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��PRESENTATION ON �FIR FILTER

BRANCH-E & TC ENGG
SUBJECT- DIGITAL SIGNAL PROCESSING
CHAPTER – 5 – FAST FOURIER TRANSFORMALGORITHM & DIGITAL FILTER
TOPIC- FIR FILTER
SEM-6^TH
FACULTY – Er. DEBASHISH PARIDA (LECTURER E & TC ENGG DEPARTMENT)
AY-2021-2022, SUMMER-2022

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FIR FILTER

Filter design steps

- The design of a digital filter involves five steps:

(1) Specifications of the filter requirements

(2) calculation of suitable filter coefficients

(3) Representation of the filter by a suitable structure (realization)

(4) Analysis of the effects of finite wordlength on the filter performance

(5) Implementation of filter in software and/or hardware

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Filter design

Need to decide :

Type of filter
Amplitude and/or phase responses
Tolerances
Sampling frequency
Wordlength of the input data

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Filter specifications

Important parameters

Another important parameter

peak passband deviation (or ripples)

stopband deviation

passband edge frequency

stopband edge frequency

sampling frequency

Filter order N

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ILPF

Fig. 7-3.

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FIR coefficient calculation

Most common methods used for calculating

Window method
Optimal method

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The window method of calculating FIR filter coefficients

Step 1 : specify the desired frequency response of filter,
Step 2 : obtain the impulse response, , of desired filter by

evaluating the inverse Fourier transform

Step 3 : select a window function and then determine the number of

coefficients using the appropriate relationship between the filter

length and the transition width,

Step 4 : obtain values of for chosen window function and the values

of the actual FIR coefficient, , by multiplying by

(7-26)

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Design of FIR filter using window method

Frequency response of filter,
Impulse response,

Ideal lowpass response

Window method

(7-20)

(7-19)

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Table 7.2 Summary of ideal impulse responses for standard frequency selective filters

and are the normalized passband or stopband cutoff frequencies

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Fig. 7-4.

(The frequency scale is normalized by T = 1)

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Truncation for FIR

Rectangular window

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Fig. 7-5.

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Fig. 7-6.

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Fig. 7-7.

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Some common window functions

Hamming window

Appropriate relationship between transition width and filter length

where N is filter order and

is normalized transition width

(7-21)

(7-22)

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Fig. 7-8. Window functions: (a) Rectangular, (b) Hamming, (c) Blackman

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Table 7.3 Summary of important features of common window functions

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THANK YOU

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