1.1 The filter in part a is a a) highpass filter. b) lowpass filter. c) bandpass filter.
1.2 The filter in part b is a) an IIR filter. b) a FIR filter.
1.3 The filter in part b is a) stable. b) unstable.
1.4 The region of convergence of the z-transform of the filter in part b a) contains the unit circle. b) does not contain the unit circle.
1.5 If the region of convergence of the z-transform of a system contains the unit circle, the system is a) stable. b) unstable.
1.6 What are the values of the non-zero filter block coefficients in part a? (Note: a0 is always 1) a) a1=1 b0=0.9 b) a1=-0.9 b0=1.0 c) a1=0.9 b0=1.0 a1=0.81
2.1 The period of the impulse response in problem 2 is a) 4 samples. b) 8 samples. c) 16 samples.
2.2 A maximun in the magnitude of the frequency response occurs at what frequency? a) pi/2. b) pi/3. c) pi/4. d) 2*pi/3.
2.3 List the non-zero b filter coefficients.
2.4 List the non-zero a filter coefficients starting with a1.
3.1 If the input to this system is a sinusoid with frequency pi/2, the output at steady state will be a sinusoid scaled by a factor of a) 1.4 b) 3.6 c) 2.2
3.2 The output of the system in part a is a) 1 for all values of n>1 b) 0 for all values of n>1 c) 0 for all values of n>0 d) 1 for all values of n>0
3.3 The frequency of y[n], the output of the system, in part b is a) pi/2 b) pi/3 c) pi/4 d) none of the above
3.4 List the non-zero b filter coefficients.
3.5 Give some reasons for the behavior of the system in this problem.
4.1 The pole-zero plot in figure a represents a) an IIR filter. b) a FIR filter.
4.2 The pole-zero plot in figure b represents a) a FIR filter. b) an IIR filter.
4.3 The output of system a to the triangle input is a) positive for all values of n. b) negative for all values of n. c) alternating positive and negative.
4.4 What are the values of the non-zero filter block coefficients in part a? (Note: a0 is always 1) a) b0=1 a1=-0.9 a2=0.325 a3=-0.05 b) b0=1.0 a1=1.0 a2=1.8 a3=0.9 c) b0=1 a1=1.0 a2=0.9
4.5 What are the values of the non-zero filter block coefficients in part b? (Note: a0 is always 1) a) b0=1 b1=-0.9 b2=0.9 b) b0=1 b1=0.6 b2=1.8 c) b0=1 b1=1.0 b2=0.5
5.1 A cascade connection of 2 systems is equivalent to a) 1 system, whose impulse response is the convolution of the impulse responses of the 2 cascaded systems b) 1 system, whose impulse response is the sum of the impulse responses of the 2 cascaded systems c) 1 system, whose impulse response is the product of the impulse responses of the 2 cascaded systems
5.2 A parallel connection of 2 systems is equivalent to a) 1 system, whose impulse response is the convolution of the impulse responses of the 2 cascaded systems b) 1 system, whose impulse response is the sum of the impulse responses of the 2 cascaded systems c) 1 system, whose impulse response is the product of the impulse responses of the 2 cascaded systems
5.3 The poles of the system function is part a, ii are located at a) 0.5 and 0.25 b) -0.5 and 0.25 c) 1 and 0.5
5.4 What are the values of the filter block coefficients of the two filters in part a (i)? (Note: a0 is always 1) a) b0=1 a1=-0.5 and b0=-0.25 a1=1 b) b0=-0.8 a1=1 and b0=-0.25 a1=1 c) b0=1 a1=-0.5 and b0=1 a1=-0.25
5.5 What are the values of the filter block coefficients of the single filter in part a (ii)? (Note: a0 is always 1) a) b0=1 a1=-0.75 a2=0.125 a3=0.25 b) b0=1 a1=-0.75 a2=0.125 c) b0=1 a1=-0.5 a2=1 a3=-0.25
5.6 What are the values of the filter block coefficients of the two filters in part b (i)? (Note: a0 is always 1) a) b0=1 a1=-0.5 and b0=2 a1=0.9 b) b0=1 a1=0.5 and b0=2 a1=-0.9 c) b0=1 a1=0.75 and b0=1 a1=0.9
5.7 What are the values of the filter block coefficients of the single filter in part b (ii)? (Note: a0 is always 1) a) b0=3 b1=0.75 a1=1.8 a2=0.25 b) b0=1 a1=0.75 a2=1.8 c) b0=3 b1=-0.1 a1=0.4 a2=-0.45
6.1 What effect does a pole in a system's transfer function tend to have on the magnitude of the frequency response? a) It creates a valley in the magnitude response. b) It creates a peak in the magnitude response. c) It has no effect.
6.2 What effect does a zero in a system's transfer function tend to have on the magnitude of the frequency response? a) It creates a valley in the magnitude response. b) It creates a peak in the magnitude response. c) It has no effect.
6.3 Where are the poles and zeros located in part (a)? H(z)=(1-1.2z-1)/( 1 - 0.5z-1) a) One zero at (1/1.2) and one pole at (1/0.5). b) One zero at 1.2 and one pole at 0.5. c) One pole at 1.2 and one zero at 0.5.
6.4 Where are the zeros located in the transfer function if H(z)=1-z-3?
6.5 How many poles does the transfer function H(z)=1/( 1 - 0.85z-5) have? a) 1 pole at z=0.85(1/5) and 4 complex poles which form 2 complex conjugate pairs. b) 5 repeated poles at z=0.85(1/5). c) 1 pole at z=0.85(1/5).
6.6 What effect do poles at the origin(0 + 0i) have on the magnitude of the frequency response of a system? a) They cause a peak at frequency of 0 radians. b) They have no effect. c) They cause a valley at frequency of 0 radians.
6.7 The transfer function in part a has a pole and a zero both located at 0 radians. Why is there a valley in the magnitude response at 0 radians instead of a peak? a) Zeros always have a stronger influence that poles when located at the same frequcncy. b) The magnitude of the zero is greater that the magnitude of the pole. c) The zero is closer to the unit circle than the pole.
7.1 If h1[n]=anu[n] and h2[n]=a(n-1)u[n-1], what is true about the magnitude of the frequency response of h1[n] and h2[n]? a) They will have different shapes. b) They will be exactly the same. c) The will differ only by a gain factor.
7.2 What form does the analytical impulse response in problem 2 have? a) rncos(a*n)u[n] with |r|<1 A sinusoidally decaying exponential.> b) anu[n] with |a|<1. A decaying exponential. .> c) cos(a*n)u[n] An oscillator.
7.3 In problem 2, as the poles move away from the unit circle a) the peaks in the frequency response become sharper. b) the peaks become smaller. c) the bandwidth of the sytem decreases.
8.1 What kind of filter does the following pole-zero diagram respresent where x's are poles and o's are the zeros?
a) Lowpass filter b) Highpass filter c) Bandpass filter d) Bandstop filter e) Allpass filter
9.1 What is the magnitude of all the poles of the system in problem 9? a) 1.1 b) 0.9 c) 0.8 d) 1.2
9.2 What is the magnitude of all the zeros of the system in problem 9? a) 1.1 b) 0.9 c) 0.8 d) 1.2
9.3 What can be said about the distance of the poles and zeros from the unit circle? a) The poles and zeros are about the same distance from the unit circle. b) The zeros are much farther from the unit circle than the poles. c) The poles are much farther from the unit circle than the zeros.
9.4 The system in this problem is a) a lowpass filter. b) an allpass filter. c) a highpass filter. d) a bandpass filter.
Place 26 figures in one word file and label them.
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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.