A third reason for the importance of Fourier series in system analysis is that it provides one way of determining what happens to a periodic waveform when it is passed through a system that alters the relative magnitudes and phases of the various frequency components.Looking at this sketch: The net area of the square wave from L to L is zero. It is basically an average of f(x) in that range. a 0 is the net area between L and L, then divided by 2L. Such techniques turn out to be closely related to Fourier series, and a thorough understanding of Fourier series is essential in avoiding many problems that might otherwise arise. Example: This Square Wave: L (the Period is 2 ) The square wave is from h to h Now our job is to calculate a 0, a n and b n. A much more important reason concerns computer-oriented numerical techniques for analyzing signals that are not periodic but necessarily must exist for only a finite time duration.One reason is simply the physical insight that it provides concerning the frequency composition of complicated periodic waveforms.There are a number of reasons why Fourier series analysis is important in the study of signals and systems. $f(t)=\frac\] Fourier analysis Advantages Let us begin by considering a function f (t) which is periodic of period T that is,Īs Fourier showed, if f (t) satisfies a set of rather general conditions, it may be represented by the infinite series of sinusoids You May Also Read: Exponential Fourier Series with Solved Example.
0 Comments
Leave a Reply. |