Digital Signal Processing Practice Test 7

1. The filter designs that contain maximum number of alternations are called as ______________

Equi ripple filters

None of the mentioned

Extra ripple filters

Maximal ripple filters

2. What is the Fourier transform of the rectangular window of length M-1?

\(e^{-jω(M+1)/2} \frac{sin⁡(\frac{ωM}{2})}{sin⁡(\frac{ω}{2})}\)

\(e^{-jω(M-1)/2} \frac{sin⁡(\frac{ωM}{2})}{sin⁡(\frac{ω}{2})}\)

\(e^{jω(M-1)/2} \frac{sin⁡(\frac{ωM}{2})}{sin⁡(\frac{ω}{2})}\)

\(e^{jω(M+1)/2} \frac{sin⁡(\frac{ωM}{2})}{sin⁡(\frac{ω}{2})}\)

3. If H(z) is the z-transform of the impulse response of an FIR filter, then which of the following relation is true?

z^-(M+1).H(z^-1)=±H(z)

z^M+1.H(z^-1)=±H(z)

z^(M-1).H(z^-1)=±H(z)

z^-(M-1).H(z^-1)=±H(z)

4. The lower and upper limits on the convolution sum reflect the causality and finite duration characteristics of the filter.

True

False

5. What is the desired response of the differentiator in the frequency range 2πf_p ≤ ω ≤ π?

Constrained to be zero

Left unconstrained

None of the mentioned

Left unconstrained or Constrained to be zero

6. The roots of the equation H(z) must occur in ________________

Identical

Conjugate pairs

Reciprocal pairs

Zero

7. What is the relation between H(k+α) and h(n)?

H(k+α)=\(\sum_{n=0}^{M+1} h(n)e^{-j2π(k+α)n/M}\); k=0,1,2...M+1

H(k+α)=\(\sum_{n=0}^{M-1} h(n)e^{-j2π(k+α)n/M}\); k=0,1,2...M-1

H(k+α)=\(\sum_{n=0}^M h(n)e^{-j2π(k+α)n/M}\); k=0,1,2...M

None of the mentioned

8. If the unit sample response h(n) of the filter is real, complex valued roots need not occur in complex conjugate pairs.

False

True

9. The roots of the polynomial H(z) are identical to the roots of the polynomial H(z^-1).

True

False

10. Which of the following is the first method proposed for design of FIR filters?

Frequency sampling method

None of the mentioned

Windowing technique

Chebyshev approximation