How to decide on Window function parameters while finding Transfer function using Tfestimate function

Hello Everyone,

 N = 204800;
 Fs = 200;
 NFFT = [32768, 131072];
 [Txy,F]=tfestimate(input,output,hann(X),nooverlaps,NFFT,Fs);

as a part of my thesis work, i have to find a tranfer function between an input signal and output signal. I am using tfestimate function to do this. As the input signal is aperiodic, inorder to find FFT, i am using a Hanning window with nooverlaps to avoid the leakage effects. The inout signal duration is 1000 sec, sampling frequency is 200Hz, i have in total N= 204800 samples in time domain. I am finding it really difficult to decide upon the window parameters to get a good amplitude accuracy, and reasonably good frequnecy resolution.I have tried with a few configurations of window parameters, but could not figure out which is best suited for my case and which one i have to believe to be correct. I have attached a picture which shows the transfer function for different window paramaters and NFFT. My doubt is should we define window parameters based on the number of samples in time domain (N) or based on the NFFT that we take for FFT calculation. What does hann(X) mean, is X = number of segments (windows) in to which the signal is divided or Length of each segment(window). Please help me with this. Thanks in advance.

Answer 1

[Shubh Sahu]

The actual FFT transform assumes that it is a finite data set, a continuous spectrum that is one period of a periodic signal. But, many times, the measured signal isn’t an integer number of periods due to this sharp transition come in picture. Windowing is done basically to minimize the effect of FFT over a non-integer number of cycles. For more insight on windowing you can refer to: http://download.ni.com/evaluation/pxi/Understanding%20FFTs%20and%20Windowing.pdf

Where as in hann(x), ‘x’ is the length of each window segment. Here is the link you can refer to: https://www.mathworks.com/help/signal/ref/hann.html

In order to select the window size, don’t select bigger window length because it makes the signal non-stationary so the best way to choose the window size is to choose small size (in your case 800-1000) but not to too small.