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 log_{2}N, 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) y_{k}(n)=∑Nm=0x(m)W−k(n−m)N

b) y_{k}(n)=∑N+1m=0x(m)W−k(n−m)N

c) y_{k}(n)=∑N−1m=0x(m)W−k(n+m)N**d) y _{k}(n)=∑N−1m=0x(m)W−k(n−m)N**

4. If y_{k}(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 h_{k}(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 y_{k}(n) recursively?

a) y_{k}(n)=W_{N}^{-ky}_{k}(n+1)+x(n)**b) y _{k}(n)=W_{N}^{-ky}_{k}(n-1)+x(n)**

c) y

_{k}(n)=W

_{N}ky

_{k}(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 z_{k} are N equally spaced points, then what is the value of z_{k}?

a) re^{-j2πkn/N}

b) re^{jπkn/N}

c) re^{j2πkn}**d) re ^{j2πkn/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) R _{0}>1**

b) R

_{0}<1

c) R

_{0}=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) log_{2}M**b) Mlog _{2}M**

c) (M-1)log

_{2}M

d) Mlog

_{2}(M-1)