Digital Signal Processing

Summary:

Multirate digital signal processing (DSP) involves the manipulation of signals at different sampling rates to reduce complexity and increase efficiency. The multistage approach can be used when the changes in sampling rates are large, where the operation is performed in multiple stages with Mi(Li) factors. The optimum number of stages leads to the least computational effort. Polyphase filters facilitate computational savings in both hardware and software, allowing more efficient realisation of the sampling-rate converter. Oversampling is a common technique implemented in CD players and digital processing systems of music signals to protect against image frequency bands. It causes the image frequencies to be much higher and easier to filter out, reducing the anti-alias filter specification and reducing noise power spectral density. This reduction in noise power spectral density means that the tolerable noise level can be increased by a factor of 8, allowing a reduction in the number of bits for the DAC process, as shown in the reduction in the number of bits for the DAC process given by Equation 9.4.

Excerpt:

Multirate Digital Signal Processing

9.1 Introduction
Multirate systems have gained popularity since the early 1980s, and they are commonly used for audio and video
processing, communications systems, and transform analysis, to name but a few. In most applications, multi-rate systems are used to improve performance, or for increased computational efficiency. The two basic operations in a multi-rate system are decreasing (decimation) and increasing (interpolation) the sampling rate of a signal. Multirate systems are sometimes used for sampling-rate conversion, which involves both decimation and interpolation.

9.2 Decimation
Decimation can be regarded as the discrete-time counterpart of sampling. Whereas in sampling we start with a
continuous-time signal x(t) and convert it into a sequence of samples x[n], in decimation, we start with a discrete-time signal x[n] and convert it into another discrete-time signal y[n], which consists of sub-samples of x[n]. Thus, the formal definition of M-fold decimation, or down-sampling, is defined by Equation 9.1. In decimation, the sampling rate is reduced from Fs to Fs/M by discarding M – 1 samples for every M sample in the original sequence.