Nachweis von Perioden durch Phasen- und Amplitudendiagramm mit Anwendungen aus der Biologie, Medizin und Psychologie

Blume, J.

doi:10.1007/978-3-663-07312-3

Cited by 10 publications

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“…As a comparison of the method of analysis proposed in this paper, a method of Fourier analysis u tilizing a moving interval was carried out. The technique of Blume (1965) has the advantages of detecting oscillations even though the period may not be strictly constant, as often encountered in biological data, and even makes clear sudden phase-shifts of such an oscillation. First, a trial analysis i s made utilizing an interval chosen to contain a multiple of the period expected.…”

Section: Resultsmentioning

confidence: 99%

The Determination of Periodicities in Short‐term Time‐series Data in the Presence of High Frequency Noise and Long‐term Trend

Hopkins

Deitzer

Wagner

1979

Photochem & Photobiology

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The presence of periodicities in biological data may often be obscured by superposition of a background trend or high frequency oscillations. A method of least squares curve fitting was utilized to remove the trend in signal level. Subsequent removal of higher frequency noise utilizing smoothing convolution functions allows the determination of rhythmic components. A new "noise" convolution function gives a measure of the noise in data containing both signal and noise and allows the estimation of a limit above which an observed oscillation is considered significant. The effects of treating data with these convolution functions are discussed with reference to amplitude-frequency response curves. The results of data analysis utilizing convolution functions are compared with results obtained utilizing a moving interval Fourier technique (Blume. 1965). The convolution analysis have the advantages that they are easily programmed and rapidly calculated by programmable calculators, give results relatively insensitive to the length of convolution interval, and allow estimation of the variation in period and amplitude of the rhythm investigated.

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Section: Resultsmentioning

confidence: 99%

The Determination of Periodicities in Short‐term Time‐series Data in the Presence of High Frequency Noise and Long‐term Trend

Hopkins

Deitzer

Wagner

1979

Photochem & Photobiology

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“…Therefore the usual spectral approach for an analysis cannot be used with great success and special procedures must be developped (Sollberger, 1970). We have chosen two of these methods for a comparison: the numerical signal averaging of De Prins and Cornelissen (1975) and the pergressive Fourier analysis of Blume (1955Blume ( , 1965Blume ( , 1975. Both methods assume the time series model f(t)=s(t)+e(t) (signal plus noise), and they provide estimates of period length, amplitude and phase of the signal.…”

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confidence: 99%

“…Following Blume (1965) we ujed R=5% and R=6 for the application of the pergressive Fourier analysis. Applying tfie numerical signal averaging, we used starting values S=P 0 +P 0 /12 with P o the true period length.…”

Section: Empirical Comparison Of the Quality Of Estimatesmentioning

confidence: 99%

“…Blume's pergressive Fourier analysis is closely related to the complex demodulation, a well-known procedure in time series analysis (Tukey, 1961;Granger and Hatanaka, 1964;Bingham et al, 1967;Welch, 1967). Complex demodulation is briefly described by the following steps, (i) Multiply the time series X(t) with a periodic complex exponential X jU (t):=e-i / /t X(t), (ii) use a narrow-band, low-pass filter L to get Zjult) := L (X^t)), (iii) with we get estimates of the 'average' amplitude an.d 'average' phase of the frequency band f(/u) d/i at time t. Assuming that a periodicity of length T:=ju~' is present in a time series i.e., that there is a major peak at frequency /* in the spectrum, then it can be shown (Blume, 1955(Blume, , 1965Bingham et al, 1967) that the phase ç», (¿i) of Z/u(t) is linear in t and can be used to estimate p, the underlying frequency. 409 Downloaded by [North Carolina State University] at 23:06 15 March 2015…”

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A comparison of the numerical signal averaging of de prins and Cornelissen and Blume's pergressive fourier analysis

