One fundamental component of DSP is the FIR filter, so I've decided to dedicate the next two columns to FIR techniques for waveform resampling. The endgame is to formulate the popular polyphase resampling structure, which provides a very efficient implementation.

There are two motivations for resampling a sampled waveform: Either you need to change the underlying sample rate, or you need to resample the signal at an alternate sample phase. A common use of the resampler occurs in demodulation when resampling a waveform at baud centers for symbol-decision purposes.

Due to its structure, the polyphase resampler is limited to altering the sample rate of the original waveform by a rational number. (Quick refresher for those who need one: Rational numbers are real numbers formed by dividing two integers. Thus, 4/5 and 15/7 are rational numbers, while numbers such as pi and e are not.) This restriction on the resampler isn't terribly limiting and, as we'll see, you can select rational numbers to achieve the desired accuracy with almost no penalty.