In this chapter we examine how noise degrades the accuracy of digital data transmission and the fidelity of analog transmission. We begin with an explanation of matched filtering, a subject which came up in Chapter 22. We show that, for binary data links using matched filtering and coherent detection, the probability of error depends only on the noise level at the input of the receiver and on the energy, but not the shape, of the transmitted pulses. We look at two example systems: BPSK (binary phase-shift keying) with coherent detection and OOK (on–off keying) with envelope detection. The error rates and channel capacities (maximum error-free data rates when using forward error correction coding) are calculated and compared with Shannon's expression for the capacity of a band-limited channel. Finally, traditional AM and FM are examined with respect to their noise characteristics.

Matched filtering

We stated in Chapter 22 that, in the presence of noise, the post-detection signal-to-noise ratio is maximized when the predetection bandpass shape of the receiver is that of a matched filter.

A matched filter is one whose impulse response is proportional to the time-reversed waveform of the incoming signal pulse, as will be shown below. For example, if the input signal is a pulse whose shape is the same as the symmetric impulse response of a root raised-cosine filter, then the receiver should use a root raised-cosine filter or an equivalent cascade of filters.