Signal processing wavelet transforms

BAYDAR, N. BALL, A. (2003) Detection of gear failures via vibration and acoustic signals using wavelet transform. Mechanical Systems and Signal Processing, 17 (4), pp. 787-804. 

Advanced signal processing techniques provides more elaborated approaches to the analysis and interpretation. In our study, we continue to promote the use of a continuous wavelet transform. We believe that its higher computational complexity are comparable to the Fourier transformation but the continuous wavelet transform makes the convenient assessment of amplitude, scale and phase of signal oscillations. Wavelet transform allows us to isolate a given structure in time and frequency space. Let us define the wavelet trans-... 

A12] Boles, W. W. and B. Boashash, A Human Identification Technique Using Images of te Ms and Wavelet Transform, IEEE Transactions on Signal Processing, Vol. 46, No. 4, April 1998... 

Starck, J.L., and A. Bijaoui. 1994. A signal processing filtering and deconvolution by the wavelet transform. Signal Proc. 35 195-211. 

L.J. Bao, J.Y. Mo and Z.Y. Tang, Comparative Study on Signal Processing in Analytical Chemistry by Fourier and Wavelet Transforms, Acta Chimica Sinica, 55... 

Before 1989, Fourier transform (FT) and fast Fourier transform (FFT) were employed mainly by chemists to manipulate data from analytical studies [5-7]. After the publication of an important paper by Daubechies [8] in 1988, a new transformation algorithm called wavelet transform (WT) became a popular method in various fields of science and engineering for signal processing. This new technique has been demonstrated to be fast in computation, with localization and quick decay properties, in contrast to existing methods such as FFT. A few chemists have applied this new method for... 

Despite recent advances, the problem of spectral libraries size build-up, and search speed receives still considerable amount of attention. Most of the commercial databases to date use Fast Fourier Transform (FFT) for spectra compression. However, the past ten years have brought explosive growth of wavelet applications in signal processing. The IR spectra show many ab-... 

The application of wavelet transforms to the analysis of spectra and other chemical data has gained popularity in chemistry [22-30]. Examples of typical chemical signal processing application are ... 

Wavelet transform (WT), a modern tool of applied mathematics, is a signal processing technique that has shown higher performance compared to Fourier transform and Short Time Fourier Transform in analyzing non-stationary signals. These advantages are due to its good localization properties in both, the time- and frequency domain. 

The basic idea of WT is to correlate any arbitrary function f t) with the set of wavelet functions obtained by dilation and translation. A stretched wavelet correlates with low frequency characteristics of the signal, while a compressed wavelet correlates with high frequency characteristics (Blatter 1988). Technically, we can say that scale parameter v relates the spectral content of the function f t) at a different positions X (translation parameter, see Figure 9.9). The correlation process described is the Continuous Wavelet Transform (CWT) of a signal, mathematically described as... 

Akay, M. Time Frequency and wavelets. In Akay, M. (ed.) Biomedical Signal Processing IEEE Press Series in Biomedical Engineering. Wiley—IEEE Press, Piscataway (1997) Alsberg, B.K., Woodward, A.M., Kell, D.B. An introduction to wavelet transform for chemometricians a time-frequency approach. Chemometr. Intell. Lab. Syst. 37, 215-239... 

PAYA, B. A. ESAT, I. I. (1997) Artificial neural network based fault diagnostics of rotating machinery using wavelet transforms asapreprocessor. Mechanical Systems and Signal Processing, 11 (5), pp. 751-765. 

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