Chapter: Digital Signal Processing - FIR Filter Design

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Important Short Questions and Answers: FIR Filter Design

Digital Signal Processing - FIR Filter Design - Important Short Questions and Answers: FIR Filter Design

FIR FILTER DESIGN

 

1.What is the condition satisfied by linear phase FIR filter?

The condition for constant phase delay are

Phase delay, α = (N-1)/2 (i.e., phase delay is constant)

Impulse response, h(n) = h(N-1-n) (i.e., impulse response is symmetric)

 

2.What are the desirable characteristics of the frequency response of window function?

Advantages:

a)        FIR filters have exact linear phase.

b)       FIR filters are always stable.

c)        FIR filters can be realized in both recursive and non recursive structure.

d)       Filters with any arbitrary magnitude response can be tackled using FIR sequency.

Disadvantages:

a)        For the same filter specifications the order of FIR filter design can be as high as 5 to n10 times that of IIR design.

b)       Large storage requirements needed.

c)        Powerful computational facilities required for the implementation.

 

3.What is meant by optimum equiripple design criterion.

The Optimum Equiripple design Criterion is used for designing FIR Filters with Equal level filteration throughout the Design.

  

4.What are the merits and demerits of FIR filters?

 

Merits:

1. FIR Filter is always stable.

2. FIR Filter with exactly linear phase can easily be designed.

Demerits:

1. High Cost.

2.Require more Memory.

 

5.For what type of filters frequency sampling method is suitable?

 

FIR FIlters

 

6.What are the properties of FIR filters?

 

a) FIR Filter is always stable.

 

b)A Realizable filter can always be obtained.

 

7.What is known as Gibbs phenomenon?

 

In the filter design by Fourier series method the infinite duration impulse response is truncated to finite duration impulse response at n= (N-1/2). The abrupt truncation of impulse introduces oscillations in the pass band and stop band. This effect is known as Gibb’s phenomenon.

 

8.Mention various methods available for the design of FIR filter.Also list a few window for the design of FIR filters.

 

There are three well known method of design technique for linear phase FIR filter. They are

 

a)        Fourier series method and window method

b)       Frequency sampling method

c)        Optimal filter design methods.

Windows: i.Rectangular ii.Hamming iii.Hanning iv.Blackman v.Kaiser

 

9.List any two advantages of FIR filters.

a)        FIR filters have exact linear phase.

b)       FIR filters are always stable.

c)        FIR filters can be realized in both recursive and non recursive structure.

 10.Mention some realization methods available to realize FIR filter

 

i.Direct form. ii.Cascade form iii.Linear phase realization.

 

11.Mention some design methods available to design FIR filter.

 

There are three well known method of design technique for linear phase FIR filter. They are

a)        Fourier series method and window method

b)       Frequency sampling method

c)        Optimal filter design methods.

Windows: i.Rectangular ii.Hamming iii.Hanning iv.Blackman v.Kaiser

 

12.What are FIR filters?

 

The specifications of the desired filter will be given in terms of ideal frequency response Hd( ω). The impulse response hd(n) of desired filter can be obtained by inverse Fourier transform of hd(ω), which consists of infinite samples. The filters designed by selecting finite number of samples of impulse response are called FIR filters.

 

13.What are the conditions to be satisfied for constant phase delay in linear phase FIR filter?

 

The condition for constant phase delay are

Phase delay, α = (N-1)/2 (i.e., phase delay is constant) Impulse response, h(n) = h(N-1-n) (i.e., impulse response is

symmetric)

14.What is the reason that FIR filter is always stable?

FIR filter is always stable because all its poles are at the origin.

 15.What are the possible types of impulse response for linear phase FIR filter?

 

There are four types of impulse response for linear phase FIR filters

a)        Symmetric impulse response when N is odd.

b)       Symmetric impulse response when N is even.

c)        Antisymmetric impulse response when N is odd

d)       Antisymmetric impulse response when is even.

 

16.Write the procedure for designing FIR filter using window.

 

1. Choose the desired frequency response of the filter Hd (w)

2. Take inverse Fourier transform of Hd(w) to obtain the desired impulse response hd (n).

3.Choose a window sequence w(n) and multiply hd(n) by w(n) to convert the infinite duration impulse response to finite duration impulse response h(n).

4. The Transfer function H(z) of the filter is obtained by taking z-transform of h(n).

 

17.Write the procedure for FIR filter design by frequency sampling method.

