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to rmsnoise.Wenotethatthematchedfilterachieves
this result by (1) removing all phase dispersion (lining
up all frequencies in the signal so that their peaks occur
together at t = 0), and (2) weighting each component
directly in proportion to the signal component amplitude
to noise power spectral density at that frequency.
When f(t) is an RF or IF signal rather than a baseband
signal, the relations (C12) and (C16) require that g(t)
also be a RF or IF signal. The gating then amounts to a
kind of generalized homodyning operation which excludes
the noise power that is in quadrature with the
carrier. One cannot use a matched filter at RF or IF as
specified by equation (C 17) or (C18) followed by, say, a
linear or square law detector and achieve the S/N ratios
given by equations (C14) and (C15). The gate at t = 0 is
needed to exclude the quadrature noise power. The most
practical method of realizing full matched filter performance
is usually to homodyne the received signals to
baseband and do all gating and filtering in that frequency
range. In this way, the use of nonlinear detectors is
avoided. (See Appendix D on square-law detection
theory.)
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