Reference no: EM131419935
Problem 1 -
Expand the function f(x) = x2 in a Fourier series valid on the interval - π ≤ x ≤ π. Plot both f and the partial of its Fourier series,
SN(x) = k=0∑N ak cos (kx) + bk sin (kx)
For N = 1, 2, 5, 7. Observe hoe the graphs of the partial sums SN(x) approximate the graph of f. Plot the same graph over the interval - 2π ≤ x ≤ 2π.
Problem 2 -
Generate a square pulse of sampling frequency 150 Hz. The time vector magnitude is 1 sec and the width of the rectangle is 0.2.
a) Plot the amplitude of the square pulse signal as a function of time.
b) Using fft command (fast fourier transform), find the frequency vector and plot the power spectrum of a square pulse (Frequency Vs Power).
Problem 3 -
Let y(t) = e-t^2/10 (sin(2t) + 2 cos(4t) + 0.4sintsin10t) be the function used to generate a signal S over the interval [0, 2π). The signal is sampled at 28 equally spaced nodes.
a) Find the fft of this signal and plot the signal and the filtered signal with FFT.
b) Use the functions: compress.m and fftcomp.m to plot the filtered signal with a compression of 75%.
Problem 4 -
Let a signal S be represented by the function x = sin(30πt) + sin(80πt) on the time interval [0, 99].
a) Compute the DFT (Discrete fourier transform) of the signal, the magnitude and phase of the transformed sequence.
b) Plot the magnitude and the phase using subplot.
Attachment:- Assignment File.rar
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