# Lecture6 - Lecture 6 The STFT EE214A Abeer Alwan The Short...

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1 Lecture 6: The STFT EE214A Abeer Alwan ) ( | ) ( | ) ( ) ( ) ( ) ( ) ( n j j n n n m m j j n e e X jb a e m n w m x e X The Short Time Fourier Transform (STFT) w(n-m) is a real window that determines the portion of the signal to be analyzed. The STFT is sometimes written as . It is a function of discrete time and continuous frequency. ) , ( n X

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2 even though they are only de m and n m .) ˆ ˆ ˆ 1) n-fixed: )] ( ) ( [ ) ( m n w m x F e X j n )] ( [ * )] ( [ m n w F m x F ) ( j e X ) ( j n j e W e d e W e e X j n j j ) ( ) ( 2 1 ) ( ) ( 2 ) ( ) ( ) ( 2 1 d e X e e W j n j j Two Interpretations of the STFT
3 )) ( ( ) ( ) ( 1 j n e X F m x m n w d e e X m x m n w m j j n ) ( 2 1 ) ( ) ( 2 ) ( ) 0 ( 2 1 ) ( d e e X w n x m j j n assuming w(0) is not zero. Signal Recovery from the STFT How to choose the window?

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• Winter '11
• ALWAN
• j, Rectangular Window, Hamming Window, Short-time Fourier transform, STFT, Fricative Spectrograms

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