Signals and Systems Laboratory 7 Fourier series Objectives: Explore signals in the frequency domain with Fourier Series Understand the relationship between a signal and the different Fourier components of the signal. fft(x) ifftx)Compute the inverse discrete Fourier transform of the vector x Compute the discrete Fourier transform (DFT) of the vector x Introduction Look at the usage of the tr. or m atlab commands. The command xk_npN produces a length N vector containing the DTFS coefficient XIk]. Similarly given the DTFS coefficient in a vector xk, the command xn-ifft(xk "N produces the vector xn that represents one period of the time domain signal xn. Computing the Diserete-Time Fourier (DTFS) series with fft The DTFS s the DFT scaled by 1/N. The DTFS is a frequency-domain representation for periodic discrete-time sequences. For a signal x[n with fundamental period N, the DTFS synthesis and anal ysis equations are given by To compute Equations (2) we use the function ft scaled by N