9. What is the advatage of cascade realiatio? Quatiatio errors ca be miimied if we realie a LTI system i cascade form. 0. What are the differet types of filters based o impulse respose? Based o impulse respose the filters are of two types. IIR filter. FIR filter The IIR filters are of recursive type, whereby the preset output sample depeds o the reset iput, past iputs samples ad output samples. The FIR filters are of o recursive type whereby the preset output sample is depeds o the preset iput sample ad previous iput samples.. What is the geeral form of IIR filter? The most geeral form of IIR filter ca be writte as M bk k 0 H a k k k

28 . Give the magitude of Butterworth filter. What is the effect of varyig order of o magitude ad phase respose? The magitude fuctio of the Butterworth filter is give by H j,, 3... c Where is the order of the filter ad c is the cut off frequecy. The magitude respose of the Butterworth filter closely approimates the ideal respose as the order icreases. The phase respose becomes more o-liear as icreases. 3. Give ay two properties of Butterworth lowpass filters.. The magitude respose of the Butterworth filter decreases mootoically as the frequecy icreases from 0 to α.. The magitude respose of the Butterworth filter closely approimates the ideal respose as the order icreases. 3. The Butterworth filters are all pole desigs. 4. The poles of the Butterworth filter lies o a circle. 5. At the cut off frequecy c, the magitude of ormalied Butterworth filter is. 4. What is Butterworth approimatio? I Butterworth approimatio, the error fuctio is selected such that the magitude is maimally flat i the origi i.e., at =0 ad mootoically decreasig with icreasig. 5. How the poles of Butterworth trasfer fuctio are located i s- plae? The poles of the ormalied Butterworth trasfer fuctio symmetrically lies o a uit circle i s-plae with agular spacig of. 6. What is Chebyshev approimatio? I Chebyshev approimatio, the approimatio fuctio is selected such that the error is miimied over a prescribed bad of frequecies. 7. What is Type Chebyshev approimatio? I type Chebyshev approimatio, the error fuctio is selected such that, the magitude respose is equiripple i the pass bad ad mootoic i the stop bad.

29 8. What is Type Chebyshev approimatio? I type Chebyshev approimatio, the error fuctio is selected such that, the magitude respose is mootoic i pass bad ad equiripple i the stop bad. The Type - magitude respose is called iverse Chebyshev respose. 9. Write the magitude fuctio of Chebyshev low pass filter? The magitude respose of Type - low pass Chebyshev filter is give by H a C c where is atteuatio costat ad C is the Chebyshev polyomial of the first kid of degree. c 0. How the order of the filter affects the frequecy respose of Chebyshev filter. From the magitude respose of Type - Chebyshev filter it ca be observed that the magitude respose approaches the ideal respose as the order of the filter is icreased.. How will you determie the order of Chebyshev filter. The order of the Chebyshev filter is give by Where cosh s cosh p p 0 s. What are the properties of Chebyshev filter?. The magitude respose of the Chebyshev filter ehibits i ripple either i pass bad or i the stop bad accordig to the type.. The magitude respose approaches the ideal respose as the value of icreases. 3. The Chebyshev type filter are all pole desigs. 4. The poles of Chebyshev filter lies o a ellipse. 5. The ormalied magitude fuctio has a value of at the cutoff frequecy c.

