signal-processing,fft,wavelet,haar-wavelet,wavelet-transform , How the window function works in STFT


How the window function works in STFT

Question:

Tag: signal-processing,fft,wavelet,haar-wavelet,wavelet-transform

Can anyone experienced in signal processing and STFT explains to me why the window function in the below posted image is from (t-t'), given that t is the total time and t' is the width of the window?

I can not figure it out because, initially, the window is located at t=0, and if the window length for an example is 3, then the window will spans from t=0 -> t=3, and if the total time T = 10 for an example then the window function will be like w(T-3), which is 7?! I really can not understand it and I believe there is any hidden thing I can not comprehend.

Kindly please clarify it and guide. Thanks Image: enter image description here


Answer:

note that, the width of the winow function is constant throughout the entire STFT process. and the time (t) in the function g(t-t') indicate sthat, t: is the current time on the time axis and it is variable each time the window is moved/shifted to the righ to overlap the main signal.

in other words, and i hope this clarifies better, the "t" at the end of the time axis is NOT the "t" in the function g(t-t'). as i stated earlir in the function g(t-t'), t: is the current time on the time axis and it is variable for each shift of the window function and t': is the width of the window and it is constant throughout the entire STFT process.


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