Fourier coeffs of a function in Matlab

[Alexandr]

Please, people, need help!

I have a harmonic function which is a product of cosines (something with many cos(k*phi)) and it can be represented as a finite series with only cos terms... We know it...

Now. Every step we multiply this function by one more cos and want to find the Fourier coefs.

So, I don't understand two things...
1. There is no any method in Matlab to generate functions of variables as I understand... So, how can I provide this updating? I need that function of phi...
2. Is there any command for finding nth Fourier coefficient of function, not a vector?

Any useful tips?

 

[Dr Transport]

If you can write the function, set a vector of points x where the delta is very small, evaluate the function then take the FFT, the coefficients should pop right out as the real part.

 

[oswaler]

Hello, I am happy to help with your question about Fourier coefficients in Matlab. First, let's discuss what Fourier coefficients are. They are a way to represent a periodic function as a sum of simpler periodic functions, such as sine and cosine waves. In Matlab, you can use the "fft" function to calculate the Fourier coefficients of a given function. This function takes in a vector of values and returns a vector of complex numbers representing the Fourier coefficients.

To generate functions with variables in Matlab, you can use the "syms" function to create symbolic variables and then use them in your function. For example, if you want to create a function of phi, you can use the following code:

syms phi
f = cos(phi)

This will create a symbolic function of phi that you can use in your calculations. You can also use the "subs" function to substitute different values for phi in your function.

As for finding the nth Fourier coefficient of a function, you can use the "fft" function and then access the specific coefficient you want from the resulting vector. For example, if you want the 5th Fourier coefficient, you can use "fft(f)(5)".

I hope this helps and good luck with your research!