30 3. Compare the Butterworth ad Chebyshev Type - filter. May/Jue 009 Sl.o Butterworth filter Chebyshev filter. All pole desig All pole desig. The poles lie o a circle i s-plae The poles lie o a ellipse i s-plae 3. The magitude respose is maimally flat at the origi ad mootoically decreasig fuctio of. 4. The ormalied magitude respose has a value of at the cut off frequecy c. 5. Oly few parameters has to be calculated to determie the trasfer fuctio. The magitude respose is equiripple i pass bad ad mootoically decreasig i the stop bad. The ormalied magitude respose has a value of at the cut off frequecy c. A large umber of parameter has to be calculated to determie the trasfer fuctio. 4. What are the differet types of filters based o the frequecy respose? The filters ca be classified based o frequecy respose. They are i low pass filter ii high pass filter iii Bad pass filter iv Bad reject filter. 5. Distiguish betwee FIR ad IIR filter. ov/dec 008 Sl.o FIR filter IIR filter. These filters ca be easily desiged to These filters do ot have liear phase. have perfectly liear phase.. FIR filters ca be realied recursively IIR filters are easily realied recursively. ad o recursively. 3. Greater fleibility to cotrol the shape of their magitude respose. Less fleibility, usually limited to specific kid of filters. 4. Error due to roud off oise are less severe i FIR filters, maily because feedback is ot used. The roud off oise i IIR filters are more. 6. What are the desig techiques of desigig FIR filters? These are three well-kow methods for desigig FIR filters with liear phase. These are Widows method Frequecy samplig method 3 Optimal or miima desig.

31 7. What do you uderstad by liear phase respose? For a liear phase filter. The liear phase filter did ot alter the shape of the origial sigal. If the phase respose of the filter is o liear the output sigal may be distorted oe. I may cases a liear phase characteristic is required throughout the passbad of the filter to preserve the shape of a give sigal with i the pass bad. IIR filter caot produce a liear phase. The FIR filter ca give liear phase, whe the impulse respose of the filter is symmetric about its mid poit. 8. For what kid of applicatio, the atisymmetrical impulse respose ca be used? The atisymmetrical impulse respose ca be used to desig Hilbert trasformers ad differetiators. 9. For what kid of applicatio, the symmetrical impulse respose ca be used? The impulse respose, which is symmetric havig odd umber of samples ca be used to desig all types of filters, i.e., lowpass, highpass, badpass ad badreject. The symmetric impulse respose havig eve umber of samples ca be used to desig lowpass ad badpass filter. 30. How ca you desig digital filters from the aalog filters?. Map the desired digital filter specificatios ito those for a equivalet aalog filter.. Derive the aalog trasfer fuctio for the aalog prototype. 3. Trasform the trasfer fuctio of the aalog prototype ito a equivalet digital filter trasfer fuctio. 3. Metio ay two procedures for digitiig the trasfer fuctio of a aalog filter. The two importat procedures for digitiig the trasfer fuctio of a aalog filter are. Impulse ivariace method.. Biliear trasformatio method. 3. What are the requiremets for a digital filter to be stable ad causal? i The digital trasfer fuctio H should be a ratioal fuctio of ad the co-efficiet of should be real. ii The poles should lie iside the uit circle i -plae. iiithe umber of eros should be less tha or equal to umber of poles. 33. What are the requiremets for a aalog filter to be stable ad causal? i The digital trasfer fuctio Has should be a ratioal fuctio of s ad the co-efficiet of s should be real. ii The poles should lie o the left half of s-plae. iii The umber of eros should be less tha or equal to umber of poles.

32 34. What are the advatages ad disadvatages of digital filters? Advatages:. High thermal stability due to absece of resistors, iductors ad capacitors.. The performace characteristics like accuracy, dyamic rage, stability ad tolerace ca be ehaced by icreasig the legth of the registers. 3. The digital filters are programmable. 4. Multipleig ad adaptive filterig are possible. Disadvatages:. The badwidth of the discrete sigal is limited by the samplig frequecy.. The performace of the digital filter depeds o the hardware used to implemet the filter. 35. What is impulse ivariat trasformatio? The trasformatio of aalog filter to digital filter without modifyig the impulse respose of the filter is called impulse ivariat trasformatio i.e., i this trasformatio the impulse respose of the digital filter will be sampled versio of the impulse respose of the aalog filter. 36. What is the mai objective of impulse ivariat trasformatio? The objective of this method is to develop a IIR filter trasfer fuctio whose impulse is the sampled versio of the impulse respose of the aalog filter. Therefore the frequecy respose characteristics of the aalog filter are preserved. 37. Write the impulse ivariat trasformatio used to trasform real poles with ad without multiplicity. The impulse ivariat trasformatio used to trasform real poles at s = - pi without multiplicity is s p i is trasformedto e The impulse ivariat trasformatio used to trasform multiple real pole at s = - pi is is trasformed to m m m pit s p m dp e i 38. What is the relatio betwee digital ad aalog frequecy i impulse ivariat trasformatio. The relatio betwee aalog ad digital frequecy i impulse ivariat trasformatio is give by Digital frequecy, T where, - Aalog frequecy ad T - Samplig time period d p T i m i

