Applied Digital Signal Processing Theory and Practice

A key feature of the discrete-time systems discussed so far is that the signals at the input, output, and every internal node have the same sampling rate. However, there are many practical applications that either require or can be implemented more efficiently by processing signals at different sampling rates. Discrete-time systems with different sampling rates at various parts of the system are called multirate systems. The practical implementation of multirate systems requires changing the sampling rate of a signal using discrete-time operations, that is, without reconstructing and resampling a continuous-time signal. The fundamental operations for changing the sampling rate are decimation and interpolation. The subject of this chapter is the analysis, design, and efficient implementation of decimation and interpolation systems, and their application to two important areas of multirate signal processing: sampling rate conversion and multirate filter banks.

Study objectives

After studying this chapter you should be able to:

• Understand the operations of decimation, interpolation, and arbitrary sampling rate change in the time and frequency domains.

• Understand the efficient implementation of discrete-time systems for sampling rate conversion using polyphase structures.

• Design a special type of filter (Nyquist filters), which are widely used for the efficient implementation of multirate filters and filter banks.

• Understand the operation, properties, and design of two-channel filter banks with perfect reconstruction analysis and synthesis capabilities.

Sampling rate conversion

The need for sampling rate conversion arises in many practical applications, including digital audio, communication systems, image processing, and high-definition television.