Digital Filters Design for Signal and Image Processing

3.1. Introduction

This chapter discusses frequential representations of signals and filters. We will introduce the Fourier transform of continuous-time signals by first presenting the Fourier series decomposition of periodic signals. Properties and basic calculation methods will be demonstrated. We will then present the frequential analysis of discrete-time signals from the discrete Fourier transform using the standard and most rapid versions. These concepts will then be illustrated using the example of speech signals from a common time-frequency-energy representation – the spectrogram.