090206Lecture13

090206Lecture13 - ECE 700 Digital Signal Processing Lecture...

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ECE 700 ECE 700 WI 2009 Digital Signal Processing Lecture 13 02/06/09 1
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STFT Tiling of the T-F plane The set of basis functions used for the Short Time Fourier Transform are , ( ) ( ) . j t b t w t e τ = - Thus the basis function can be regarded as a centered at the point in the time-frequency plane. 0 0 , ( ) b t 0 0 ( , ) 0 0 0 , Let ( , ) and ( , ) be the time and frequency extent of ( ). b t ECE 700 WI 2009 0 0 0 0 0 Uniform tiling of the T-F plane.
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Continuous Wavelet Transform (CWT) A non-uniform tiling of the T-F plane, in which the lower frequencies have wider time windows is desirable. ECE 700 WI 2009 The Continuous Wavelet Transform achieves this by using time-shifted and time-scaled versions of a prototype waveform called the “mother” wavelet. Note that time-scaling is related to, but is not the same as frequency translation. This means that with wavelets we look at Time-Scale plots, not Time-Frequency plots.
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CWT Definition Starting with a mother wavelet ψ ( t ), the basis functions are defined as , 2 , 1 ( ) ( ) where ( ) 0 .
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This note was uploaded on 04/18/2009 for the course ECE 700 taught by Professor Un during the Winter '09 term at Ohio State.

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090206Lecture13 - ECE 700 Digital Signal Processing Lecture...

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