Embedded Signal Processing with the Micro Signal Architecture

Chapter 3

Frequency-Domain Analysis and Processing

This chapter introduces frequency-domain techniques for analyzing digital signals and systems. In particular, we focus on z-transform, system concepts, and discrete Fourier transform with their applications. We use these frequency-analysis methods to analyze and explain the noise reduction examples introduced in Chapter 2 and use frequency-domain techniques to design more advanced filters for reducing noises. In addition, we use several examples and hands-on experiments to introduce some useful MATLAB and Blackfin tools for analysis and design of DSP algorithms.

3.1    INTRODUCTION

In Chapter 2, we introduced simple time-domain techniques such as moving-average filters, Hanning filters, and nonlinear median filters for removing noises that corrupted the desired signals. In particular, we described those filters with time-domain methods such as I/O equations and signal-flow diagrams and used them to enhance sine waves embedded in white noise. We learned that they worked for some conditions, but failed for others. In this chapter, we introduce frequency-domain techniques to analyze those signals and systems and thus to understand their characteristics and explain the results obtained in Chapter 2. In addition, we use frequency-domain concepts and techniques to design effective filters for reducing noises.

In Example 2.3, we used a moving-average filter with length L = 5, 10, and 20 to enhance a sine wave corrupted by white noise. ...