Prepare the answers of the following questions.
1.1 True or False. A sytem with symmetric impulse response has linear phase. a) True b) False
1.2 If a sytem has transfer function H(z)=1 - z-1 - z-2 + z-3 what type of symmetry does its impulse response have? a) Type I b) Type II c) Type III d) Type IV
1.3 What is the symmetry condition in the Z-domain for h1[n]? a) H1(z) = z -M H1(z -1) where M=6. b) H1(z) = z -M H1(z -1) where M=7. c) H1(z) = -z -M H1(z -1) where M=6. d) H1(z) = -z -M H1(z -1) where M=7.
1.4 What is the symmetry condition in the Z-domain for h2[n]? a) H2(z) = z -M H2(z -1) where M=6. b) H2(z) = z -M H2(z -1) where M=7. c) H2(z) = -z -M H2(z -1) where M=6. d) H1(z) = -z -M H2(z -1) where M=7.
1.5 What is the symmetry condition in the Z-domain for h3[n]? a) H3(z) = z -M H3(z -1) where M=6. b) H3(z) = z -M H3(z -1) where M=7. c) H3(z) = -z -M H3(z -1) where M=6. d) H3(z) = -z -M H3(z -1) where M=7.
1.6 What is the symmetry condition in the Z-domain for h4[n]? a) H4(z) = z -M H4(z -1) where M=6. b) H4(z) = z -M H4(z -1) where M=7. c) H4(z) = -z -M H4(z -1) where M=6. d) H4(z) = -z -M H4(z -1) where M=7.
1.7 What is the group delay in problem 1 for system h1[n] and h3[n]? a) 3 b) 3.5 c) 171.8 d) 200.5
1.8 What is the group delay in problem 1 for system h2[n] and h4[n]? a) 3 b) 3.5 c) 171.8 d) 200.5
1.9 The zeros of H2(z) and H4(z) are symmetric about a) the imaginary axis only. b) the real axis only. c) the real axis and the imaginary axis. d) neither the real axis nor the imaginary axis.
1.10 The zeros of H1(z) and H3(z) are symmetric about a) the imaginary axis only. b) the real axis only. c) the real axis and the imaginary axis. d) neither the real axis nor the imaginary axis.
1.11 If a causal sytem has a symmetric impulse response which is nonzero up to n=M, the group delay of the system will be a) M. b) M/2. c) (M-1)/2. d) M-1.
1.12 A filter with type II symmetry as in part b will always have a zero at a) 0 radians. b) pi radians. c) pi/2 radians. d) 3*pi/2 radians.
1.13 A filter with type III symmetry, as in part c, will always have a zero or zeros at what frequencies? a) 0 and pi radians b) 0 radians only c) pi radians only
Hint: for these problems look at the plots on a decibel scale.
2.1 After truncating the sinc function in problem 2, which window type gave the narrowest transition region(sharpest cutoff) in the frequency domain? a) rectangular b) bartlett c) hamming
2.2 After truncating the sinc function in problem 2, which window type gave the largest side lobes in the frequency domain? a) rectangular b) bartlett c) hamming
2.3 After truncating the sinc function in problem 2, which window type gave the wider transition region in the frequency domain? a) rectangular b) hamming
3.1 What is the correct value of M in problem 3? a) 50 b) 52 c) 25 d) 26
3.2 Why is it necessary to round M up to the next highest even integer instead of down to the next lowest even integer? a) It ensures the filter will have linear phase. b) By doing so, we guarantee that the filter specifications will be met or exceeded in both the passband and the stopband. c) None of the above
3.3 Why must M be an even integer in this problem instead of odd? a) Linear phase can only be accomplished if M is even. b) If M were odd, we would force a zero at pi radians thus destroying our highpass filter. c) The impulse response would not have been symmetric had M been odd.
