## How do you code a Fourier transform in MATLAB?

Use a time vector sampled in increments of 1 50 of a second over a period of 10 seconds. Compute the Fourier transform of the signal, and create the vector f that corresponds to the signal’s sampling in frequency space. y = fft(x); fs = 1/Ts; f = (0:length(y)-1)*fs/length(y);

## How do I plot a Fourier series in MATLAB?

Here is a simple MATLAB script to plot the above expansion:

1. x = 0:1/1000:2*pi; %discretize interval.
2. f = exp(x). *sin(2*x); Þclare function.
3. f_exp=0; %initialize expansion.
4. N = 6; %number of harmonics.
5. for n=1:N %iterate partial sum.
6. An = (exp(2*pi)-1)/(2*pi)*(4*n^2-20)/(n^4-6*n^2+25);

How do you find the Fourier coefficient in MATLAB?

Calculating Fourier Series Coefficients Using Custom Matlab…

1. function[ak] = cal_fs(x, w0, N)
2. ak = zeros(1,2*N+1); %intialize a row vector of 2N+1 zeros.
3. T = 2*pi/w0; Êlculate the period and store in T.
4. syms t;
5. for k = -N:N.
6. ak = 1/T * int(x * exp(-1i*k*w0*t), t); % ak is fourier coefficient.
7. end.

### How do you write a sinc function in MATLAB?

Viewed as a function of time, or space, the sinc function is the inverse Fourier transform of the rectangular pulse in frequency centered at zero, with width 2 π and unit height: sinc x = 1 2 π ∫ – π π e j ω x d ω = { sin π x π x , x ≠ 0 , 1 , x = 0 .

### How do you plot FFT of signal in MATLAB?

Y = fft( X ) computes the discrete Fourier transform (DFT) of X using a fast Fourier transform (FFT) algorithm.

1. If X is a vector, then fft(X) returns the Fourier transform of the vector.
2. If X is a matrix, then fft(X) treats the columns of X as vectors and returns the Fourier transform of each column.

How do you find the coefficient of a Fourier series?

So this is what we do: Take our target function, multiply it by sine (or cosine) and integrate (find the area) Do that for n=0, n=1, etc to calculate each coefficient.

## What does Syms do in MATLAB?

The syms function creates a symbolic object that is automatically assigned to a MATLAB® variable with the same name. The sym function refers to a symbolic object that can be assigned to a MATLAB variable with the same name or a different name.