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

Answer: A

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 F_{s}=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

Answer: C

When a continuous-time signal x(t) with spectrum X(F) is sampled at a rate F_{s}=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 F_{s}=1/T samples per second, then what is the scaled spectrum?

A. X(F)
B. F_{s}.X(F)
C. X(F)/F_{s}
D. None of the mentioned

Answer: B

When a continuous-time signal x(t) with spectrum X(F) is sampled at a rate F_{s}=1/T samples per second, the spectrum of the sampled signal is a periodic repetition of the scaled spectrum F_{s}.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

Answer: B

We know that z=e^{sT}
Now substitute s=σ+jΩ and z=r.e^{jω}, which represents ‘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/F_{s}
B. F.F_{s}
C. F_{s}/F
D. None of the mentioned

Answer: A

In the impulse invariance method, the normalized frequency f is given by
f= F/F_{s}.

7. Aliasing occurs if the sampling rate F_{s} is more than twice the highest frequency contained in X(F).

A. True
B. False

Answer: B

Aliasing occurs if the sampling rate F_{s} is less than twice the highest frequency contained in X(F).

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

A. True
B. False

Answer: A

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

Answer: B

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 the impulse invariance method?

A. Low pass
B. Bandpass
C. Low and bandpass
D. High pass

Answer: D

It is clear that the impulse invariance method is inappropriate for designing high pass filters due to the spectrum aliasing that results from the sampling process.