Signal processing transforms

H.S. Malvar, "Signal processing with lapped transforms", Ed. Artech House, Inc., 1992. 

By means of numerical convolution one can obtain Xg t) directly from sampled values of G t) and Xj(t) at regular intervals of time t. Similarly, numerical deconvolution yields Xj(t) from sampled values of G(t) and Xg(t). The numerical method of convolution and deconvolution has been worked out in detail by Rescigno and Segre [1]. These procedures are discussed more generally in Chapter 40 on signal processing in the context of the Fourier transform. 

Transforms are important in signal processing. An important objective of signal processing is to improve the signal-to-noise ratio of a signal. This can be done in the time domain and in the frequency domain. Signals are composed of a deterministic part, which carries the chemical information and a stochastic or random part which is caused by deficiencies of the instmmentation, e.g. shot noise... 

Modern IR spectrometers do not use light dispersion to acquire spectra. Rather, they utilize a device called an interferometer between the source and the sample. This design requires a signal processing circuit that performs a mathematical operation called a Fourier transformation to obtain the spectra. 

A.M. Bruckstein, T.J. Richardson - A Holographic Transform Domain Image Watermarking Method. Circuits Systems Signal Processing, Vol. 17, No. 3, 1998, pp. 361-389. 

Fig. 3.2. The individual steps of intercellular communication. Upon reception of a triggering stimulus, the signal is transformed into a chemical messenger within the signaling cell. The messenger is secreted and transported to the target cell, where the signal is registered, transmitted further, and finally converted into a biochemical reaction. Not shown are processes of termination or regulation of communication which can act at any of the above steps.

The nature of the signal processing, and its potential effectiveness, depends on the characteristics of the auditory system. The ear transforms the incoming acoustic signal into mechanical motion, and this motion ultimately triggers neural pulses that carry the auditory information to the brain. The essential components of the ear are shown in Fig 6.1. 

Anderson, 1996] Anderson, D. (1996). Speech analysis and coding using a multiresolution sinusoidal transform. In Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing., pages 1037-1040, Atlanta, GA. 

Nawab and Quatieri, 1988a] Nawab, H. and Quatieri, T. (1988a). Short-time fourier transform. In Lim, J. S. and Oppenheim, A. V., editors, Advanced Topics in Signal Processing. Prentice Hall, Englewood Cliffs, New Jersey. 

Nawab et al., 1983] Nawab, S., Quatieri, T., and Lim, J. (1983). Signal Reconstruction from Short-Time Fourier Transform Magnitude. IEEE Trans. Acoust., Speech, Signal Processing ASSP-31(4) 986-998. 

Zelinski and Noll, 1977] Zelinski, R. and Noll, P. (1977). Adaptive transform coding of speech signals. IEEE Trans. Acoust,. Speech, and Signal Processing, 25 299-309. 

The first artificial reverberators based on discrete-time signal processing were constructed by Schroeder in the early 1960 s [Schroeder, 1962], and most of the important ideas about reverberation algorithms can be traced to his original papers. Schroeder s original proposal was based on comb and allpass filters. The comb filter is shown in figure 3.12 and consists of a delay whose output is recirculated to the input. The z transform of the comb filter is given by ... 

Dembo and Malah, 1988] Dembo, A. and Malah, D. (1988). Signal synthesis from modified discrete short-time transform. IEEE Trans. Acoust., Speech, Signal Processing, ASSP-36(2) 168-181. 

Malvar, 1990] Malvar, H. S. (1990). Lapped transforms for efficient trans-form/subband coding. In IEEE Trans. Acoust., Speech and Signal Processing, volume 38, pages 969-978. 

Quatieri and McAulay, 1986] Quatieri, T. and McAulay, R. (1986). Speech transformations based on a sinusoidal representation. IEEE Trans, on Acoustics, Speech, and Signal Processing, ASSP-34(6) 1449-1464. 

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