Cascade of filters

It is often of interest to construct a more complicated filter by combining simpler filters. As a simple example of this, consider a cascade of two filters:

Each filter has the effect of multiplying the complex exponential by its transfer function. Thus we arrive at the basic rule:

When two filters are cascaded, the transfer function of the resulting filter is the product of the transfer functions of the individual filters.

For example, an ideal bandpass filter can be constructed from a cascade of an ideal lowpass filter and an ideal highpass filter with overlapping passbands.

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