Digital Signal Processing Mock Test 6

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Question 1 of 10

1. Which of the following equation is True?

\([\frac{\Omega_S}{\Omega_C} ]^{2N} = 10^{-K_S/10}-1\)

\([\frac{\Omega_S}{\Omega_C} ]^{2N} = 10^{K_S/10}+1\)

None of the mentioned

\([\frac{\Omega_S}{\Omega_C} ]^{2N} = 10^{-K_S/10}+1\)

Question 1 of 10

Question 2 of 10

2. If s=σ+jΩ and z=re^jω and r=1, then which of the following inference is correct?

LHS of the s-plane is mapped inside the circle, |z|=1

Imaginary axis in the s-plane is mapped to the circle, |z|=1

RHS of the s-plane is mapped outside the circle, |z|=1

None of the mentioned

Question 2 of 10

Question 3 of 10

3. If the discrimination factor 'd' and the selectivity factor 'k' of a chebyshev I filter are 0.077 and 0.769 respectively, then what is the order of the filter?

Question 3 of 10

Question 4 of 10

4. What is the system function of the Butterworth filter with specifications as pass band gain K_P=-1 dB at Ω_P=4 rad/sec and stop band attenuation greater than or equal to 20dB at Ω_S=8 rad/sec?

\(\frac{2012.4}{s^5+14.82s^4+109.8s^3+502.6s^2+1422.3s+2012.4}\)

\(\frac{1}{s^5+14.82s^4+109.8s^3+502.6s^2+1422.3s+2012.4}\)

None of the mentioned

\(\frac{1}{s^5+14.82s^4+109.8s^3+502.6s^2+1422.3s+1}\)

Question 4 of 10

Question 5 of 10

5. Bilinear Transformation is used for transforming an analog filter to a digital filter.

False

True

Question 5 of 10

Question 6 of 10

6. What is the stop band frequency of the normalized low pass Butterworth filter used to design a analog band pass filter with -3.0103dB upper and lower cutoff frequency of 50Hz and 20KHz and a stop band attenuation 20dB at 20Hz and 45KHz?

2.25 rad/sec

2 rad/sec

2 Hz

2.25 Hz

Question 6 of 10

Question 7 of 10

7. The system function of a general IIR filter is given as H(z)=\(\frac{\sum_{k=0}^M b_k z^{-k}}{1+\sum_{k=1}^N a_k z^{-k}}\).

True

False

Question 7 of 10

Question 8 of 10

8. If H(s)=\(\frac{1}{s^2+s+1}\) represent the transfer function of a low pass filter (not Butterworth) with a pass band of 1 rad/sec, then what is the system function of a low pass filter with a pass band 10 rad/sec?

None of the mentioned

\(\frac{s^2}{s^2+10s+100}\)

\(\frac{100}{s^2+10s+100}\)

\(\frac{s^2}{s^2+s+1}\)

Question 8 of 10

Question 9 of 10

9. Which of the following is the expression for \(\frac{∂p_i}{∂a_k}\)?

\(\frac{-p_i^{N+k}}{\prod_{l=1}^n p_i-p_l}\)

\(\frac{p_i^{N-k}}{\prod_{l=1}^n p_i-p_l}\)

None of the mentioned

\(\frac{-p_i^{N-k}}{\prod_{l=1}^n p_i-p_l}\)

Question 9 of 10

Question 10 of 10

10. What is the z-transform of the first backward difference equation of y(n)?

\(\frac{1+z^1}{T}\) Y(z)

\(\frac{1+z^{-1}}{T}\) Y(z)

None of the mentioned

\(\frac{1-z^{-1}}{T}\) Y(z)

Question 10 of 10