fft verses wavelength/wave number plot
ashu
I would like to know How to convert frequency to wavelength or
wavenumber for plotting fft verses wavelength for a time series.(Is
there no role of velocity factor).
please help.
Rune Allnor
Frequency to wavelength is basic maths:
c = Lf
where c is the wave speed, L is wavelength and f is the frequency.
The wavenumber relates to wavelengt in space the same way
angular frequency relates to wave period in time:
k = 2*pi/L = 2*pi*f/c
As you can see, you do need to know the wave speed c to be able
to convert from L to k.
Rune
ashu
Thanks.But in time series analysis. we don't have the speed of time
series. we have sampling frequency only.
Then how this will work without speed information.
please reply
Rune Allnor
You can not get from time or frequency domain (t or f), to space or
wavenumber domain (L or k) without using the wave speed, c.
If you don't have the speed of the wave, you can't do the conversion.
Rune
Greg Heath
What physical phenonema are you trying to characterize?
I don't understand how or why you are trying to establish
a relationship between the sampling frequency of a time
series and wavelength.
Hope this helps.
Greg
ashu
Thanks. But in different applications I have seen the plots of power
spectrum verses wavelength/wavenumber for power spectral behaviour
analysis.My problem is regarding this thing that how to convert
frequency axis to wavelength/wavenumber axis.
Ashu
Greg Heath
That's what you said before... it doesn't help.
You didn't answer my question...that doesn't help either.
So, let me guess that your real problem is spatial and not temporal.
Accordingly, you want to know how to use FFT to yield a spatial
power spectrum.
Make the following analogies:
Temporal variations: cos(wt),sin(wt) w*t = 2*pi*f*t
Spatial variations: cos(kx),sin(kx) k*x =
(2*pi/lambda)*x
Hope this helps.
Greg
Rune Allnor
Do you mean that you have SPATIAL data you want to plot in spectrum
domain? You mentioned "time series analysis" before, which may have
been a bit confusing.
You need the spatial sampling period Dx. Insert Dx for T in the
spectrum equations, and you get what I suspect you want:
N = length(x);
Dx = 10; % [m]
k_vec = [0:N-1]*2*pi/Dx;
k_spectrum = fft(x);
Pk = abs(k_spectrum).^2;
plot(k_vec,Pk)
and you should have the spatial power spectrum Pk plotted
as function of the wavenumber k.
Rune
Ken Davis
news:ef3a...@webcrossing.raydaftYaTP...
Wavenumbers and wavelengths describe sinusoidal variations with
space/distance while frequencies describe sinusoidal variations with time.
They can be related to one another only when you have sinusoids varying with
space and time. The propagation speed (of the phase fronts) is how you
cnooect them together, as others have already said.
NZTideMan
You haven't told us what your application is.
If it's turbulence, then you should use Taylor's hypothesis to convert
frequency to wave number. In the freestream, use the temporal mean
velocity, but if you are close to a wall, you need to use the eddy
velocity.
Interestingly, G I Taylor assumed this relationship in order to convert
measurements from wave number to frequency. He was demonstrating the
validity of the Weiner-Kinchine relationship between autocorrelation
and the spectrum (50 years prior to FFT).
Pau GALLES
I am trying to apply a numerical approach to a problem by multiplying the FFT2 of a spatial signal with its wavenumber Kx.
[KX,KY] = meshgrid(kx,ky);
K = sqrt(KX.*KX + KY.*KY);
myFFTsolution =( KX.*fft_SlpX + KY.*fft_SlpY).*(i./(K);
where i is the complex
fft_SlpX is a fft2 of a spatial signal
K is the radial wavenumber defined above
I usually define Kx = [-N/2:N/2]./(N·dx) being N the number of samples.
However I saw your K definition like:
k_vec = [0:N-1]*2*pi/Dx;
To be honest I am a bit unsure about how to define my kx and ky
Many thanks,
Pau
Bruno Luong
>
> I usually define Kx = [-N/2:N/2]./(N·dx) being N the number of samples.
>
> However I saw your K definition like:
>
> k_vec = [0:N-1]*2*pi/Dx;
>
It is a matter of how you want to interpret the frequency spectrum, yours made the spectrum centered about 0, and supposes the low frequency is dominant. Rune's does not.
I would say your is more conventional.
Pau GALLES
However I believe there has to be a right definition because a spatial signal fft has
kx = 1/wavelengthx
meaning the wavelengths solved in my problem won't be the same for the 2 different alternative definitons for the kx.
Pau GALLES
However I am still concerned about only 1 definition being the right answer. It is my understanding that kx defines the wavelength range for a spatial signal.
kx = 1/=wavelengthx
Is the wavelength solved varying depending on the kx definition?
Bruno Luong
> Thanks Bruno,
>
> However I am still concerned about only 1 definition being the right answer. It is my understanding that kx defines the wavelength range for a spatial signal.
>
> kx = 1/=wavelengthx
>
> Is the wavelength solved varying depending on the kx definition?
When you sample the data with a step dx, frequencies with separation = 1/dx cannot be not be distinguished due to aliasing.
So to be more accurate, both answers are actually wrong because you can never know the full real spectrum from the discrete data.
Now the standard way of interpreting frequency spectrum is yours (symmetric centered about 0), not Rune's, since centering usually represents better the physics. But keep in mind that is not always the case.
Pau GALLES
If I center the frequencies I will get negative wavelengths. What are they meaning? I am going to filter by wavelengths afterwards. so I assume I should keep my frequencies positive?
I just cannot stop asking, sorry xD
Regards,
Pau
Bruno Luong
>
> If I center the frequencies I will get negative wavelengths. What are they meaning? I am going to filter by wavelengths afterwards. so I assume I should keep my frequencies positive?