Identifying wave-number sign after FFT2

Hi,

I am plotting a simple wave equation y=Acos(kx-wt) in time 't' and space 'x' domain (i.e. a color plot in 2D domain). Here A,k and w denote amplitude, wave-number and angular frequency respectively.

I then do FFT2 of function y in 2D domain and use function fftshift in order to get low frequency components at the center. I now take only 'positive' angular frequency values hence just half of the domain.

As a result I have all wave-number values (both positive and negative) with only positive angular frequency. I notice that my solution has 'negative' wave-number, which indicates that wave is propagating towards -X direction. However it is not the case with the analytical expression: y=Acos(kx-wt). It is clearly a wave propagating in +X direction.

I would like to know what is the correct way of interpreting FFT2 results in terms of signs of wavenumber.

A sample code is attached.

Thank you in advance, Rajesh

[Rik]

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Answer 1

[Youssef Khmou]

The general solution for a wave travelling in the +X direction is, at point X :

 y(0,t)=A exp(j(wt))
 y(X,t)=A exp(j(wt-KX));