This set of Digital Signal Processing Questions for campus interviews focuses on “IIR Filter Design by Impulse Invariance”.

1. By impulse invariance method, the IIR filter will have a unit sample response h(n) that is the sampled version of the analog filter.

a) True

b) False

View Answer

Explanation: In the impulse invariance method, our objective is to design an IIR filter having a unit sample response h(n) that is the sampled version of the impulse response of the analog filter. That is

h(n)=h(nT) ; n=0,1,2…

where T is the sampling interval.

2. If a continuous time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, the spectrum of the sampled signal is:

a) Non periodic repetition

b) Non periodic non-repetition

c) Periodic repetition

d) None of the mentioned

View Answer

Explanation: When a continuous time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, the spectrum of the sampled signal is periodic repetition.

3. If a continuous time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, then what is the scaled spectrum?

a) X(F)

b) Fs.X(F)

c) X(F)/ Fs

d) None of the mentioned

View Answer

Explanation: When a continuous time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, the spectrum of the sampled signal is periodic repetition of the scaled spectrum Fs.X(F).

4. When σ=0, then what is the condition on ‘r’?

a) 0<r<1

b) r=1

c) r>1

d) None of the mentioned

View Answer

Explanation: We know that z=e

^{sT}

Now substitute s=σ+jΩ and z=r.e

^{jω}, that is represent ‘z’ in the polar form

On equating both sides, we get

r=e

^{σT}

Thus when σ=0, the value of ‘r’ varies from r=1.

5. What is the equation for normalized frequency?

a) F/Fs

b) F.Fs

c) Fs/F

d) None of the mentioned

View Answer

Explanation: In the impulse invariance method, the normalized frequency f is given by

f= F/Fs

6. Aliasing occurs if the sampling rate Fs is more than twice the highest frequency contained in X(F).

a) True

b) False

View Answer

Explanation: Aliasing occurs if the sampling rate Fs is less than twice the highest frequency contained in X(F).

7. Which of the filters have a frequency response as shown in the figure below?

a) Analog filter

b) Digital filter without aliasing

c) Digital filter with aliasing

d) None of the mentioned

View Answer

Explanation: In the given diagram, the continuous line is the frequency response of analog filter and dotted line is the frequency response of the corresponding digital filter with aliasing.

8. The frequency response given in the above question is for a low pass digital filter.

a) True

b) False

View Answer

Explanation: The above given frequency response depicts the frequency response of a low pass analog filter and the frequency response of the corresponding digital filter.

9. Sampling interval T is selected sufficiently large to completely avoid or at least minimize the effects of aliasing.

a) True

b) False

View Answer

Explanation: The digital filter with frequency response H(ω) has the frequency response characteristics of the corresponding analog filter if the sampling interval T is selected sufficiently small to completely avoid or at least minimize the effects of aliasing.

10. Which of the following filters cannot be designed using impulse invariance method?

a) Low pass

b) Band pass

c) Low and band pass

d) High pass

View Answer

Explanation: It is clear that the impulse invariance method is in -appropriate for designing high pass filter due to the spectrum aliasing that results from the sampling process.

11. Which of the following is the correct relation between ω and Ω?

a) Ω=ωT

b) T=Ωω

c) ω=ΩT

d) None of the mentioned

View Answer

Explanation: We know that z=e

^{sT}

Now substitute s=σ+jΩ and z=r.e

^{jω}, that is represent ‘z’ in the polar form

On equating both sides, we get

ω=ΩT.

12. When σ<0, then what is the condition on ‘r’?

a) 0<r<1

b) r=1

c) r>1

d) None of the mentioned

View Answer

Explanation: We know that z=e

^{sT}

Now substitute s=σ+jΩ and z=r.e

^{jω}, that is represent ‘z’ in the polar form

On equating both sides, we get

r=e

^{σT}

Thus when σ<0, the value of ‘r’ varies from 0<r<1.

13. When σ>0, then what is the condition on ‘r’?

a) 0<r<1

b) r=1

c) r>1

d) None of the mentioned

View Answer

Explanation: We know that z=e

^{sT}

Now substitute s=σ+jΩ and z=r.e

^{jω}, that is represent ‘z’ in the polar form

On equating both sides, we get

r=e

^{σT}

Thus when σ>0, the value of ‘r’ varies from r>1.

14. What is the period of the scaled spectrum Fs.X(F)?

a) 2Fs

b) Fs/2

c) 4Fs

d) Fs

View Answer

Explanation: When a continuous time signal x(t) with spectrum X(F) is sampled at a rate Fs=1/T samples per second, the spectrum of the sampled signal is periodic repetition of the scaled spectrum Fs.X(F) with period Fs.

**Sanfoundry Global Education & Learning Series – Digital Signal Processing.**

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