two dim fft matlab

I have a vector X of size 2x1000. In the first row (X1) each bit is either zero or one which are amplitude. The second row (x2) represents position starting from zero to all the way upto 999. How can I have FFT(X1,X2) in MATLAB?

Answer 1

[Image Analyst]

That doesn't make sense. You don't want to take the Fourier transform of the location/position of the signal. Just do the amplitude in the first row:

ft = fft(X(1, :));

[Mohammad Sojib]

perhaps I could not describe well enough. Please visualize a strinng of "0" and "1" say 011100111110110000.. and the size could be anything 1x1000 or 1x4500. from the beginning, I assign each bit a position with respect to origin. It will result in an aperiodic square wave. Now I want to remove any pulse or part of the bitstring with width less than a particular number say 3nm. so a bit-string like one 000001111100011000011101 will turn into 000001111100000000011100 or 000001111100011111111111. I also need to apply lowpass filter with custom cutoff to remove high frequency components. I think it helps to understand the problem. Plese let me know if it doesn't.

[Image Analyst]

Then you don't need FFT. You can just do it in the spatial domain with bwareaopen():

v = [0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 1 1 1 0 1]
out = bwareaopen(v, 3)

out =

1×24 logical array

0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0 1 1 1 0 0

[Mohammad Sojib]

Thanks for the answer.

Even though I understand the operation but it is not suited for my case. for me I could have 1x1000 or even large vector size and each bit is randomly either "0" or "1". So, if I do bwareaopen(v, 50) (I need width 40 to 50 at least) it turns everything into either "0" or "1". Let me give you another example. I have 1x1000 vector. from 50 to 200 and 500 to 505 I have all 1. Everything else is zero. now obviously, both pulses have some frequencies in common. that is why I want to take FFT to resolve the pulses in their frequency components. Then I need to remove (by LPF) these common frequncies while keeping others. then I need to take IFFT and round() to have 1x1000 vector with only values 1 from 50 to 200 or less but atleast with width>=50.

Please let me know if you have any questions.