Confusion about STFT calculation

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paul simmons

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Hi,
I now it is a novice question but I am confused.

In Rabiner's Speech Proc. STFT is defined as:

\[X_n(e^{j\omega})=\sum_{m=-\infty}^{\infty } w(n-m)x(m)e^{-j\omega m}\]

Suppose our signal is all 1s, and window function is unit impulse (just for simplicity). So that in every window we again have unit impulse. And if we take STFT at t=1, we get \[e^{-j\omega }\] as STFT but at t=2 we get \[e^{-j\omega 2}\]

Am I calculating wrong? If not; then am I thinking wrong to assume all transforms will be same; if the corresponding signals within windows at any time are same?
 
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Do u have code for STFT of Linear chirp signal?
 

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