April 2024
Intermediate to advanced
400 pages
12h 28m
English
Content preview from Digital Signal Processing, 10th Edition
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5Finite Impulse Response (FIR) Filters
Digital FIR filters are discrete linear time-invariant systems in which an output number, representing a sample of the filtered signal, is obtained by weighted summation of a finite set of input numbers, representing samples of the signal to be filtered. The coefficients of the weighted summation constitute the filter’s impulse response and only a finite number of them take nonzero values. This is a “finite memory” filter – that is, it determines its output as a function of input data of limited age. It is frequently called a non-recursive filter because, unlike the infinite impulse response filter, it does not require a feedback loop in its implementation.
The properties of FIR filters will be illustrated by two simple examples.
5.1 FIR Filters
Consider a signal x(t) represented by its samples x(nT), taken at frequency fs = 1/T, and examine the effect on its spectrum of replacing the set x(nT) with the set y(nT) defined by the equation:
(5.1)
This set is also obtained by sampling the signal y(t) such that:
If Y(f) and X(f) denote the Fourier transforms of the signals y(t) and x(t), then:
Such an operation corresponds to the transfer ...
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