VISUALIZATION OF THE ABSTRACT THEORIES IN DSP COURSE BASED ON CDIO CONCEPT

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1 VISUALIZATION OF THE ABSTRACT THEORIES IN DSP COURSE BASED ON CDIO CONCEPT Wang L-uan, L Jan, Zhen Xao-qong Chengdu Unvesty of Infomaton Technology ABSTRACT The pape analyzes the chaactestcs of many fomulas and abstact theoes n Dgtal Sgnal Pocessng(abb.DSP couse, efeng to the concept of CDIO Conceve Desgn, ntends to smulate the fomulas, theoems and popetes wth the natual thngs o thngs n lfe. It s ted to vsualze the abstact theoes n DSP couse, to gude the students to memoze and undestand the theoes. Expements fo moe than 2 students show that ths method s welcome and vey effectve. KEYWORDS CDIO, DSP, fomula, theoem, popety, CDIO Standads 8..THE METHOD VISUALIZATION LEARNING FOR ABSTRACT THEOREMS CDIO engneeng educaton mode s the achevement of ntenatonal engneeng educaton efomaton fo last ten yeas. It means Conceve- Desgn- Implement- Opeate. It s emphaszed to encouage students to study actvely. Refeng to the concept of Conceve- Desgn, t s ted to gude the students to smulate the fomulas, theoems and popetes wth the natual thngs o thngs n lfe. That can help them to memoze and undestand these fomulas, theoems and popetes. The method s named afte vsualzaton leanng fo abstact theoems. (.Wte down the fomula (2.Analyze the physcal meanng of the fomula (4.Fnd the smlaty between the natue thng/phenomenon and fomula (3.Conceve a natue thng o phenomenon smla to the physcal Fg.. Flow Chat of the method Vsualzaton of Abstact theoy

2 Hee, a flow chat fo descbng ths method thought s dawn as Fg.. The pocedue of the method s descbed as below: ( Wte down the fomula; (2 Analyze the physcal meanng of the fomula; (3 Conceve a natue thng o phenomenon smla to the physcal meanng; (4 Fnd the smlaty between the natue thng/phenomenon and fomula; (5 Retun to (. Theefoe, a closed loop s consttuted as abstacton to vsualzaton then to abstacton. Wth the help of ths closed loop, the students can undestand those abstact fomulas, theoems, and popetes. Then, we use ths method to study some mpotant knowledge ponts n Dgtal sgnal pocessng couse, abbevated as DSP below. 2.THE METHOD IS USED FOR STUDYING DSP COURSE Thee ae manly thee pats fo DSP couse: ( Dscete Foue Tansfom (DFT; (2 Fast Foue Tansfom (FFT; (3 Dgtal flte desgn. Then, how to use the method to memoze and undestand the thee pats? 2. DFT DFT s the FT(Foue Tansfom of fnte sequence. In ths pat, thee s an mpotant and dffcult knowledge pont: the popety conugate symmety of DFT. xn ( = x ( n + x ( n ep DFT/ IDFT X ( k = X ( k + X ( k op x( n = x ( n + x ( n DFT/ IDFT Xk ( = X ( k + X ( k ep op Fg.2.conugate symmety popety I Fg.3. conugate symmety popety II The popety s defned as: the DFT of sgnal xn ( s X( k, xn ( can be descbed as the sum of conugate symmety pat component x ( e n and conugate ant-symmety component x ( n, then the DFT of conugate symmety op pat component x ( e p n s X ( k the eal pat of X( k ; On the othe hand, the DFT of conugate ant-symmety pat component x ( o p n s X ( k ---the mage pat of X( k multpled by. Ths popety can be smply shown as Fg.2 conugate p

3 symmety popety I. Fg.3 shows anothe knd of ccumstance--- xn ( s descbed as the sum of eal pat x ( n and mage pat x ( n multpled by. Subsequently, to analyze the physcal meanng of the popetes, to smulate the popetes wth the natual thngs o thngs n lfe. Take the example of conugate symmety popety I. In lfe, symmety s often consdeed as chaactestc of beautful thng. So, Chnese tadtonal peacock dance s exemplfed to llustate the concept of conugate symmety and conugate ant-symmety (Fg.4. x ( e p n = + DFT/IDFT X ( k Even Odd xn ( X( k + x ( o p n = + DFT/IDFT X ( k Odd Even Fg.4. vsualzaton Fgue fo conugate symmety popety I As the left hand sde of Fg.4, conugate symmetc sgnal x ( e n s the sum of even functon and *odd functon. Whle, conugate ant-symmetc sgnal x ( o n s the sum of odd functon and *even functon. Fnally, sgnal xn ( can be gotten by addng x ( e p n to x ( o p n. Then, look at the ght hand sde of Fg.4, t vsualzes X( k the DFT of p p xn. ( The eal peson smulates X ( k the eal pat of Xk (, the + and the shadow smulates X ( k the mage pat of Xk (. So fa, we vsualze the conugate symmety

