Digital Signal Processing Practice Test 3

1. Which of the following is true?

None of the mentioned

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

W_N^-1=W_N*

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

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

\(\frac{1}{1-2acosω+a^2}\)

\(\frac{1}{1+2acosω-a^2}\)

\(\frac{1}{1-2acosω-a^2}\)

\(\frac{1}{1+2acosω+a^2}\)

3. What is the magnitude of the frequency response of the system described by the difference equation y(n)=ay(n-1)+bx(n), 0<a<1?

\(\frac{|b|}{1-2acosω+a^2}\)

\(\frac{|b|}{\sqrt{1+2acosω+a^2}}\)

\(\frac{|b|}{\sqrt{1-2acosω+a^2}}\)

\(\frac{|b|}{1+2acosω+a^2}\)

4. If X(ω) is the Fourier transform of the signal x(n), then what is the Fourier transform of the signal x(n-k)?

e^-jωk. X(-ω)

e^-jωk. X(ω)

e^jωk. X(ω)

e^jωk. X(-ω)

5. What is the response of the system with impulse response h(n)=(1/2)ⁿu(n) and the input signal x(n)=10-5sinπn/2+20cosπn?

20-\(\frac{10}{\sqrt{5}} sin(π/2n+26.60)+ \frac{40}{3cosπn}\)

20-\(\frac{10}{\sqrt{5}} sin(π/2n-26.60)+ 40cosπn\)

None of the mentioned

20-\(\frac{10}{\sqrt{5}} sin(π/2n-26.60)+ \frac{40}{3}cosπn\)

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

{1,2,3,2,1}

{1,1,1,1,1}

{1,2,3,2,1}

{1,1,1,1,1}

7. If x(n) and X(k) are an N-point DFT pair, then x(n+N)=x(n).

False

True

8. If x(n) is a stable sequence so that X(z) converges on to a unit circle, then the complex cepstrum signal is defined as ____________

ln X(z)

X(ln X(z))

X^-1(ln X(z))

None of the mentioned

9. An ideal filter should have zero gain in their stop band.

True

False

10. What are the main characteristics of Anti aliasing filter?

All of the mentioned

To limit the additive noise spectrum and other interference, which corrupts the signal

None of the mentioned

Ensures that bandwidth of signal to be sampled is limited to frequency range