Errors in digital processing of signals (Gold and Rader, 1969)

Gold, B.; Rader, Charles M.

doi:10.1109/msp.1981.237661

Cited by 23 publications

(47 citation statements)

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“…8(b) and (c). The corresponding DFT relation is cyclic expander (9) for (This is similar to the periodic extension idea in DFT theory [8]). Since are the -point DFT coefficients of , the -point DFT has the period We can define fractional decimators in a manner analogous to the noncyclic case (for example, as in [23,).…”

Section: B Cyclic Decimators and Expandersmentioning

confidence: 94%

“…Related Literature: Since circular convolution is an integral part of DSP, we can regard cyclic LTI filtering as one of the earliest known DSP techniques [8]. The use of circular filtering in image subband coding (where images have finite size [7]) was motivated by the work of Smith and Eddins on symmetric extension techniques [19].…”

Section: A Motivation and Scopementioning

confidence: 99%

“…We say that is a cyclic LTI system. For the purpose of interpretation, we can also regard to be a periodicinput for which the LTI system yields the periodicoutput Circular or cyclic convolution has been at the center of digital signal processing from its early days [8]. Indeed, fast algorithms for ordinary convolution routinely convert the problem into a cyclic convolution and then use the FFT.…”

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confidence: 99%

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Cyclic LTI Systems in Digital Signal Processing

Vaidyanathan¹

1998

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Abstract-Cyclic signal processing refers to situations where all the time indices are interpreted modulo some integer L.In such cases, the frequency domain is defined as a uniform discrete grid (as in L-point DFT). This offers more freedom in theoretical as well as design aspects. While circular convolution has been the centerpiece of many algorithms in signal processing for decades, such freedom, especially from the viewpoint of linear system theory, has not been studied in the past. In this paper, we introduce the fundamentals of cyclic multirate systems and filter banks, presenting several important differences between the cyclic and noncyclic cases. Cyclic systems with allpass and paraunitary properties are studied. The paraunitary interpolation problem is introduced, and it is shown that the interpolation does not always succeed. State-space descriptions of cyclic LTI systems are introduced, and the notions of reachability and observability of state equations are revisited. It is shown that unlike in traditional linear systems, these two notions are not related to the system minimality in a simple way. Throughout the paper, a number of open problems are pointed out from the perspective of the signal processor as well as the system theorist.

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Section: B Cyclic Decimators and Expandersmentioning

confidence: 94%

Section: A Motivation and Scopementioning

confidence: 99%

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confidence: 99%

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Cyclic LTI Systems in Digital Signal Processing

Vaidyanathan¹

1998

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“…Below, additional facts of symmetries also indicate that this is a regular distribution. In digital signal processing, bit-reversal permutations play an important role; they are connected, in particularly, with quasi-holographic models, noise-immunity coding, and with algorithms of fast Fourier transform [12][13][14][15][16]. The bit-reversal permutation is a permutation of a sequence of n items, where n = 2 k , k-positive integer.…”

Section: Black and White Cells Of Genetic Matrices [C A; T G] (2) Amentioning

confidence: 99%

Symmetries in Genetic Systems and the Concept of Geno-Logical Coding

Petoukhov

Petukhova

2016

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Abstract:The genetic code of amino acid sequences in proteins does not allow understanding and modeling of inherited processes such as inborn coordinated motions of living bodies, innate principles of sensory information processing, quasi-holographic properties, etc. To be able to model these phenomena, the concept of geno-logical coding, which is connected with logical functions and Boolean algebra, is put forward. The article describes basic pieces of evidence in favor of the existence of the geno-logical code, which exists in parallel with the known genetic code of amino acid sequences but which serves for transferring inherited processes along chains of generations. These pieces of evidence have been received due to the analysis of symmetries in structures of molecular-genetic systems. The analysis has revealed a close connection of the genetic system with dyadic groups of binary numbers and with other mathematical objects, which are related with dyadic groups: Walsh functions (which are algebraic characters of dyadic groups), bit-reversal permutations, logical holography, etc. These results provide a new approach for mathematical modeling of genetic structures, which uses known mathematical formalisms from technological fields of noise-immunity coding of information, binary analysis, logical holography, and digital devices of artificial intellect. Some opportunities for a development of algebraic-logical biology are opened.