33 39. What is biliear trasformatio? April/May 008 The Biliear trasformatio is a coformal mappig that trasforms the s-plae to -plae. I this mappig the imagiary ais of s-plae is mapped ito the uit circle i -plae, the left half of s-plae is mapped ito iterior of uit circle i -plae ad the right half of s-plae is mapped ito eterior of uit circle i -plae. The Biliear mappig is a oe to-oe mappig ad it is accomplished whe s T 40. What is the relatio betwee digital ad aalog frequecy i Biliear trasformatio? I Biliear trasformatio, the digital frequecy ad aalog frequecy are related by the equatio, T Digital frequecy, ta or Aalog frequecy ta T Where, - Aalog frequecy T - Samplig time period 4. What is frequecy warpig? ov/dec 008 I biliear trasformatio the relatio betwee aalog ad digital frequecies is oliear. Whe the s- plae is mapped ito -plae usig biliear trasformatio, this oliear relatioship itroduces distortio i frequecy ais, which is called frequecy warpig. 4. What is prewarpig? Why it is employed? April/May 008 I IIR filter desig usig biliear trasformatio, the coversio of the specified digital frequecies to aalog frequecies is called prewarpig. The prewarpig is ecessary to elimiate the effect of warpig o amplitude respose. 43. Defie prewarpig i IIR filter. I IIR filter desig usig biliear trasformatio the specified digital frequecies are coverted to aalog equivalet frequecies, which are called prewarp frequecies. Usig the prewarp frequecies, the aalog filter trasfer fuctio is desiged ad the it is trasformed to digital filter trasfer fuctio.

34 44. Compare the impulse ivariat ad biliear trasformatios. Sl.o Impulse Ivariat trasformatio Biliear trasformatio. It is may to oe mappig It is oe to oe mappig.. The relatio betwee aalog ad digital frequecy is liear. 3. To prevet the problem of aliasig the aalog filters should be bad limited. The magitude ad phase respose of 4. aalog filter ca be preserved by choosig low samplig time or high samplig frequecy. The relatio betwee aalog ad digital frequecy is oliear. There is o problem of aliasig ad so the aalog filter eed ot be bad limited. Due to the effect of warpig, the phase respose of aalog filter caot be preserved. But the magitude respose ca be preserved by prewarpig.

35 PART B 6 MARKS. Determie the system fuctio of the IIR digital filter for the aalog trasfer fuctio with T 0. secod usig impulse ivariat method. 6 [/D 4]. A digital filter with a 3 db badwidth of 0.5π is to be desiged from the aalog filter whose system respose is usig biliear trasformatio ad obtai. 3. Desig a Butterworth digital filter usig biliear trasformatio that satisfy the followig specificatios 0.89 [/D 4] 6 [/D 3] 4. Discuss the limitatio of desigig a IIR filter usig impulse ivariat method 6 [/D 3] 5. Covert the aalog filter with the system trasfer fuctio usig biliear 0 [/D 3] trasformatio. 6. The specificatio of the desired low pass digital filter is 6 [/D ] Desig a Chebyshev digital filter usig impulse ivariace trasformatio. 7. The specificatio of the desired low pass digital filter is 6 [/D ] Desig a Butterworth filter usig biliear trasformatio. 8. Desig a digital low pass filter usig biliear trasformatio, for the give aalog trasfer fuctio. Assume samplig frequecy of 00 rad/sec. 6 [/D 0]

