hi farshad

you can easily make smooth  in MATLAB

it  command  is : " smooth " only

i suggest you use MATLAB 

Best Regards 

Alireza

First interpolate your data in time domain and then take its Fourier transform, the resulting Fourier transform will be a smoothed version of the data. 

If you need a higher resolution at low frequencies and you have a function that approaches zero for t->inf you could just pad the function in real space with a lot of zeros.

Zero filling (outside the data region) in one domain will zoom/interpolate the function in the corresponding Fourier domain. So, transform the data, add zeros around the data (this will increase the vector size) and transform back to the domain where you want to analyze the data. Before transforming back, adding some sort of smoothing function like a Hanning window to bring the edge of the data smoothly to zero when you are doing the zero filling will lead to a smoothed profile in the analysis domain by avoiding Gibbs ringing artifact. 

On Excel, you can run a moving average, which is very easy to implement. Lets say you want to run a moving average with a window length of 9 points. You have your frequencies in column A, your original amplitude data in column B and you want your filtered amplitude data in column C. Then on cell C5, type "=AVERAGE(B1:B9)". Drag down this formula and you have applied a running average smoothing filter. For extremities, you need to reduce the window length. For example, on cell C4 = AVERAGE(B1:B8) ; C3 = AVERAGE(B1:B7) etc.

Then create a scatter plot with x = column A and y = column C, and you have your filtered spectrum.

 I think my friend you will need some filters for white noise or something like that and one for the frequency of the power network supply,try if you want butterworth filters equations or gaussian filter,or both of them or default filters on matlab,but you have to use filters for more clear graphs,if i was you i would also make a function for cut off frequencies by scalar, a  new array with the filtered signal and then reassemply the signal with higher FS sampling freq.i wish you good luck with your project!!I agree with the other answers that was friends gave to you! 

hi ,

please try these function

 pwelch() or pmtm()

(http://www.mathworks.com/matlabcentral/answers/111037-how-i-can-smooth-my-fourier-amplitude-spectra)

http://faculty.olin.edu/bstorey/Notes/Fourier.pdf

http://in.mathworks.com/matlabcentral/newsreader/view_thread/312373

https://holometer.fnal.gov/GH_FFT.pdf

You can filter the spectrum using a low pass filter. Ah, and zero padding in time does NOT increase frequeny resolution, contrary to what some respondents here said!

What you desire has been addressed by multi taper methods.

Here a paper that will give you a lot of background knowledge:

http://www.mit.edu/~gprieto/pubs/gprieto_07b.pdf

If you google a bit, you will find implementations for fortran, python, matlab and probably others as well.

Hi my friend .

you can use flac 2d with fft fish function to determine both frequencies in your earthquake signal and in your soil profil .

good luck

Hi my friend .

you can use flac 2d with fft fish function to determine both frequencies in your earthquake signal and in your soil profil .

good luck

interesting

Probably this might be a little too late to answer, but I will anyway.

I guess the Savitsky-Golay filter could be of help:

https://en.wikipedia.org/wiki/Savitzky%E2%80%93Golay_filter

There is a function in MATLAB as well: sgolayfilt

ou can apply savitzky-Golay Filter to smooth out FFT. If P is FFT output, you can use savitzky-Golay filter with order and window size to smooth the response. In Matlab you can call sgolayfilt(P, 6, 55); Where 6 is order to polynomial and 55 is window size.

Hello Friends..

if you have the XY data for Fourier spectrum you can perform smoothing easily using abacus output (Operate on XY data) and choosing Smooth2(X,F), where X is is the data set of FFT , and F is the resolution factor..

If any one need to more understand that you can whatsapp me at +961 3 668 491