3.4 What is the group delay for the filter in this problem? a) 26 b) 25 c) 52 d) 50
3.5 What is the expression for the analytical impulse response of the filter in problem 3? a) h[n] = 0.4*sinc(0.4*pi(n-26)) b) h[n] = sinc(pi(n-26)) c) h[n] = sinc(pi(n-26)) - 0.4*sinc(0.4*pi(n-26)) d) h[n] = 0.4*sinc(pi(n-26)) - 0.4*cos(0.4*pi)
3.6 What is the value of the Kaiser filter parameter beta that meets the specifications in problem 3? a) 2.31 b) 1.92 c) 1.51 d) 4.0
4.1 The frequency response in the frequency sampling method was improved a) With transition band b) Without transition band
4.2 The frequency sampling filter design is a linear phase FIR filter a) True b) False
5.1 Filters designed using the Parks-McClellan algorithm are always stable a) True b) False
5.2 For the specifications: Filter type = LPF, wp1 = 0.1*pi, ws1 = 0.3*pi, PB = 3dB, and SB = 20dB. Which of the following filter design methods results in the narrowest transition and the best rejection characteristics in the stopband? a) Kaiser method b) Window method c) Parks-McClellan method
5.3 For the specifications given in problem 5.2 (For the LPF case) , the Parks-McClellan method and the Kaiser method result in the following filter orders respectively a) 7,6 b) 9,9 c) 9,12 d) 7,9 e) 7,7
6.1 For the specifications given in problem 6, which filter has the best sidelobe level (the lowest) a) Frequency sampling b) Kaiser window c) Parks-McClellan
6.2 Which filter is equiripple in the stop band? a) Frequency sampling b) Kaiser window c) Parks-McClellan
6.3 For the specifications given in problem 6, which filter has more prominent “Gibbs effect? (Hint: Check the linear scale of the frequency response of all filters and zoom in) a) Frequency sampling b) Kaiser window c) Parks-McClellan
6.4 Frequency sampling, because of the straight lines of the interface, gives improved linear phase relative to the other methods. a) True b) False
6.5 Which filter design is more “optimal?in the sense that it comes closer to the desired frequency response? a) Frequency sampling b) Kaiser window c) Parks-McClellan
6.6 If you were going to design a filter which one you would prefer (Kaiser window, frequency sampling, Parks McClellan)? Can you justify your answer?
6.7 Which one do you think is more complex, in terms of computations, to implement?
7.1 Which filter design method requires the highest order to meet the specifications? a) Butterworth b) Chebychev I c) Chebychev II d) Elliptic
7.2 Which filter design method requires the lowest order to meet the specifications? a) Butterworth b) Chebychev I c) Chebychev II d) Elliptic
7.3 Which of the 4 design methods produces a stable filter? a) Butterworth b) Chebychev I c) Chebychev II d) Elliptic e) All of the above
7.4 Filters designed with these 4 IIR methods have linear phase? a) True b) False
7.5 Which filter is equiripple in the stopband and monotonic in the passband? a) Butterworth b) Chebychev I c) Chebychev II d) Elliptic
7.6 Which filter is monotonic in the stopband and equiripple in the passband? a) Butterworth b) Chebychev I c) Chebychev II d) Elliptic
7.7 Which filter is equiripple in the both the passband and the stopband? a) Butterworth b) Chebychev I c) Chebychev II d) Elliptic
7.8 Which filter is monotonic in the both the passband and the stopband? a) Butterworth b) Chebychev I c) Chebychev II d) Elliptic
7.9 For the filters which are monotonic in the stopband, where are all the zeros located? a) z=1 b) z=exp(j*pi/2) c) z= -1 d) z=exp(-j*pi/2)
8.1 What features of J-DSP do you think could be improved? Don't be afraid to be critical. Your comments will be appreciated.
8.2 Did you find any bugs in J-DSP? If so, please describe them.
Place 18 figures in one word file and label them.
Copyright 2008 Andreas Spanias, MIDL, Arizona State University JDSP and Report Submission Software Developed by ASU-MIDL For questions contact Prof. Spanias spanias@asu.edu.