EECS 451 EXAM #3 Winter 2009PRINT YOUR NAME HERE:HONOR CODE PLEDGE: ”I have neither given nor received aid on this exam, nor have Iconcealed any violations of the honor code.” Closed book; 4 sides of 8.5×11 ”cheat sheet.”SIGN YOUR NAME HERE:CIRCLE ONE: Undergraduate GraduateWrite your answer to each question in the answer space to the right of that question.Problems #1-20 are multiple choice (here same as fill-in-the-blank) wort h 5 points each.For Problems #1-3: T=0.1. The analog filter is: Ha(s)=40ss2+400. ha(t)=40 cos(20t)u(t).1. h[n] designed using impulse invariance is: (a) 4 cos(2n)u[n] (b) 40 cos(20n)u[n](c) 400 cos(200n)u[n] (d) 0.4 cos(0.2n)u[n] (e) 2 cos(2n)u[ n]2. H(z) using bilinear transform is: (a)z−1z+1(b)2zz2+2(c)4zz2+2(d)2zz2+1(e)z2−1z2+13. Usi ng a bilinear transform, the continuous-time frequency Ω = 20 maps to discrete-time frequency ω =: (a) 2 0 (b)π4(c)π3(d)π2(e) πCan do #3 independently of #2; no partial credit if wrong #2 leads to wrong #3.4. IIR filters are guaranteed to be stable if designed from a stable analog filter using:(a) Impulse invariance (b) Bilinear transform (c) Both (d) Neither (e) Can’t tellA differentiator has: Ha(s)=s and H(ejω)=jω for |ω| < π and h[n]=(−1)nn, n 6= 0.For problems #5-7: Design a linear-phase length=3 noncausal FIR differentiator using:5. Frequency sampling with: H(ej0)=0. H(ejπ/2)=jπ/2. H(ejπ)=0 (not π) :(a) {−14,12, −14} (b) {π4, 0, −π4} (c) {−π4,π2, −π4} (d) {π4,π2,π4} (e) {1, 0, −1}6. A rectangular window applied to t he ideal digit al different iator:(a) {−14,12, −14} (b) {π4, 0, −π4} (c) {−π4,π2, −π4} (d) {π4,π2,π4} (e) {1, 0, −1}7. An equiripple filter, now wi th H(ejπ)=jπ. The Matlab command designing it:(a) fir1(2,[0,1],[0,1]) (b) fir2(2,[0,1],[0,1]) (c) firpm(2,[0,1],[0,1])(d) firpm(2,[0,1],[0,pi/2],’hilbert’) (e) firpm(2,[0,1],[0,pi],’hilbert’)8. The IIR filter for an ideal integrator designed using bilinear transform with T=2:(a) y[n]+y[n-1]=x[n]+x[n-1] (b) y[n]–y[n-1]=x[n]+x[n-1] (c) y[n]=x[n]+x[n-1](d) y[n]–y[n-1] = x[n]–x[ n-1] (e) y[n]+y[n-1]=x[n]–x[n-1] (f) y[n]=x[n]–x[n-1]For #9-11: A 200 Hz sinusoid is input to a DSP system with sampling rate 1000SAMPLESECOND.Sampler (A/D) and reconstructor (D/A) are not show n. No antiali as filter is used.9. 20 0 Hz→ ↓ 2 →? (a) 100 Hz (b) 100&400 Hz (c) 400 Hz (d) 4 00&600 Hz (e) 600 Hz10. 2 00 Hz→ ↑ 2 →? (a) 100 Hz (b) 100&400 Hz (c) 400 Hz (d) 400&600 H z (e) 600 Hz11. If input is a 200 Hz sinusoid, which DSP system outputs only a 300 Hz sinusoid?LPF is an ideal Low Pass Filter (not bandpass) with a single cutoff frequency.(a) →↑ 3 → ↓ 2 → LPF → (b) → ↓ 3 → ↑ 2 → LPF → (c) → ↑ 3 → LPF → ↓ 2 →(d) →↓ 3 → LPF → ↑ 2 → (e) → ↑ 2 → ↓ 3 → LPF → (f) → ↑ 2 → LPF → ↓ 3 →12. For which frequency ωoare the outputs x[n] of these two systems identical?In both systems, LPF is an ideal lowpass filter with cutoff frequency π/3.#1: cos(ωon) →↑ 3 → LPF → x[n] #2: cos(ωon) → ↓ 3 → LPF → x[n](a) 0.3π (b) 0 .5π (c) 0.6π (d) 0.75π (e) (c) & (d)For #13-16: x[n]=Acos(ω0n)+Bcos(ω1n) for 0≤n≤L-1; use an N-point DFT of x[n].13. To help resolve the two peaks, we should do which o f the foll owing:(a) Increase L (b) Increase N (c) Use Hamming window (d) (a)&(c) (e) (b)&(c)14. To make the spectrum smoot her, we should do which of the following:(a) Increase L (b) Increase N (c) Use Hamming window (d) (a)&(c) (e) (b)&(c)15. To reduce sidelobes aro und t he peaks, we should do which of the following:(a) Increase L (b) Increase N (c) Use Hamming window (d) (a)&(c) (e) (b)&(c)16. Which of these makes it harder to resolve the two peaks:(a) Decrease L (b) Decrease N (c) Use Hamming window (d) (a )&(c) (e) (b)&(c)17. The filter type designed by firpm(10,[0,0.2,0.3,0.7,0.8,1],[0,0,1,1,0,0]) is:(a) Lowpass (b) Bandpass (c) Highpass (d) Band-reject (e) Notch (f) Comb18. The filter with h[n]={a, b, c, d, 0, −d, −c, −b, −a} is guaranteed to be:(a) Lowpass (b) Bandpass (c) Highpass (d) Band-reject (e) Notch (f) Comb19. The 2-D filter having 2-D impulse response h[i, j]=1 −2 1−2 4 −21 −2 1is:(a) Lowpass (b) Bandpass (c) Highpass (d) Band-reject (e) Notch (f) CombHINT: h[i,j] is separable: h[i,j]=h[i]h[j]. What are h[i] and h[j] and what do they do?20. “ DSP” stands for: (a) Digital Signal Processing (b) Drivel Spewed by Professor(c) Dumbest Subject Partaken (d) Drive Slowly Please (e) Dummies Should