Implementation of Frequency Reassignment

Question

yair amar 2020-10-6

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回答： Addy 2021-3-31

Hello everyone!

I am trying to implement TF-Reassignment for a project, relying on: https://www.researchgate.net/publication/241765281_TimeAiFrequency_Reassignment_From_Principles_to_Algorithms

(page 14):

when

and

is the STFT of the signal x, and the d stands for a derivative of the window h.

Our implementation follows the above mentioned calculations and yet does not work.

Any ideas as to what we miss here/ can be doen better?

%	Init function handles
hann_func = @(n,N) 0.5*(1 - cos(2*pi*n/(N-1)));
hann_d_func = @(n,N,fs) (pi*fs/(N-1))*sin(2*pi*n/(N-1));
%   intializing parameters
fs = 44100; N = 8192;	f1 = 150;   f2 = 420;
t_orig = 0:(1/fs):2.5;
x = cos(2*pi*f1*t_orig);
%   creating windows
win = hann_func(1:N,N);
win_d = hann_d_func(1:N, N, fs);
%	Applying STFTs with OL 50%
[X, f, t] = stft(x,fs,'Window',win,'OverlapLength',N/2,'fftLength',N);
[Xd, ~, ~] = stft(x,fs,'Window',win_d,'OverlapLength',N/2,'fftLength',N);
X_conj_over_norm = conj(X)./ (sum(abs(X)).^2);
Xdphase_dt = -imag(Xd .* X_conj_over_norm);
reass_f_X = f + Xdphase_dt/(2*pi);

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Answer 1

Addy 2021-3-31

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restft_demo.zip

I'm don't know much about the mathematics. But I saw that they referred to tfrrsp function which can be found in the reference [3]. The [3] is the TF toolbox found in http://tftb.nongnu.org. So, I tried to compare apples to apples with tfrrsp vs MATLAB's STFT.

I have attached the necessary mfiles from that toolbox to produce reassigned stft.

The results are as follows: