Digital Filters Design topics include: The design of low pass butterworth filters and chebyshev filters, bilinear transformations, filter coefficient quantization, design considerations for filters, FIR filter design using windows, forward and backward difference methods, filter design using frequency sampling method, FIR differentiator design, Hilbert transformer design, IIR filter design, approximation of derivatives, impulse variance, analog filter characteristics, various approximation methods, sampling rate conversion and interpolation techniques. Digital filter design involves using... Show more

Digital Filters Design topics include: The design of low pass butterworth filters and chebyshev filters, bilinear transformations, filter coefficient quantization, design considerations for filters, FIR filter design using windows, forward and backward difference methods, filter design using frequency sampling method, FIR differentiator design, Hilbert transformer design, IIR filter design, approximation of derivatives, impulse variance, analog filter characteristics, various approximation methods, sampling rate conversion and interpolation techniques.

Digital filter design involves using both frequency domain and time domain techniques. The filter specifications are often specified in the frequency domain and the implementation is done in time-domain in the form of difference equations. 

The steps in digital filter design are:
Determine specifications
Find a transfer function
Choose a realization structure
Implement the filter 

The two fundamental types of digital filters are finite impulse response (FIR) and infinite impulse response (IIR).

A digital filter is a mathematical algorithm implemented in hardware and/or software that operates on a digital input signal to produce a digital output signal.
 
Digital filters have the following advantages:
They require only the arithmetic operations of addition, subtraction, and multiplication
They do not drift with temperature or humidity or require precision components
They have a superior performance-to-cost ratio
They do not suffer from manufacturing variations or aging

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Digital Signal Processing Practice Test: Digital Filters Design

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25 Questions

1. What is the unit sample response corresponding to H_d(ω)?

\(\frac{sin⁡πn}{n}\) n.sin πn\(\frac{cos⁡πn}{n}\) n.cos⁡ πn

2. What is the width of the main lobe of the frequency response of a rectangular window of length M-1?

π/M2π/M4π/M8π/M

3. Which of the following technique is more preferable for design of linear phase FIR filter?

Frequency samplingNone of theseWindow designChebyshev approximation

4. What is the expression for cutoff frequency in terms of pass band gain?

\(\frac{\Omega_P}{(10^{K_P/10}-1)^{1/2N}}\) None of these\(\frac{\Omega_P}{(10^{-K_P/10}+1)^{1/2N}}\) \(\frac{\Omega_P}{(10^{-K_P/10}-1)^{1/2N}}\)

5. Which of the following window is used in the design of a low pass filter to have a frequency response as shown in the figure?

Hamming windowBlackman windowHanning windowKaiser window

6. The sampling interval in the matched z-transform must be properly selected to yield the pole and zero locations at the equivalent position in the z-plane.

Don't KnowTrueFalseMaybe

7. The oscillatory behavior near the band edge of the low pass filter is known as Gibbs phenomenon.

MaybeDon't KnowTrueFalse

8. For an analog LTI system to be stable, where should the poles of system function H(s) lie?

Right half of s-planeAt originLeft half of s-planeOn the imaginary axis

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

Don't KnowFalseTrueMaybe

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

None of theseAnalog filterDigital filter with aliasingDigital filter without aliasing

11. The H_I(ω) is uniquely determined from H_R(ω) through the integral relationship. This integral is called as Continuous Hilbert transform.

MaybeDon't KnowFalseTrue

12. The anti-symmetric condition is not used in the design of low pass linear phase FIR filter.

FalseTrueMaybeDon't Know

13. The frequency ω_P is called as ______________

Stop band edge ripplePass band rippleStop band ripplePass band edge ripple

14. What is the expression for system function in z-domain?

\(\frac{2}{T}[\frac{1+z^{-1}}{1-z^1}]\) \(\frac{T}{2}[\frac{1+z^{-1}}{1-z^1}]\) \(\frac{T}{2}[\frac{1-z^{-1}}{1+z^{-1}}]\)

15. What is the value of T_N(0) for even degree N?

+10-1±1

16. Which of the following is equal to the value of H(k+α)?

H*(M-k+α)H*(M+k-α)H*(M-k-α)H*(M+k+α)

17. Remez exchange algorithm is an iterative algorithm used in error approximation.

TrueMaybeFalseDon't Know

18. Bessel filters exhibit a linear phase response over the pass band of the filter.

MaybeFalseDon't KnowTrue

19. Which of the following is true in matched z-transform?

Zeros of H(s) are directly mapped to poles in z-planePoles & Zeros of H(s) are directly mapped to poles in z-planePoles of H(s) are directly mapped to poles in z-planeNone of these

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

MaybeTrueFalseDon't Know

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

IdenticalZeroConjugate pairsReciprocal pairs

22. It is impossible to design an all-pass digital Hilbert transformer.

Don't KnowMaybeFalseTrue

23. The filter designs that contain more than L+2 alternations are called as ______________

Maximal ripple filtersEqui ripple filtersNone of theseExtra ripple filters

24. Which of the following in z-domain is equal to s-domain of second order derivate?

None of these\((\frac{1-z^{-1}}{T})^2\) \((\frac{1+z^{-1}}{T})^2\) \((\frac{1+z^{-1}}{T})^{-2}\)

25. In matched z-transform, the poles and zeros of H(s) are directly mapped into poles and zeros in z-plane.

MaybeFalseTrueDon't Know