4 popety I Fg.2 as Fg.3. In the same way, we can vsualze the conugate symmety popety II Fg FFT(Fast Foue Tansfom Thee ae many fast algothms fo DFT, 2-based FFT s equed fo undegaduates to maste. The coe thought of ths algothm s constuctng a knd of buttefly opeaton as Fg.5.a and Fg.5.c whch show the opeatonal flow chats fo 8-dot DIT-FFT(decmaton-n-tme FFT and 8-dot DIF- FFT(decmaton-n-tme FFT. Fo vsualzng these two opeatonal flow chats, we smulate the buttefly opeaton wth buttefly as Fg.5.b and Fg.5.d. Smultaneously look at Fg.5.a and Fg.5.b, nput sgnals ae sequenced n bnay evese ode fom the left wngs of buttefly. Up aow means buttefly ae head towads the up. Fom left to ght, the buttefles ae two tmes moe than the pevous. The output sgnals ae outputted fom ght wngs n sequence. Once, someone knows ths vsualzaton fo DIT-FFT and DIF-FFT, he/she can easly wtes down the opeatonal flow chats. x( x(4 x(2 x(6 x( x(5 x(3 x(7 X3( X3( X4( X4( X5( X5( X6( X6( X( X( X(2 X(3 X2( X2( X2(2 X2(3 2 3 Fg.5.a. 8-dot DIT-FFT X( X( X(2 X(3 X(4 X(5 X(6 X(7 x( x(4 x(2 x(6 x( x(5 x(3 x(7 Fg.5.b. vsualzaton of 8-dot DIT-FFT X( X( X(2 X(3 X(4 X(5 X(6 X(7 x( X( X3( X( x( x(2 x(3 x(4 x(5 x(6 x(7 2 3 X( X(2 X(3 X2( X2( X2(2 X2(3 X3( X4( X4( X5( X5( X6( X6( X(4 X(2 X(6 X( X(5 X(3 X(7 Fg.5.c.8-dot DIF-FFT Fg.5.d.vsualzaton of 8-dot DIF-FFT

5 2.3. Desgn of Dgtal flte Thee ae two knds of desgn fo IIR Dgtal flte and FIR Dgtal flte. No matte whch one, the desgn thought s to desgn a classc o deal analogc flte H (e Ω, then t can be tansfomed to dgtal flte H (e ω / H ( z. At fst, to wte down the fomula H (e Ω ampltude-fequency esponse functon of analog flte, the fomula H ( s tansfe fauncton of analog flte, the fomula H (e ω ampltude-fequency esponse functon of dgtal flte, and the fomula H ( z system functon of dgtal flte, H (e Ω = h(t e Ωt dt ; H ( s = h(t e st dt ; + + H (e ω = h(ne ω n ; H ( z = h(n z n. Fo H (e Ω + ] shown as Fg.6.a, whle H (e ω s a peodc, Ω s n the ange of [ - functon wth the cycle 2π shown as Fg.6.b. H (e ω H (e Ω -2π Ω Fg.6.a.ampltudefequency cuve of analogc fllte π -π 2π Fg.6.b.ampltude-fequency cuve of dgtal fllte Ω Re( z σ Im( z Fg.6.c.S-plane of analogc Fg.6.d.Z-plane of dgtal flte flte Too lage to move H (e Ω o Ω Re( z the analog flte nto compute, how do we do? The answe: Ω / σ Roll t up! Fg.6.e.vsualzaton of analogc Im( z Fg.6.f.vsualzaton of dgtal flte flte

6 Fo H( s, the doman of convegence s the left half-plane as Fg.6.c., whle fo H( z, the doman of convegence s a ccle Fg.6.d. In the pocedue of tansfomng the analogc flte to dgtal flte, many students ae confused that how does the ampltude-fequency cuve of analogc flte Fg.6.a be changed to the ampltude-fequency cuve of dgtal flte Fg.6.b? How does the S doman of convegence egon fo analogc flte Fg.6.c be changed to t the S doman of convegence egon fo dgtal flte Fg.6.d? Then, accodng to the chaactestcs of He ( Ω, H( s, H (e ω and H( z,we thnk of wallpape, whch s too bg to take n the oom, so they ae usually olled up. Ths s seemed that analog flte s too long( He ( Ω n [ - +, ] o too bg( H( s n the whole left half-plane to move nto compute, So, n the same way, we oll ( H s / He ( Ω n up as H( z lke Fg.6.e and Fg.6.f. At last, we vsualze the pocedue fom analog flte to dgtal flte. 3.CONCLUSION The pape puts fowad a method vsualzaton leanng fo abstact theoems based on CDIO concept. And ths method s used n the educaton fo DSP couse, whch helps the students to memoze and undestand the fomulas, theoems, and popetes of some algothms. What s moe, the students ae moe nteested n ths couse when you change the abstact fomulas, theoems and popetes to vsual thngs. REFERENCES Wu Da-Qn, Yao Wen-Xue,( Publcaton Yea: 2, Desgn and mplementaton of CDIO capablty evaluaton system based on expet system, Mechatonc Scence, Electc Engneeng and Compute (MEC, 2 Intenatonal Confeence on DOI:.9/MEC Page(s: Cted by: Papes (. Jang Jn-gang, Zhang Yong-de, Shao Jun-peng, Su Xu-ln, Zhang Jan-y(Publcaton Yea: 24, Educaton and cultvaton eseach of engneeng undegaduate's nnovatve ablty based on TRIZ-CDIO theoy, Compute Scence & Educaton (ICCSE, 24 9th Intenatonal Confeence on DOI:.9/ICCSE , Page(s: BIOGRAPHICAL INFORMATION

7 Wangluan, Maste mao n Sgnal Pocessng. She teaches DSP couse n Chengdu Unvesty of Infomaton Technology, and has focused on the educaton fo DSP couse fo 4 yeas, hopng to engage students dectly n thnkng and poblem solvng actvtes. L Jan, Maste mao n Sgnal Pocessng. He s the co-autho fo ths atcle, gves some dea fo the vsualzaton educaton fo DSP couse. Zhen Xao-qong, Maste mao n Sgnal Pocessng. She s anothe co-autho fo ths atcle, also gves some dea fo the vsualzaton educaton fo DSP couse. Coespondng autho Wangluan Chengdu Unvesty of Infomaton Technology 6225, Chna wl@cut.edu.cn Ths wok s lcensed unde a Ceatve Commons Attbuton-NonCommecal-NoDevs 3. Unpoted Lcense.