Mulirate Signal Processing

EEE305, EEE801 Part A: digital Signal Processing

Chapter 9: Multirate Digital Signal Processing

Chapter 9 Multirate Digital Signal Processing
9.1 Introduction
Multirate systems have gained popularity since the earliest 1980s and they are commonly used for audio and television processing, communications systems, and transform analysis to name but a few. In most applications multirate systems are used to improve the performance, or for increased computational efficiency. The two basic operations in a multirate system are decreasing (decimation) and increasing (interpolation) the consume-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 rise 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 evening gown 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 samples in the original sequence.





y[n] = v[nM ] =

k = ??

? h[k ]x[nM ? k ]
Digital anti-aliasing filter x[n] v[n] h[k] ?M Sampling-rate compressor y[n]

?

(9.1)

Fs

Fs/M

experience 9.1: give up diagram notation of decimation, by a factor of M. The handicap diagram notation of the decimation process is depicted in Figure 9.1. An anti-aliasing digital filter precedes the down-sampler to prevent aliasing from occurring, due to the lower sampling rate. The subject of aliasing in decimated signals is covered in more circumstance in Section 9.4. In Figure 9.2 below, it illustrates the concept of 3-fold decimation i.e. M = 3. Here, the samples of x[n] corresponding to n = …, -2, 1, 4,… and n = …, -1,...If you want to get a full essay, order it on our website: Orderessay



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