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Discrete-TIme Filtering

Module by: Hyeokho Choi. E-mail the author

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Discrete-Time Filtering

Most of you should be already familiar with continuous-time filters, which takes continuous-time input signal and output a continuous-time signal. Discrete-time filters, which the sampling device and digital-to-analog converter, can perform the same function as the continuous-time filters with properly designed system blocks. Continuous-time filters are fully specified by its impulse response ht h t and the output signal yt y t for input signal xt x t is given by the convolution integral

(1)

Similarly, discrete-time filters are specified by their unit sample response hn h n . The output signal yn y n for the input signal xn x n (samples of input continuous-time signal xt x t ) is given by the discrete-time convolution

(2)

Discrete-Time Filter Design

The discrete-time filter design problem is to design the impulse response hn h n so that the discrete-time filter, together with the sampling device and the discrete-to-continuous time converter, performs the same signal processing functions as an analog filter. There are many algorithms to design hn h n to implement desired filtering.

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