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Digital signal processing question:
1. Consider the STDTFT defined as jwk where n] is the speech signal and wIn] is the window sequence. Prove the following properties a. Linearity -if n]-ax[n]+by[n], then V(o,n)-aX(o,n)+bY(o,n b. Shifting-ifYn]=x(n-n] , then V(a,n)-X(a,n-nen, c. Modulation _ ifv[n] =x(n em, , then l(?,n)=X(?-o,,n). d. Show that can be put in the form ie. X(a,n) is a smoothed spectral estimate of X(?) at frequency ?,

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0 w(n) window sequence2 K. themthe Specta a eunatuen T-300 Th the Smoothed ycealmate(w) aTL je n

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