Digital Signal Processing Mock Test 4

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Question 1 of 10

1. If x(n)=cosω₀n and W(ω) is the Fourier transform of the rectangular signal w(n), then what is the Fourier transform of the signal x(n).w(n)?

[W(ω-ω₀)- W(ω+ω₀)]

[W(ω-ω₀)+ W(ω+ω₀)]

1/2[W(ω-ω₀)- W(ω+ω₀)]

1/2[W(ω-ω₀)+ W(ω+ω₀)]

Question 1 of 10

Question 2 of 10

2. What is the highest frequency that is contained in the sampled signal?

None of the mentioned

F_s/2

F_s

2Fs

Question 2 of 10

Question 3 of 10

3. 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.

True

False

Question 3 of 10

Question 4 of 10

4. What is the circular convolution of the sequences X₁(n)={2,1,2,1} and x₂(n)={1,2,3,4}, find using the DFT and IDFT concepts?

{14,16,14,16}

{14,14,16,16}

None of the mentioned

{16,16,14,14}

Question 4 of 10

Question 5 of 10

5. We can view y(n)=-\(\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k)\) as the computational procedure (an algorithm) for determining the output sequence y(n) of the system from the input sequence x(n).

False

True

Question 5 of 10

Question 6 of 10

6. If X(k) is the DFT of x(n) which is defined as x(n)=x₁(n)+jx₂(n), 0≤ n≤ N-1, then what is the DFT of x₁(n)?

\(\frac{1}{2} [X*(k)-X*(N-k)]\)

\(\frac{1}{2} [X*(k)+X*(N-k)]\)

\(\frac{1}{2j} [X*(k)-X*(N-k)]\)

\(\frac{1}{2j} [X*(k)+X*(N-k)]\)

Question 6 of 10

Question 7 of 10

7. Which of the following is the rational system function of an LTI system characterized by the difference equation y(n)=-\(\sum_{k=1}^N a_k y(n-k)+\sum_{k=0}^N b_k x(n-k)\)?

\(\frac{\sum_{k=0}^N b_k x(n-k)}{1+\sum_{k=1}^N a_k y(n-k)}\)

\(\frac{\sum_{k=0}^N b_k x(n-k)}{1+\sum_{k=0}^N a_k y(n-k)}\)

\(\frac{1+\sum_{k=0}^N a_k y(n-k)}{\sum_{k=0}^N b_k x(n-k)}\)

\(\frac{1+\sum_{k=1}^N a_k y(n-k)}{\sum_{k=0}^N b_k x(n-k)}\)

Question 7 of 10

Question 8 of 10

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

Question 8 of 10

Question 9 of 10

9. According to Goertzel Algorithm, if the computation of DFT is expressed as a linear filtering operation, then which of the following is true?

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

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

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

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

Question 9 of 10

Question 10 of 10

10. Finite word length effects refer to the quantization effects that are inherent in any digital implementation of the system, either in hardware or software.

True

False

Question 10 of 10