Frequency Analysis Frequency analysis of any given signal involves the transformation of a time-domain signal into its frequency components. The need for describing a signal in the frequency domain exists because signal processing is generally accomplished using systems that are described in terms of frequency response. Converting the time-domain signals and systems into the frequency domain is extremely helpful in understanding the characteristics of both signals and systems. In Section , the Fourier series and Fourier transform will be introduced. The Fourier series is an effective technique for handling periodic functions. It provides a method for expressing a periodic function as. | Real-Time Digital Signal Processing. Sen M Kuo Bob H Lee Copyright 2001 John Wiley Sons Ltd ISBNs 0-470-84137-0 Hardback 0-470-84534-1 Electronic 4 Frequency Analysis Frequency analysis of any given signal involves the transformation of a time-domain signal into its frequency components. The need for describing a signal in the frequency domain exists because signal processing is generally accomplished using systems that are described in terms of frequency response. Converting the time-domain signals and systems into the frequency domain is extremely helpful in understanding the characteristics of both signals and systems. In Section the Fourier series and Fourier transfomi will be introduced. The Fourier series is an effective technique for handling periodic functions. It provides a method for expressing a periodic function as the linear combination of sinusoidal functions. The Fourier transform is needed to develop the concept of frequency-domain signal processing. Section introduces the z-transform its important properties and its inverse transform. Section shows the analysis and implementation of digital systems using the z-transform. Basic concepts of discrete Fourier transforms will be introduced in Section but detailed treatments will be presented in Chapter 7. The application of frequency analysis techniques using MATLAB to design notch filters and analyze room acoustics will be presented in Section . Finally real-time experiments using the TMS320C55x will be presented in Section . Fourier Series and Transform In this section we wi 11 introduce the representation of analog periodic signals using Fourier series. We will then expand the analysis to the Fourier transform representation of broad classes of finite energy signals. Fourier Series Any periodic signal x t can be represented as the srn of an infinite number of harmonically related sinusoids and complex exponentials. The basic mathematical representation of periodic .
