Questions for Problem 1

1.2 To calculate the z-transform in part b, the following z-transform property is useful
a) multiplication by an exponential sequence.
b) differentiation of X(z).
c) time shifting.

1.3 The filter in part c is
a) an IIR filter.
b) a FIR filter.

1.4 The region of convergence of the z-transform of the filter in part b is:
a) |z| < 0.9.
b) |z| > 0.9.
c) |z| >= 0.9.

1.5 The filter in part c is
a) stable.
b) unstable.

1.6 The region of convergence of the z-transform of the filter in part c
a) contains the unit circle.
b) does not contain the unit circle.

1.7 If the region of convergence of the z-transform of a system contains the unit circle, the system is 
a) stable.
b) unstable.

1.8 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

1.9 What are the values of the non-zero filter block coefficients in part b? (Note: a₀ is always 1)
a) b₀=0 b₁=1.0 a₁=-1.8 a₂=0.81 
b) b₀=1.0 b₁=1.0 a₁=1.8 a₂=1.0 
c) b₀=0 b₁=1.0 a₁=2.0 a₂=2.4 

1.10 List the non-zero b filter coefficients for part c.

1.11 List the non-zero a filter coefficients for part c starting with a₁.

1.12 Enter one paragraph of observations for problem 1.

Questions for Problem 2

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.

2.5 Enter one paragraph of observations for problem 2.

Questions for Problem 3

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 Enter one paragraph of observations for problem 3.

Questions for Problem 4

4.2 Which of the following is true about the phase response?
a) It has a constant value at all frequencies.
b) It has a constant slope at all frequencies.
c) It has neither constant value nor constant slope.

4.3 What is the effect of the phase response in this sytem on a signal that is applied at its input?
a) It changes the signal's frequency.
b) It has no effect on the signal at all.
c) It causes a constant delay in the signal from input to output for signals of all frequencies.

4.4 List the non-zero b filter coefficients.

4.5 Enter one paragraph of observations for problem 4.

Questions for Problem 5

5.2 The pole-zero plot in figure b represents
a) a FIR filter.
b) an IIR filter.

5.3 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.

5.4 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

5.5 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

5.6 Enter one paragraph of observations for problem 5.

Questions for Problem 6

6.2 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

6.3 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

6.4 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

6.5 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

6.6 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

6.7 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

6.8 Enter one paragraph of observations for problem 6.