3.1 Discrete-time filtering

Discrete-time filtering

Most of you should be already familiar with continuous-time filters, which takes continuous-time input signal and output acontinuous-time signal. Discrete-time filters, which the sampling device and digital-to-analog converter, can performthe same function as the continuous-time filters with properly designed system blocks. Continuous-time filters are fullyspecified by its impulse response $h(t)$ and the output signal $y(t)$ for input signal $x(t)$ is given by the convolution integral

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

Discrete-time filter design

The discrete-time filter design problem is to design the impulse response $h(n)$ 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 $h(n)$ to implement desired filtering.