Different forms of the discrete Fourier Transform

[koab1mjr]

Hi

I am trying to program excel to take the DFT of a signal, then bring it back to the time domain after a low pass filter. I have a code that can handle simple data for example
t = [ 0, 1, 2, 3]
y = [2, 3, -1, 4]

So I think everything is great and so I plug in my real signal and things go off the rails. Firstly my transform doesn't seem to work. In the simple cases I have a start frequency of 0 and an end frequency of 4. Everything works. I know my data has equal spacing, but I do not know my frequency to start or stop so I pick 0 and some arbitrary numbers. I have the number of points within the frequency interval as variable.

My output looks like no transform I have ever seen and bringing it back to time is equally bad. Am I missing something when I move to real data?

Now I was following this blog http://excelunusual.com/spectral-analysis-a-fourier-transform-tutorial/, as a basis for my code and I found that gave me a decent looking tranform of my real data but failed on a simple problem as stated above. The expression for the transform is different.

G(f) = ∫g(t)e^-2π*j*f*t where as most textbooks have n/N in the exponent.

Not sure what the disconnect is but looking for some opinions on this.

Thanks in advance.

 

[Dr. Courtney]

Look at the link in my sig and download some code that has been debugged for computing Fourier transforms.

You can also download the file cos10000.txt as a sample input. You will see it is the sum of 5 cosine terms for 10000 points. Testing Fourier transform code on a known input like this is a valuable step in validation.