If we can assume that the channel is distortion free or has been equalized to remove the distortion, then we can introduce
the concept of a matched filter pair, with one filter
performing the pulse shaping in the transmitter and the other performing matched detection
in the receiver. We already have a requirement for paired filtering, however, driven by
the desire to achieve zero intersymbol interference. The important question is: does the Nyquist filtering requirement for zero ISI conflict with the
matched filtering requirement for optimum S/N ratio? Fortunately it has been
proven mathematically (Schwartz, 1990) that the root raised cosine filter pair satisfies both criteria, which
explains its popularity with modem designers around the world.
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