Section 3: Fourier Analysis Fourier analysis says that a real, odd, periodic signal can be represented as a sum of sine functions. Consider the following signal, where fo = 0.01 Hz. X(t) = 4 sin(27[2k - 1]fot) (2k-1) (2) As the number of sine functions added together increases, a) What shape does the new waveform take? b) Equation (2) is therefore the Fourier series representation of what type of signal? c) What happens to the sharpness of the corners and the ripples near these corners? 5. Add all 40 sine functions together and call it x_sum". Plot a graph of x_sum, add a title and labels, adjust axes and obtain a printout of the graph. 6. The amplitudes can also be plotted using the stem" function. >> stem([1:40), amplitudes); Which sine functions have the largest amplitudes and are therefore most dominant? Plot this graph, add a title and labels and obtain a printout. 7. Let fo = 0.02 Hz in equation (2) above. What are the frequencies of the sine functions k = 1, k = 2, k = 3 and k = 4? What harmonics do these correspond to? (Hint: use the definition of harmonics in section 1). Therefore in general, which harmonics are present in equation (2) and which are absent