Signal representation

Preprocessor. A device in a data-acquisition system that performs a significant amount of data reduction by extracting specific information from raw signal representations in advance of the main processing operation. A preprocessor can constitute the whole of a data-acquisition interface, in which case it must also perform the data-acquisition task (conversion of spectrometer signal to computer representation), or it can specialize solely in data treatment. 

This signal representation with only odd harmonics is an approximate model for a clarinet as with a uniform tube closed at one end and open at the other. In order to capture the time-varying envelope and bandwidth, one applies a A(n ) with a fast attack and slow release, and also makes the modulation index I(n ) inversely proportional to this envelope, thus emulating the decreasing bandwidth as a function of time. 

In the internal representation approach the quality of an audio device is measured by mapping the reference and output of the device from the physical signal representation (measured in dB, seconds, Hertz) onto a psychoacoustic (internal) representation (measured in compressed Sone, seconds, Bark). From the difference in internal representation the perceptual audio quality measure (PAQM) can be calculated which shows good correlation with the subjectively perceived audio quality. 

By exploiting the analytic signal representation of h(n), Key, Fowle, and Haggarty [Key et al., 1959] have shown that, under a large time-bandwidth product constraint, specifying the two amplitude components, a(n) and M(a), in Equation (4.22) is sufficient to determine approximately the remaining two phase components. How large the time-bandwidth product must be for these relations to hold accurately depends on the shape of the functions a(n) and M(oo) [Cook and Bemfeld, 1967, Fowle, 1967]. 

Temporal Envelope. Temporal envelope is sometimes defined, typically in the context of bandpass signals, as the magnitude of the analytic signal representation [Oppen-heim and Schafer, 1975], Other definitions of temporal envelope have been proposed based on estimates of attack and release dynamics [Blesser, 1969]. One approach to time-scale modification, given the spectral envelope of a signal, is to select a Fourier-... 

The analytic signal representation of sm ( ) is next constructed to obtain a signal of the forms,m(n) = a (n) exp[/( )i (n)] from which an estimate of/and also (Omn by fitting a straight line to < >i (n) is obtained. If the original signal does not follow the assumed FM model then a phase residual will result from the least-squared error... 

An illustration of a path constructed by truncating this series to a finite number of terms is given in Figure 4B. The use of other reference paths besides a straight-line path (e.g., the path of a harmonic oscillator) has been explored elsewhere in the literature [85]. Alternatively, one might also consider using other signal representations to describe the paths. For example,... 

Unlike representation of functions using wavelet basis functions, there are many different combinations of wavelet packet basis functions that can be used in signal representation. Hence there is some degree of redundancy. With redundancy comes choice, and Section 3 discusses one approach for selecting a set of basis functions. 

H.H. Szu, B. Telfer, and S. Kadambe, Neural Network Adaptive Wavelets for Signal Representation and Classification, Optical Engineering 31 (1992), 1907-1916. 

S. Mallat and S. Zhong, Complete Signal Representation with Multiscale Edges, Robotics Report No. 219 483, Courant Institute of Mathematical Sciences, New York University, 1989. 

Figure 12 The signal representation or basis of the (a) pyramid algorithm and two examples (b, c) of selected representations from the entire hierarchy computed by the WPT are shown. The WPT allows for optimal signal basis selection by enumerating the complete decomposition tree, so that all signal representations can be evaluated.

I., Moosburger, R., Freund, R., Richter, A., Georgi, S., Breuer, B., and Hamster, H. (2000) Multiple signal representation simulation of photonic devices, systems, and networks. IEEE J. Set. Top. Quantum Electron., 6 (2), 282-296. 

Muller, S.H., Bauml, R.W., Fisher, R.F.H. OFDM with reduced Peak to Average power ratio by multiple signal representation Annals of telecommunications, vol. 52(1-2) (February 1997)... 

All of these procedures require that adjacent or overlapping windows contribute independently to the signal representation, which means that the collection of waveforms should constitute an orthogonal basis. Unfortunately, this is not possible for Gabor functions due to the Balian-Low phenomenon, a mathematical obstruction. But it is possible for lapped orthogonal functions, also known as local sines and cosines, which are very similar. ... 

Spiridonakos M, Fassois S (2014a) Adaptable functional series TARMA models for non-stationary signal representation and their application to mechanical random vibration modeling. Signal Process 96 63-79... 

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