Digital Signal Processing Mock Test 3

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Question 1 of 10

1. If X₁(k) and X₂(k) are the N-point DFTs of X₁(n) and x₂(n) respectively, then what is the N-point DFT of x(n)=ax₁(n)+bx₂(n)?

None of the mentioned

aX₁(k)+bX₂(k)

e^akX₁(k)+e^bkX₂(k)

X₁(ak)+X₂(bk)

Question 1 of 10

Question 2 of 10

2. The filter with the system function H(z)=z^-k is a ____________

Notch filter

None of the mentioned

All pass filter

Band pass filter

Question 2 of 10

Question 3 of 10

3. What is the energy density spectrum of the signal x(n)=aⁿu(n), |a|<1?

\(\frac{1}{1-2acosω-a^2}\)

\(\frac{1}{1-2acosω+a^2}\)

\(\frac{1}{1+2acosω+a^2}\)

\(\frac{1}{1+2acosω-a^2}\)

Question 3 of 10

Question 4 of 10

4. Which of the following is true?

W_N*=\(\frac{1}{N} W_N^{-1}\)

W_N^-1=\(\frac{1}{N} W_N*\)

W_N^-1=W_N*

None of the mentioned

Question 4 of 10

Question 5 of 10

5. What is the convolution of the sequences of x₁(n)=x₂(n)={1,1,1}?

{1,1,1,1,1}

{1,2,3,2,1}

{1,1,1,1,1}

{1,2,3,2,1}

Question 5 of 10

Question 6 of 10

6. An ideal filter should have unity gain in their stop band.

True

False

Question 6 of 10

Question 7 of 10

7. What is the Fourier transform X(ω) of a finite energy discrete time signal x(n)?

\(\sum_{n=-∞}^∞x(n)e^{-jωn}\)

\(\sum_{n=0}^∞x(n)e^{-jωn}\)

None of the mentioned

\(\sum_{n=0}^{N-1}x(n)e^{-jωn}\)

Question 7 of 10

Question 8 of 10

8. If W₄¹⁰⁰=W_x²⁰⁰, then what is the value of x?

Question 8 of 10

Question 9 of 10

9. If a system is said to be invertible, then?

One-to-one correspondence between its input and output signals

One-to-many correspondence between its input and output signals

Many-to-one correspondence between its input and output signals

None of the mentioned

Question 9 of 10

Question 10 of 10

10. What is the Fourier series representation of a signal x(n) whose period is N?

\(\sum_{k=-\infty}^{\infty}|c_k|^2\)

\(\sum_{k=-\infty}^0|c_k|^2\)

\(\sum_{k=-\infty}^{\infty}|c_k|\)

\(\sum_{k=0}^{\infty}|c_k|^2\)

Question 10 of 10