36 9. Desig FIR filter usig impulse ivariace techique. Give that ad implemet 6 [/D 0] the resultig digital filter by adder, multipliers ad delays. Assume samplig period T= sec. 0. Desig a digital Chebyshevfilter usig biliear trasformatio satisfyig the followig costraits. Assume T = sec. 6 [M/J 4]. Realie the followig FIR system with differece equatio i direct form I. 6 [M/J 4]. Aalye briefly the differet structures of IIR filter. 0 [M/J 4] 3. Obtai the direct form I, direct form II, cascade ad parallel realiatio for the followig system 8 [M/J 3] 4. For the aalog trasfer fuctio. Determie usig impulse ivariace method. Assume T = sec. 8 [M/J 3] 5. A impulse respose, ht=ep-0.5tut of certai LTI system. Fid the T.F. H use impulse ivariat techique. Assume T= sec. 8 [M/J ] 6 Compare the aalog filters with digital filters. 4 [M/J ] 7. Differetiate betwee biliear trasformatios with frequecy traslatio of filter trasfer fuctio. 4 [M/J ] 8. Draw the ideal gai vs frequecy characteristics of HPF ad BPF ad also how the above filters practically specified. 8 [M/J ] 9. Write short otes o frequecy traslatio i both aalog ad digital domai. 8 [M/J ] 0. Fid correspodig to the impulse ivariace desig usig a sample rate of /T samples/sec for a aalog filter with trasfer fuctio specified as follows: 6 [M/J ].. Desig a digital low pass filter usig biliear trasform to satisfy the followig characteristics Mootoic stop bad ad pass bad -3dB cutoff frequecy of 0.5 rad 3 magitude dow at 0 [M/J ]

37 least -5 db at 0.75 rad.. Desig a IIR filter usig impulse ivariace techique for the give aalog trasfer fuctio 6 [M/J ]. Assume T=sec. Realie this filter usig direct form I ad direct form II.

38 UIT IV : FIR FILTER DESGI PART A MARKS. What is the coditio for the impulse respose of FIR filter to satisfy for costat group ad phase delay ad for oly costat group delay? For liear phase FIR filter to have both costat group delay ad costat phase delay. For satisfyig above coditio h h that is the impulse respose must be symmetrical about If oe costat group delay is desired the For satisfyig the above coditio h h that is the impulse respose must be atisymmetrical about. What are the properties of FIR filter? a FIR filter is always stable because all its poles are at the origi. b A realiable filter ca always be obtaied. c FIR filter has a liear phase respose. 3. What are the steps ivolved i the FIR filter desig? i Choose the desired ideal frequecy respose H. ii Take iverse Fourier trasform of H to get h d. iii Covert the ifiite duratio h d to a fiite duratio sequece h. d iv Take Z trasform of h to get the trasfer fuctio H of the FIR filter. d 4. What is the ecessary ad sufficiet coditio for the liear phase characteristic of a FIR filter? May/Jue 006 The ecessary ad sufficiet coditio for the liear phase characteristic of a FIR filter is that the phase fuctio should be a liear fuctio of, which i tur requires costat phase delay or costat group delay.

