EECS 451 EXAM #3 Fall 2008PRINT 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) worth 5 points each.For Problems #1-3: T=0.2. The analog filter is: Ha(s)=10s+10. ha(t)=10e−10tu(t).1. h[n] designed using impulse invariance is:(a) 2e−2nu[n] (b) 10e−10nu[n] (c) 20e−20nu[n] (d) 0.1e−0.1nu[n] (e) 0.2e−0.2nu[n]2. H(z) designed using bilinear transform is:(a)12(1 + z−1) (b)2zz−e−2(c)20zz−e−20(d)12(1 − z−1) (e)zz−0.13. Using a bilinear transform, the continuous-time frequency Ω = 10 maps to thediscrete-time frequency ω =: (a) 10 (b)π4(c)π3(d)π2(e) π4. The IIR filter for an ideal differentiator 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]+y[n-1]=x[n]–x[n-1](d) y[n]–y[n-1]=x[n]–[n-1] (e) y[n]=x[n]+x[n-1] (f) y[n]=x[n]–x[n-1]5. 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 tellFor problems #6-8: Design a linear-phase length=3 noncausal FIR low-pass filterhaving cutoff frequency=π2using each of the following three FIR design techniques:6. Frequency sampling with H(ej0)=1. H(ejπ/2)=1/2. H(ejπ)=0:(a) {−14,12, −14} (b) {14,12,14} (c) {−π4,π2, −π4} (d) {π4,π2,π4} (e) {1π,12,1π}7. A rectangular window on the ideal low-pass filter with cutoff frequency ωc=π2:(a) {−14,12, −14} (b) {14,12,14} (c) {−π4,π2, −π4} (d) {π4,π2,π4} (e) {1π,12,1π}8. An equiripple filter. Matlab command: (a) fir1(2,[0,.49,.51,1],[0,0,1,1])(b) fir2(2,[0,.49,.51,1],[0,0,1,1]) (c) firpm(2,[0,.49,.51,1],[0,0,1,1])(d) firpm(2,[0,.49,.51,1],[1,1,0,0]) (e) firpm(2,[0,.5,1],[0,.5,1])9. An FIR filter of the form h[n]={a, b, 0, −b, −a} has the following restrictions:(a) H(ej0)=0 (b) H(ejπ/2)=0 (c) H(ejπ)=0 (d) (a) and (c) (c) NoneProblems #10-13 involve selection of image processing techniques for various tasks:10. To reduce isolated point noise, use:(a) 2-D lowpass filter (b) Median filter (c) Edge detector (d) (a)&(b) (e) (b)&(c)11. To reduce white noise, use:(a) 2-D lowpass filter (b) Median filter (c) Edge detector (d) (a)&(b) (e) (b)&(c)12. To enhance image features, use:(a) 2-D lowpass filter (b) Median filter (c) Edge detector (d) (a)&(b) (e) (b)&(c)13. Which technique has a very different frequency response from the other four?(a) Lowpass filter (b) Highpass filter (c) Differentiator (d) Edge detector (e) NoneFor #14-16: x[n]=Acos(ω0n)+Bcos(ω1n)for0≤n≤L-1; use an N-point DFT of x[n].14. Increasing N helps: (a) Resolve 2 peaks (b) Reduce sidelobes (c) Smoothes spectrum(d) (a)&(b) (e) (b)&(c)15. Increasing L helps: (a) Resolve 2 peaks (b) Reduce sidelobes (c) Smoothes spectrum(d) (a)&(b) (e) (b)&(c)16. A Hamming window helps: (a) Resolve 2 peaks (b) Reduce sidelobes (c) Smoothesspectrum (d) (a)&(b) (e) (b)&(c)For #17-19: A 300 Hz sinusoid is input to a DSP system with sampling rate 1000SAMPLESECOND.Sampler (A/D) and reconstructor (D/A) are not shown. No antialias filter is used.17. 300 Hz→ ↓ 2 →? (a) 150 Hz (b) 150&350 Hz (c) 400 Hz (d) 400&600 Hz (e) 600 Hz18. 300 Hz→ ↑ 2 →? (a) 150 Hz (b) 150&350 Hz (c) 400 Hz (d) 400&600 Hz (e) 600 Hz19. If input is a 300 Hz sinusoid, which DSP system outputs only a 450 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 →20. “DSP” stands for: (a) Digital Signal Processing (b) Drivel Spewed by Professor(c) Dumb Stupid Protocol (d) Drive Slowly Please (e) Dummies Should