Solving Fourier Transform Problems: Why is it Wrong?

[carlosvelcab]

hello everyone
I need help with this
when I introduce this commands I didn't get the right answer, and I don't know why, somebody can help me.
For example

clear all
r = 'sin(5*t)';
syms t w;
f = eval(r)
fourier(f)
F = fourier(f);
ifourier(F,'t')

and the result is:

f =

sin(5*t)

%fourier transform which is wrong
ans =

-pi*i*(dirac(w - 5) - dirac(w + 5))

%and the inverse Fourier transform which is wrong too
ans =

i/(2*exp(5*i*t)) - (i*exp(5*i*t))/2

where is the problem?, Why is wrong?

 

[NateD]

The problem is that you are using the wrong function for calculating the Fourier transform. The correct function to use is 'fourier' instead of 'eval'. Try this instead:clear allr = 'sin(5*t)';syms t w;f = fourier(r)F = fourier(f);ifourier(F,'t')This should give you the correct answer:f = sin(5*t) %Fourier transformans = 2*exp(-5*1i*t)/1i %Inverse Fourier transformans = -pi*i*(dirac(w - 5) - dirac(w + 5))

 

[oswaler]

I understand that the Fourier transform is a mathematical tool used to decompose a signal into its frequency components. It is widely used in various fields such as signal processing, image processing, and quantum mechanics. However, it is important to note that the Fourier transform is not a simple plug-and-play tool, and it requires a deep understanding of its underlying principles and assumptions.

In this specific case, the problem may lie in the use of the "eval" function in the code. This function evaluates the string expression as a MATLAB expression, but it does not consider the symbolic variables defined later in the code. This could lead to incorrect results in the Fourier transform.

Furthermore, the Fourier transform assumes that the signal is periodic and has finite energy, which may not be the case for all signals. If the signal is not periodic, the result may not be accurate.

In order to get the correct results, it is important to carefully consider the input signal, make sure it meets the assumptions of the Fourier transform, and use the appropriate MATLAB functions for the analysis. Additionally, seeking help from a knowledgeable colleague or consulting relevant literature can also be helpful in solving Fourier transform problems.

I hope this helps in addressing your concerns. Best of luck in your research and data analysis.