Multi-Rate Discrete-Time Signal Processing

Chapter 17 presents the multi-rate signal process, starting with explanations of the up-sampling and down-sampling procedures on a discrete signal in the time domain. The operations of a down-sampler (decimator) and an up-sampler (interpolator) are analysed in the frequency domain, emphasizing the problem of possible aliasing. Complex systems that include both up-sampling and down-sampling are analysed and the problem of complexity reduction is mentioned. The operation of systems that combine an interpolator and an interpolation filter, and a decimator and a decimation lowpass filter, is presented in the time and frequency domains. In particular, the problem of reducing the complexity of a multi-rate system is addressed, and a polyphase decomposition for both finite impulse response filters and infinite impulse response filters is offered as an efficient solution.