Martin¹,

Brinkmann²

1977

Journal of Interdisciplinary Cycle Research

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Detection and measurement of periodicities in biology is often a problem, because most of the biological time series are short, i.e. only a few cycles are available. Therefore the usual spectral approach for an analysis cannot be used with great success and special procedures must be developped (Sollberger, 1970). We have chosen two of these methods for a comparison: the numerical signal averaging of De Prins and Cornelissen (1975) and the pergressive Fourier analysis of Blume (1955, 1965, 1975). Both methods assume the time series model f(t)=s(t)+e(t) (signal plus noise), and they provide estimates of period length, amplitude and phase of the signal. In order to compare both methods we have taken into account the number of necessary numerical operations (computation time) and the quality of the estimates.To test this quality, we have used computer simulated data of the above type as well as circadian rhythms of Euglena gracilis. A comparison of the results for various conditions can be used for a decision which method should be used in a future analysis. METHODSA. PERGRESSIVE FOURIER ANALYSIS. Blume's pergressive Fourier analysis is closely related to the complex demodulation, a well-known procedure in time series analysis (Tukey, 1961;Granger and Hatanaka, 1964;Bingham et al., 1967;Welch, 1967). Complex demodulation is briefly described by the following steps, (i) Multiply the time series X(t) with a periodic complex exponential X jU (t):=e-i / /t X(t), (ii) use a narrow-band, low-pass filter L to get Zjult) := L (X^t)), (iii) with we get estimates of the 'average' amplitude an.d 'average' phase of the frequency band f(/u) d/i at time t. Assuming that a periodicity of length T:=ju~' is present in a time series i.e., that there is a major peak at frequency /* in the spectrum, then it can be shown (Blume, 1955(Blume, , 1965Bingham et al., 1967) that the phase ç», (¿i) of Z/u(t) is linear in t and can be used to estimate p, the underlying frequency. 409 Downloaded by [North Carolina State University] at 23:06 15 March 2015Performing the pergressive Fourier analysis, we define a segment of the time series including L points and pass it through the total series with stepwidth of Q points. So we get a set of complex demodulates Zfil) with /i=27m/L, n=0...., L/2. Blume has now stated a heuristic principle for the choice of the phase function under the above set belonging to the periodicity in question. Having selected this phase function, we can calculate the length T of the period by T=L/R with R defined by the slope 27TR/L of the phase function.B. NUMERICAL SIGNAL AVERAGING. The term signal averaging is used to the procedure of looking for the Buys-Ballot-filter i.e., a linear nonsymmetric filter with gapped weights p Y (t) := P-1 ,£ X (t -Kj), t = 1 K, which gives an optimal signal. The Buys-Ballot-filter has the properties that for a set of discrete frequencies -A k = 2?ik/K phase shift is zero and in the limit P-co the frequenciesÀ K are isolated (De Prins and Cornelissen, 1975;Koopmans, 1974). Therefore by choic...

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“…When data are given which are subject to random fluctuations, a statistical 38.5 A sine curve is fitted to telemetric measurements of intraperitoneal temperatures of an adult female rat. For treatments that do not require high level mathematics we refer the reader to Stumpff (1937), Blume (1965), Kendall and Stuart (1966). Data were obtained in preparation for a space shot (Reprinted from Halberg, 1969) procedure is required to estimate the parameters.…”

Section: *59 Trigonometric Polynomialsmentioning

confidence: 99%

Introduction to Mathematics for Life Scientists

Batschelet¹

1979

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Nachweis von Perioden durch Phasen- und Amplitudendiagramm mit Anwendungen aus der Biologie, Medizin und Psychologie

Cited by 10 publications

References 0 publications

The Determination of Periodicities in Short‐term Time‐series Data in the Presence of High Frequency Noise and Long‐term Trend

The Determination of Periodicities in Short‐term Time‐series Data in the Presence of High Frequency Noise and Long‐term Trend

A comparison of the numerical signal averaging of de prins and Cornelissen and Blume's pergressive fourier analysis

Introduction to Mathematics for Life Scientists

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