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 the 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)=\(\sum_{m=0}^N x(m)W_N^{-k(n-m)}\)

B. yk(n)=\(\sum_{m=0}^{N+1} x(m)W_N^{-k(n-m)}\)

C. yk(n)=\(\sum_{m=0}^{N-1} x(m)W_N^{-k(n+m)}\)

D. yk(n)=\(\sum_{m=0}^{N-1} x(m)W_N^{-k(n-m)}\)

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. WN^{kn} u(n)

D. None of the mentioned

5. What is the system function of the filter with impulse response hk(n)

A. \(\frac{1}{1-W_N^{-k} z^{-1}}\)

B. \(\frac{1}{1+W_N^{-k} z^{-1}}\)

C. \(\frac{1}{1-W_N^k z^{-1}}\)

D. \(\frac{1}{1+W_N^k z^{-1}}\)

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. \(\sum_{n=0}^{N-1} x(n) z_k ^n\), k=0,1,2…L-1

B. \(\sum_{n=0}^{N-1} x(n) z_{-k}^{-n}\), k=0,1,2…L-1

C. \(\sum_{n=0}^{N-1} x(n) z_k^{-n}\), 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. 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

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 needed 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)

12. The effect of round-off errors due to the multiplications performed in the DFT with fixed-point arithmetic is known as Quantization error.

A. True

B. False

13. What is the model that has been adopted for characterizing a round-off error in multiplication?

A. Multiplicative white noise model

B. Subtractive white noise model

C. Additive white noise model

D. None of the mentioned

14. How many quantization errors are present in one complex-valued multiplication?

A. One

B. Two

C. Three

D. Four

15. What is the total number of quantization errors in the computation of single point DFT of a sequence of length N?

A. 2N

B. 4N

C. 8N

D. 12N

16. What is the range in which the quantization errors due to rounding off are uniformly distributed as random variables if Δ=2-b?

A. (0,Δ)

B. (-Δ,0)

C. (-Δ/2,Δ/2)

D. None of the mentioned

17. The 4N quantization errors are mutually uncorrelated.

A. True

B. False

18. The 4N quantization errors are correlated with the sequence {x(n)}.

A. True

B. False

19. How is the variance of the quantization error related to the size of the DFT?

A. Equal

B. Inversely proportional

C. Square proportional

D. Proportional

20. Every fourfold increase in the size N of the DFT requires an additional bit in computational precision to offset the additional quantization errors.

A. True

B. False

21. What is the variance of the output DFT coefficients |X(k)|?

A. \(\frac{1}{N}\)

B. \(\frac{1}{2N}\)

C. \(\frac{1}{3N}\)

D. \(\frac{1}{4N}\)

22. What is the signal-to-noise ratio?

A. σX2.σq2

B. σX2/σq2

C. σX2+σq2

D. σX2-σq2

23. How many number of bits are required to compute the DFT of a 1024 point sequence with an SNR of 30db?

A. 15

B. 10

C. 5

D. 20

24. How many number of butterflies are required per output point in the FFT algorithm?

A. N

B. N+1

C. 2N

D. N-1