39 5. How the costat group delay ad phase delay is achieved i liear phase FIR filters? Frequecy respose of FIR filter with costat group ad phase delay H H e j The followig coditios have to be satisfied to achieve costat group ad phase delay. Phase delay, i.e., phase delay is costat Group delay, i.e., group delay is costat Impulse respose, h = - h - i.e., impulse respose is ati symmetric 6. What are the possible types of impulse respose for liear phase FIR filters. There are four types of impulse respose for liear phase FIR filters. Symmetric impulse respose whe is odd.. Symmetric impulse respose whe is eve. 3. Atisymmetric impulse respose whe is odd. 4. Atisymmetric impulse respose whe is eve. 7. List the well kow desig techiques for liear phase FIR filter. May/Jue 006 There are three well kow methods of desig techiques for liear phase FIR filters. They are, i Fourier series method ad widow method. ii Frequecy samplig method. iii Optimal filter desig method. 8. Write the two cocepts that lead to the Fourier series or widow method of desigig FIR filters. The followig two cocepts lead to the desig of FIR filters by Fourier series method. The frequecy respose of a digital filter is periodic with period equal to samplig frequecy. Ay periodic fuctio ca be epressed as a liear combiatio of comple epoetials. 9. Write the procedure for desigig FIR filter by Fourier series method. April/May 008 i Choose the desired ideal frequecy respose H of the filter. ii Evaluate the Fourier series co-efficiet of H which gives the desired impulse respose h d. hd H d e j d iii Trucate the ifiite sequece h d to a fiite duratio sequece h. iv Take Z trasform of h to get a ocausal filter trasfer fuctio H of the FIR filter. d d

40 v Multiply H by to covert ocausal trasfer fuctio to a realiable causal FIR filter trasfer fuctio. H h0 h 0. What are the disadvatages of Fourier series method? I desigig FIR filter usig Fourier series method the ifiite duratio impulse respose is trucated at =. Direct trucatio of the series will lead to fied percetage overshoots ad udershoots before ad after a approimated discotiuity i the frequecy respose.. What is Gibbs pheomeo? ov/dec 004 j The way of fidig a FIR filter that approimates H e would be to trucate the ifiite Fourier series at =.The abrupt trucatio of the series will lead to oscillatio both i passbad ad i stopbad. This pheomeo is kow as Gibbs pheomeo.. Write the procedure for desigig FIR filter usig widows. Choose the desired ideal frequecy respose H of the filter. Evaluate the Fourier series co-efficiet of H which gives the desired impulse respose h d. 3 h H e d d j d 4 Choose a widow sequece w ad multiply the ifiite sequece h d by wto covert the ifiite duratio impulse respose to fiite duratio impulse respose h. 5 h h w d Fid the trasfer fuctio of the realiable FIR filter. H h0 h 3. What are the desirable characteristics of the widow? May/Jue 009 The desirable characteristics of the widow are. The cetral lobe of the frequecy respose of the widow should cotai most of the eergy ad should be arrow. d d

41 . The highest side lobe level of the frequecy respose should be small. 3. The side lobe of the frequecy respose should decrease i eergy rapidly as teds to. 4. What is widow ad why it is ecessary? j The way of fidig a FIR filter that approimates H e April/May 008 would be to trucate the ifiite Fourier series at =. The abrupt trucatio of the series will lead to oscillatio both i passbad ad i stopbad. These oscillatios ca be reduced through the use of less abrupt trucatio of the Fourier series. This ca be achieved by multiplyig the ifiite impulse respose with a fiite weighig w, called a widow. 5. List characteristics of FIR filter desiged usig widows. i The width of the trasitio bad depeds o the type of widow. ii The width of the trasitio bad ca be made arrow by icreasig the value of where is the legth of the widow sequece. iii The atteuatio i the stop bad is fied for a give widow, ecept i case of Kaiser widow where it is variable. 6. Write the procedure for FIR filter desig by frequecy samplig method.. Choose the desired frequecy respose H d.. ~ Take samples of H d to geerate the sequece H k. 3. ~ Take iverse DFT of H k. to get the impulse respose h. 4. The trasfer fuctio H of the filter is obtaied by takig Z trasform of impulse respose. 7. What is meat by Optimum equiripple desig criterio? Why it is followed? I FIR filter desig by Chebyshev approimatio techique, the weighted approimatio error betwee the desired frequecy ad the actual frequecy respose is spread evely across the passbad ad stopbad.the resultig filter will have ripples i both the passbad ad stopbad. This cocept of desig is called optimum equiripple desig criterio. The optimum equiripple criterio is used to desig FIR filter i order to satisfy the specificatios of passbad ad stopbad. 8. Write the epressio for frequecy respose of rectagular widow. The frequecy respose of rectagular widow is give by si WR si