Question

Write o MATLAB function [a0, an, bn] = NumFourier ((t, x, n)) that constructs the harmonic analysis of a given function x(t). The function requires the following input data: a

Answer 1

To construct the harmonic analysis of a given function x(t) in MATLAB, you can write a function called NumFourier(t, x, n) that takes in the time array, function values, and the number of harmonics as input. This function should output the DC component and the cosine and sine coefficients of the harmonics. The coefficients can be calculated using the FFT formula.

Step-by-step explanation:

To construct the harmonic analysis of a given function x(t) in MATLAB, you can write a function called NumFourier(t, x, n). This function takes in three input arguments: t, which represents the time array, x, which represents the function values at each time point, and n, which specifies the number of harmonics to include in the analysis.

The function should output three variables: a0, which represents the DC component of the signal, an, which represents the cosine coefficients of the harmonics, and bn, which represents the sine coefficients of the harmonics.

To calculate the coefficients, you can use the formulas:

• a0 = mean(x)
• an = 2 * real(fft(x)) / length(x)
• bn = -2 * imag(fft(x)) / length(x)

These formulas involve taking the Fast Fourier Transform (FFT) of the function values x and then dividing by the length of x to normalize the coefficients. The real() and imag() functions extract the real and imaginary parts of the FFT result, respectively.