1. Choose the desired frequency response Hd(w).

2. Take N-samples of Hd ( W) to generate the sequence H (K)

(Here H bar of k should come)

3. Take inverse of DFT of H (k) to get the impulse response h (n).

4. The transfer function H (z) of the filter is obtained by taking z-transform of impulse response.

 18.List the characteristic of FIR filter designed using window.

a)        The width of the transition band depends on the type of window.

b)       The width of the transition band can be made narrow by increasing the value of N where N is the length of the window sequence.

c)        The attenuation in the stop band is fixed for a given window, except in case of Kaiser Window where it is variable.

 

19.List the features of hanning window spectrum.

a)        The mainlobe width is equal to 8π/N.

b)       The maximum sidelobe magnitude is -31db.

c)        The sidelobe magnitude decreases with increasing   .

 

20. Compare the rectangular window and hanning window.


Rectangular window

1.   The width of mainlobe in window spectrum is 4π/N.

2.The maximum   sidelobe magnitude in window spectrum is -13db                  

3.   In window  spectrum  the sidelobe        magnitude   slightly decreases with increasing.

4.   In FIR filter designed using rectangular window the minimum stopband attenuation is 22db.

 Hamming window

1.   The width of mainlobe in window spectrum is 8π/N.

2.The maximum   sidelobe magnitude in window spectrum is -41db

3.   In window  spectrum  the sidelobe        magnitude   remains constant.

4.   In FIR filter designed using hamming window the minimum stopband attenuation is 51db.

 

21.Compare Hamming window with Kaiser Window.


Hamming  window

1.The main lobe width is equal to8π/N and the peak side lobe level is –41dB.

2.The low pass FIR filter designed will have first side lobe peak of –53 dB

 

Kaiser window

1. The main lobe width ,the peak side lobe level  can  be  varied  by  varying  the parameter α and N.

2. The side lobe peak can be varied by varying the parameter α.

 

 GLOSSARY:

 

FIR Filters:

 

In the Finite Impulse Response Filters the No.of. Impulses to be considered for filtering are finite. There are no feed back Connections from the Output to the Input. There are no Equivalent Structures of FIR filters in the Analog Regime.

 

Symmetric FIR Filters:

 

Symmetric FIR Filters have their Impulses that occur as the mirror image in the first quadrant and second quadrant or Third quadrant and fourth quadrant or both.

 

Anti Symmetric FIR Filters:

 

The Antisymmetric FIR Filters have their impulses that occur as the mirror image in the first quadrant and third quadrant or second quadrant and Fourth quadrant or both.

 

Linear Phase:

 

The FIR Filters are said to have linear in phase if the filter have the impulses that increases according to the Time in digital domain.

 

Frequency Response:

 

The Frequency response of the Filter is the relationship between the angular frequency and the Gain of the Filter.

 

Gibbs Phenomenon:

 

The abrupt truncation of Fourier series results in oscillation in both passband and stop band. These oscillations are due to the slow convergence of the fourier series. This is termed as Gibbs Phenomenon.

 

Windowing Technique:

 

To avoid the oscillations instead of truncating the fourier co-efficients we are multiplying the fourier series with a finite weighing sequence called a window which has non-zero values at the required interval and zero values for other Elements.

 

Quantization:

 

Total number of bits in x is reduced by using two methods namely Truncation and Rounding. These are known as quantization Processes.

 

Input Quantization Error:

 

The Quantized signal are stored in a b bit register but for nearest values the same digital equivalent may be represented. This is termed as Input Quantization Error.

 

Product Quantization Error:

 

The Multiplication of a b bit number with another b bit number results in a 2b bit number but it should be stored in a b bit register. This is termed as Product Quantization Error.

 

Co-efficient Quantization Error:

 

The Analog to Digital mapping of signals due to the Analog Co-efficient Quantization results in error due to the Fact that the stable poles marked at the edge of the jΩ axis may be marked as an unstable pole in the digital domain.

 

Limit Cycle Oscillations:

 

If the input is made zero, the output should be made zero but there is an error occur due to the quantization effect that the system oscillates at a certain band of values.

 

Overflow limit Cycle oscillations:

 

Overflow error occurs in addition due to the fact that the sum of two numbers may result in overflow. To avoid overflow error saturation arithmetic is used.

 

Dead band:

 

The range of frequencies between which the system oscillates is termed as Deadband of the Filter. It may have a fixed positive value or it may oscillate between a positive and negative value.

 

Signal scaling:

The inputs of the summer is to be scaled first before execution of the addition operation to find for any possibility of overflow to be occurred after addition. The scaling factor s0 is multiplied with the inputs to avoid overflow.

 

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