Digital Signal Processing Practice Test 6

1. 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. The frequency response H(ω) will be considerably distorted with respect to H(jΩ).

3. What is the necessary and sufficient condition for a second order filter that no zero-input overflow limit cycles occur?

4. The cutoff frequency of the low pass Butterworth filter is the arithmetic mean of the two cutoff frequencies as found above.

5. Which of the following is the characteristic equation of a Chebyshev filter?

6. If |H(ω)| is square integrable and if the integral \(\int_{-\pi}^\pi |ln⁡|H(ω)||dω\) is finite, then the filter with the frequency response H(ω)=|H(ω)|e^jθ(ω) is?

7. H_R(ω) and H_I(ω) are interdependent and cannot be specified independently when the system is causal.

8. What is the formula for chebyshev polynomial T_N(x) in recursive form?

9. If the poles are tightly clustered as they are in a narrow band filter, the lengths of |p_i-p_l| are large for the poles in the vicinity of p_i.

10. T_N(-x)=(-1)^NT_N(x).