Linear Filtering Approach to Computation of DFT

Digital Communications Systems

This set of Digital Signal Processing Multiple Choice Questions & Answers (MCQs) focuses on “Linear Filtering Approach to Computation of DFT”.

1. If the desired number of values of the DFT is less than log2N, a direct computation of the desired values is more efficient than FFT algorithm.
a) True
b) False

2. What is the transform that is suitable for evaluating the z-transform of a set of data on a variety of contours in the z-plane?
a) Goertzel Algorithm
b) Fast Fourier transform
c) Chirp-z transform
d) None of the mentioned

3. According to Goertzel Algorithm, if the computation of DFT is expressed as a linear filtering operation, then which of the following is true?
a) yk(n)=∑Nm=0x(m)W−k(n−m)N
b) yk(n)=∑N+1m=0x(m)W−k(n−m)N
c) yk(n)=∑N−1m=0x(m)W−k(n+m)N
d) yk(n)=∑N−1m=0x(m)W−k(n−m)N

4. If yk(n) is the convolution of the finite duration input sequence x(n) of length N, then what is the impulse response of the filter?
a) WN-kn
b) WN-kn u(n)
c) WNkn u(n)
d) None of the mentioned

5. What is the system function of the filter with impulse response hk(n)?
a) 11−W−kNz−1
b) 11+W−kNz−1
c) 11−WkNz−1
d) 11+WkNz−1

6. What is the expression to compute yk(n) recursively?
a) yk(n)=WN-kyk(n+1)+x(n)
b) yk(n)=WN-kyk(n-1)+x(n)
c) yk(n)=WNkyk(n+1)+x(n)
d) None of the mentioned

7. What is the equation to compute the values of the z-transform of x(n) at a set of points {zk}?
a) ∑N−1n=0x(n)znk, k=0,1,2…L-1
b) ∑N−1n=0x(n)z−n−k, k=0,1,2…L-1
c) ∑N−1n=0x(n)z−nk, k=0,1,2…L-1
d) None of the mentioned

8. If the contour is a circle of radius r and the zk are N equally spaced points, then what is the value of zk?
a) re-j2πkn/N
b) rejπkn/N
c) rej2πkn
d) rej2πkn/N

9. How many multiplications are required to calculate X(k) by chirp-z transform if x(n) is of length N?
a) N-1
b) N
c) N+1
d) None of the mentioned
(N-k).

10. If the contour on which the z-transform is evaluated is as shown below, then which of the given condition is true?

a) R0>1
b) R0<1
c) R0=1
d) None of the mentioned

11. How many complex multiplications are need to be performed to calculate chirp z-transform?(M=N+L-1)
a) log2M
b) Mlog2M
c) (M-1)log2M
d) Mlog2(M-1)

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