29 December 1992 Information-to-noise improvement in the frequency domain using the wavelet transform
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Some finite energy, causal, real-valued signals are frequency analyzed using a fast Fourier transform (FFT). Computer generated additive white noise is combined with time-domain samples, and the analysis is repeated. It is shown that the combination of noise and aliasing can hide information when high frequency noise is folded over an interesting part of the frequency domain. Aliasing cannot be avoided in exploratory physics and engineering experiments and aliased noise can drown out real peaks in the signal frequency spectrum. Time-domain filtering techniques are discussed, but they cannot always recover these lost peaks. A new method is introduced in which the wavelet transform and its inverse are used to suppress high frequency noise prior to Fourier analysis. This method is useful in improving on experimental results when aliasing of high frequency noise presents a problem.
© (1992) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Charles R. Thompson, Charles R. Thompson, Brian DeFacio, Brian DeFacio, } "Information-to-noise improvement in the frequency domain using the wavelet transform", Proc. SPIE 1767, Inverse Problems in Scattering and Imaging, (29 December 1992); doi: 10.1117/12.139008; https://doi.org/10.1117/12.139008


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