# Frequency Sampling Method FIR Design

This set of Digital Signal Processing Multiple Choice Questions & Answers focuses on “Design of Linear Phase FIR Filters by Frequency Sampling Method”.

1. In the frequency sampling method for FIR filter design, we specify the desired frequency response Hd(ω) at a set of equally spaced frequencies.
a) True
b) False

2. To reduce side lobes, in which region of the filter the frequency specifications have to be optimized?
a) Stopband
b) Passband
c) Transition band
d) None of the mentioned

3. What is the frequency response of a system with input h(n) and window length of M?
a) ∑M−1n=0h(n)ejωn
b) ∑Mn=0h(n)ejωn
c) ∑Mn=0h(n)e−jωn
d) ∑M−1n=0h(n)e−jωn

4. What is the relation between H(k+α) and h(n)?
a) H(k+α)=∑M+1n=0h(n)e−j2π(k+α)n/M; k=0,1,2…M+1
b) H(k+α)=∑M−1n=0h(n)e−j2π(k+α)n/M; k=0,1,2…M-1
c) H(k+α)=∑Mn=0h(n)e−j2π(k+α)n/M; k=0,1,2…M
d) None of the mentioned

5. Which of the following is the correct expression for h(n) in terms of H(k+α)?
a) 1M∑M−1k=0H(k+α)ej2π(k+α)n/M; n=0,1,2…M-1
b) ∑M−1k=0H(k+α)ej2π(k+α)n/M; n=0,1,2…M-1
c) 1M∑M+1k=0H(k+α)ej2π(k+α)n/M; n=0,1,2…M+1
d) ∑M+1k=0H(k+α)ej2π(k+α)n/M; n=0,1,2…M+1

6. Which of the following is equal to the value of H(k+α)?
a) H*(M-k+α)
b) H*(M+k+α)
c) H*(M+k-α)
d) H*(M-k-α)

7. The linear equations for determining {h(n)} from {H(k+α)} are not simplified.
a) True
b) False

8. The major advantage of designing linear phase FIR filter using frequency sampling method lies in the efficient frequency sampling structure.
a) True
b) False

9. Which of the following is introduced in the frequency sampling realization of the FIR filter?
a) Poles are more in number on unit circle
b) Zeros are more in number on the unit circle
c) Poles and zeros at equally spaced points on the unit circle
d) None of the mentioned

10. In a practical implementation of the frequency sampling realization, quantization effects preclude a perfect cancellation of the poles and zeros.
a) True
b) False

11. In the frequency sampling method for FIR filter design, we specify the desired frequency response Hd(ω) at a set of equally spaced frequencies.
a) True
b) False

12. What is the equation for the frequency ωk in the frequency response of an FIR filter?
a) πM(k+α)
b) 4πM(k+α)
c) 8πM(k+α)
d) 2πM(k+α)

13. Why is it desirable to optimize frequency response in the transition band of the filter?
a) Increase side lobe
b) Reduce side lobe
c) Increase main lobe
d) None of the mentioned