Starting with this column, I plan to take a hard right turn from transmitter issues to receiver issues. As such, the next few columns will investigate matched filtering.

What is a matched filter?

A matched filter is theoretically the best method to discern whether a particular waveform is present in a noisy environment. If you know the statistics of the noise and the characteristics of the particular signal, then you can build a filter that optimizes the output signal-to-noise ratio (SNR) when the signal of interest is present. A matched filter performs this function by coherently adding each Fourier component present in the signal.

Note that you're not interested in preserving the wave shape of the input signal. You're going to arrange the system so it sums all the signal energy present in the symbol waveform at one particular moment. Thus, when the signal of interest is present, the output of a matched filter appears as a narrow spike.

In digital communications systems, you transmit one of N different waveforms to represent one of N different symbols. By choosing these N waveforms wisely, you can build N matched filters, one for each waveform (symbol). You design the m th filter to detect the m th waveform while rejecting the other N-1 waveforms.

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