Frequency domain representations of wavelet transforms

Charles C. Mosher; Douglas J. Foster

doi:10.1117/12.218496

1 September 1995 Frequency domain representations of wavelet transforms

Charles C. Mosher, Douglas J. Foster

Proceedings Volume 2571, Mathematical Methods in Geophysical Imaging III; (1995) https://doi.org/10.1117/12.218496
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

Abstract

Much of the wavelet literature is focussed on wavelets with compact support in the time domain. For many geophysical applications, compact support in the frequency domain is desirable. For these applications, simple window functions can be used to construct appropriate filter banks in the frequency domain. Convolution with filter coefficients in the time domain is replaced with a Fourier transform and multiplication by window functions in the frequency domain. Given the dual nature of the Fourier transform, the time and frequency variables can be exchanged to produce a time windowing algorithm for computing wave packet transforms. Taken together, frequency-windowed and time-windowed wave packet transforms provide a comprehensive tool set for constructing new geophysical applications that take advantage of simultaneous access to time and frequency. Depending on the application, frequency windowing or time windowing may be more desirable.

Citation Download Citation

Charles C. Mosher and Douglas J. Foster "Frequency domain representations of wavelet transforms", Proc. SPIE 2571, Mathematical Methods in Geophysical Imaging III, (1 September 1995); https://doi.org/10.1117/12.218496

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KEYWORDS

Linear filtering

Transform theory

Fourier transforms

Electronic filtering

Wavelet transforms

Wavelets

Optical filters

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