SIGNALS AND SYSTEMS I Computer Assignment 1
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1 SIGNALS AND SYSTEMS I Computer Assigmet I MATLAB, sigals are represeted by colum vectors or as colums i matrices. Row vectors ca be used; however, MATLAB typically prefers colum vectors. Vector or matrices ca be etered ito MATLAB usig several differet methods icludig typig a explicit list of elemets, usig MATLAB's built-i fuctios, ad usig user defied fuctios. Geeratig Simple Sigals Short simple sigals ca easily be etered ito MATLAB by typig a list of the sigal's elemets. To eter a matrix ito MATLAB by this method. surroud the etire list of elemets with square brackets, [ ],. separate the row elemets with spaces or commas 3. separate the colum elemets with semicolos, ;. the matrix, ad the row vector, A = [ 3;4 ;] 3 A 4 x = [ i +*j (+)] x i i 4. After a matrix or vector has bee etered, MATLAB's built-i fuctios ca rearrage them if desired. if the built-i fuctios.' ad ' are placed after a vector or matrix, MATLAB performs a traspose or complex cojugate traspose operatio of the vector or matrix, respectively; that is, y = x.' ad z = x' geerate y i i i ad z. i 4 4 The built-i fuctios, flipup ad fliplr flip a matrix's rows i the up dow directio ad flip a matrix's colums i the left right directio, respectively; that is, B = flipup(a) ad C = fliplr(a) geerate Determiistic ad Stochastic Sigals ad Liear Systems by Stubberud Computer Homework Chapter Sigals. Page of Wedesday, August 4, 00
2 ad C Vectors ad matrices ca also be combied as log as their dimesios agree. D = [A A.'] Idividual matrix elemets ca be accessed by usig the typical computer row colum otatio. f = D(,) ad g = D(,3) f ad g. Multiple elemets ca be accessed by usig vectors for the rows or colums. h = D([ 3],) h. 8 Because MATLAB was developed as a matrix program, operators such as +, -, * ad ^, perform matrix operatios ad ot ecessarily sigal operatios. If a matrix operatio does ot correspod to the correspodig sigal operatio, a period is placed i frot of the operatio to perform sigal operatios. if x = [ 3].' ad y = [4 3 ].' ad a = x+y, b = x-y, ad c = *x the 3, b ad c 4. Because additio, subtractio ad scalar multiplicatio for matrices ad sigals reder idetical results, matrix additio, subtractio ad scalar multiplicatio is used to perform sigal additio, subtractio ad scalar multiplicatio, respectively. O the other had, because matrix multiplicatio is differet from sigal multiplicatio, sigal multiplicatio uses the.* operatio. For example, if x = [ 3] ad y = [3 4 ] ad a = x.' * y, b = x * y.', c = x.'.* y.', ad d = x.'.^ the 4 3 a B a D , b, c ad d As illustrated by the example, the operators, * ad ^, are matrix operators, ad the operators,.* ad.^, are sigal operators. Determiistic ad Stochastic Sigals ad Liear Systems by Stubberud Computer Homework Chapter Sigals. Page of Wedesday, August 4, 00
3 Exercises. Geerate the followig sigals for - by typig a explicit list of elemets a) [], the uit impulse sequece. b) [], the uit step sequece. r() x y 0,,,3,,,0,,, 3,,0,,,3,,,0,, Plot your results usig the figure ad stem fuctio. Use the sytax stem(r, sigal) where r is the sigal you created i part. figure(#) opes a widow umbered, #.. Usig the sigals that you created i exercise, a) apped the sigals x ad y so that the resultig sigal is a periodic sigal. Plot your results usig the stem fuctio. b) Extract the 3rd sample of r(), x(), ad y(); that is, prit r(3), x(3), ad y(3). 3. Usig the elemetary sigals that you created i exercise, geerate the followig ew sigals: a) b) c[] u( ) d[] x() y() e[] x() y() f[] x() () g[] r()u( ) Plot your results usig the stem fuctio. Agai, use the sytax stem(time, sigal). Determiistic ad Stochastic Sigals ad Liear Systems by Stubberud Computer Homework Chapter Sigals. Page 3 of Wedesday, August 4, 00
4 Geeratig Sigals usig the Colo Operator MATLAB's colo operator, :, ca be used to easily defie simple vectors (sigals). Usig these simple vectors, more complicated sigals ca easily be created. The colo operator's sytax is start : icremet (default = ) : ed m = 0 : - : -0 m ad = 0 : More complicated sigals ca the be geerated usig these vectors. x = (0.).^ ad y = si(pi.*/3) the sigals for 0 0. ad The vectors geerated usig MATLAB's colo operator, :, ca be also be used to access elemets of a matrix. if = 0 : 0 the m = ([::0]) or m = ([::ed]) m Used by itself, the colo operator will iclude a etire row or colum. if 3 the x() A 4 a = A(,:) a 3 y() si 3 MATLAB has built-i fuctios that ca easily create commoly used vectors ad matrices. W = oes(,3) a x3 matrix of oes, that is, W. Similarly, the MATLAB built-i fuctio zeros(n,m) a NxM matrix of zeros.. Determiistic ad Stochastic Sigals ad Liear Systems by Stubberud Computer Homework Chapter Sigals. Page 4 of Wedesday, August 4, 00
5 Exercises 4. Geerate the followig sigals for -. a) [], the uit impulse sequece. b) [], the uit step sequece. f) x[] y[] z[] cos( / ) f[] cos( / ) Plot your results usig the stem fuctio. Use the sytax stem(, sigal) where is a appropriate time vector).. Usig the sigals that you geerated i Exercise 3, geerate the followig ew sigals: a) b) c() z() f () d[] x() e() u( ) g() u( ) h() x( ) Plot your results usig the stem fuctio. Use the sytax stem(, sigal) where is a appropriate time vector).. Geerate ad plot r() e j /. Determiistic ad Stochastic Sigals ad Liear Systems by Stubberud Computer Homework Chapter Sigals. Page of Wedesday, August 4, 00
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