Frequency domain response from time domain response using PSD

Hii all,

I used FFT in Matlab to convert time domain wave elevation to frequency domain JONSWAP spectrum. But the spectrum is supposed to be in smooth curve but I am getting unwanted peaks and noise. Please help me to get the spectrum smooth. I am attaching the matlab script below and the spectrum obtained and what I am supposed to get.

clear;

clc;

Wave1= xlsread('WaveElev_Time_LC1.xlsx');

Wave=Wave1(:,2);

figure();

plot(Wave1(:,1),Wave);

title("Wave elevation in Time Domain");

xlabel('Time(s)','linewidth',3);

ylabel('Wave Elevation(m)','linewidth',3);

xlim([0 3600]);

Ns=length(Wave);

fs=1/0.0125;

fft_Wave=fft(Wave);

fft_Wave = fft_Wave(1:Ns/2+1);

psdx = (1/(fs*Ns)) * abs(fft_Wave).^2;

psdx(2:end-1) = 2*psdx(2:end-1);

freq = 0:fs/Ns:fs/2;

y = smooth(freq, psdx);

figure();

plot(freq,y,'linewidth',2);

xlim([0 0.2])

[Mathieu NOE]

hello

try with smoothdata , I would suggest with gaussian window

adapt the window length to get the desired amount of smootihing

Answer 1

[Balavignesh]

Hi Mohammed,

As per my understanding, you are encountering spectral leakage and noise in your Fast Fourier Transform (FFT) output, which is common when dealing with finite or non-periodic signals. I would suggest you apply a window using 'hann' function to the time-domain signal before performing 'FFT' to obtain a smoother spectrum. The windowing process helps reduce spectral leakagge by tapering the beginning and end of the time-domain signal to zero.

The following code snippet may help you understand this:

% Creating a window 
window = hann(Ns);
% Applying window function to the wave
Wave_windowed = Wave.*window;
% Performing fft 
fft_Wave=fft(Wave_windowed);
fft_Wave = fft_Wave(1:Ns/2+1);

Kindly refer to the following documentation links to have more information on:

• 'hans' function: https://www.mathworks.com/help/signal/ref/hann.html
• 'psd' : https://www.mathworks.com/help/signal/ref/dspdata.psd.html