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Signals and Systems by Smarajit Ghosh

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12

Structures and Design of Digital Filters

A digital filter is simply a discrete-time, discrete-amplitude convolver. We know from basic Fourier transform theory that the linear convolution of two sequences in the time domain is the same as multiplication of two corresponding spectral sequences in the frequency domain. Filtering is in essence the multiplication of the signal spectrum by the frequency domain impulse response of the filter. For an ideal low pass filter the pass band part of the signal spectrum is multiplied by one and the stopband part of the signal by zero. Most engineers are comfortable with analog filters in time domain whereas digital filters are better conceptualized in the time domain. The aim of this chapter is to introduce ...

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