1.1 Objectives . To investigate the significance of each coefficient in the Fourier series. To use MATLAB to gain an understanding of the decomposed function. 1.2 Introduction The Fourier series is one of the most important tools in mathematical physics and engineering. It is used to represent a given periodic function in terms of sine and cosine functions. It yields a series representation of a given function in a simple fashion. The Fourier series of a periodic function of period 2L is given by nat nat f(t) = ao + n=1 (an cos + bn sin L where ao=f(t)dt an = and bn = 13 Prior investigations A periodic square wave is often employed as the input signal in circuit simulation. The periodic square wave shown in Fig. 1 can be described mathematically as f(t) cos dt, n= 1, 2, 3, ... 1.4 Lab exercise Let f(t) sindt, n = 1, 2, 3, ... f(t) = where, the function f(t) is periodic with period 7, that is, f(t +T) = f(t). T is the period of the waveform. Determine analytically the Fourier series of the periodic wave shown in Fig. 1 for an arbitrary period 7. In other words, find expressions for an and b A = So < t