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“…The FIR filters involve convolving a time series with a symmetric weight series (which may itself be considered a time series), yielding a filtered time series. Specific steps for constructing such filters (i.e., generating the weight series) have been described by Gold and Rader (1969; see also Ackroyd, 1973;Cook & Miller, 1992;Dumermuth & Molinari, 1987;Oppenheim & Schafer, 1975), and software implementing the weight-generation process is available (e.g., Cook, 1981). Briefly, the technique involves four steps, summarized in Figure 4.…”

Section: Design Of Time Domain Filters In the Frequency Domainmentioning

confidence: 99%

Digital filtering in EEG/ERP analysis: Some technical and empirical comparisons

Nitschke

Miller

Cook

1998

Behavior Research Methods, Instruments, & Computers

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A general approach to time domain digital filtering is described, and examples of some filters used in EEGIERP research are presented. Simulations are reported that evaluate the impact of the relative length of the filter weight series and the signal cycle to be flltered, the span and real-time density of the filter weights, and slow drift across the epoch being flltered. Results indicate that some fllters commonly used in the EEGIERP literature are inadequate. Frequency domain digital filtering is also briefly discussed. The fast Hartley transform, a fast but relatively unknown computational method for frequency domain filtering of ERPIEEG data, is introduced and compared with time domain flltering. Some practical recommendations are provided.The analysis of encephalographic (EEG) data, either ongoing activity or event-related potentials (ERPs), generally requires the extraction of a signal of interest from a noisy background. This filtering process may be carried out in a variety of different ways. The term digital filter refers to a wide range oftechniques that have in common the fact that they are mathematical procedures applied to discrete, numeric representations of continuous waveforms to emphasize or attenuate certain frequencies.Digitally filtering an EEG waveform in the time domain' typically involves cross-multiplying each unfiltered data point and its neighbors with a set ofweights. In effect, the weights represent a copy of the signal pattern of interest. The cross-multiplication process is repeated for each point to be filtered. The sums of these cross-products, arranged as a series, constitute the filtered waveform. An intuitive appreciation of how such a procedure can accomplish frequency-specific filtering can be gained by considering a set of weights with magnitudes forming a sine wave of a particular frequency. When data points are cross-multiplied with these weights, the sum of the crossproducts will be largest when the data predominantly consist ofa sine wave ofthe same frequency and are in phasewith the weights, such that the two sets of values rise and Portions of the introductory material in this paper are based on a more general tutorial on filtering (Cook & Miller, 1992 Copyright 1998 Psychonomic Society, Inc. 54 fall in synchrony. The sum of the cross-products will be most negative when the data have the same frequency but are inverted (180 0 out of phase). Any other pattern in the data will produce a sum closer to zero. In effect, the filter is "tuned" to detect a sinusoidal signal of a certain frequency, and signals that are nonsinusoidal or do not match the filter's frequency will not produce as much output.Digital filters ofthis type are pervasive in psychophysiology. In designing an appropriate filter for a given EEGI ERP application, the investigator faces a choice among a variety of methods for generating the weights used in the cross-multiplication function and also a choice of the set of adjacent time points to which to apply the weights. These choices affect the computational...

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Errors in digital processing of signals (Gold and Rader, 1969)

Cited by 23 publications

References 0 publications

Cyclic LTI Systems in Digital Signal Processing

Cyclic LTI Systems in Digital Signal Processing

Symmetries in Genetic Systems and the Concept of Geno-Logical Coding

Digital filtering in EEG/ERP analysis: Some technical and empirical comparisons

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