An Inequality Relating the Spectral Density and Autocorrelation Function

Biometrika ◽  
1962 ◽  
Vol 49 (1/2) ◽  
pp. 262
Author(s):  
H. E. Daniels
Keyword(s):  
Spectral Density ◽  
Autocorrelation Function

scholarly journals Characteristics of extreme heavy precipitation events occurring in the area of Cracow (Poland)

2014 ◽  
Vol 9 (No. 4) ◽  
pp. 182-191 ◽  
Author(s):  
A. Walega ◽  
B. Michalec
Keyword(s):  
Time Series ◽  
Probability Distribution ◽  
Spectral Density ◽  
Autocorrelation Function ◽  
Heavy Precipitation ◽  
Botanical Garden ◽  
Maximum Precipitation ◽  
Density Analysis ◽  
Increasing Precipitation ◽  
Precipitation Events

The variability of extremely heavy precipitation events with duration of 120 min occurring in the area of Cracow, southern Poland was assessed. The analysis was performed using time series of maximum annual precipitation events with durations t = 5, 10, 15, 30, 60, and 120 min, recorded at the Botanical Garden station at the Jagiellonian University in the period of 1906–1990. The periodicity of precipitation was analyzed using the autocorrelation function and Fourier spectral density analysis. The Probable Maximum Precipitation (PMP) was calculated by Hershfield’s statistical method. The analysis of the autocorrelation function of sequences and the Fourier spectral density revealed a clear periodicity of the maximum precipitation. For precipitation with t = 60 min, the maximum values occur every 9 years, but also shorter periods (3-year) may be observed. The PMP values calculated for Cracow differ significantly from the values calculated using the probability distribution, as well as from the ones observed and they increase with increasing precipitation duration. The differences between the PMP and probable as well as observed precipitation tend to decrease with increasing duration of precipitation.

On the autocorrelation and spectral functions of queues

1968 ◽  
Vol 5 (02) ◽  
pp. 467-475 ◽  
Author(s):  
John F. Reynolds
Keyword(s):  
Fourier Transform ◽  
Spectral Density ◽  
Autocorrelation Function ◽  
Generating Functions ◽  
Queue Length ◽  
Spectral Functions

This paper considers the autocorrelation function of queue length and the corresponding spectral density (i.e., its Fourier transform). Some general expressions are obtained using generating functions and matrices, and applied to M/M/1 and M [x]/M/∞ queues.

On the autocorrelation and spectral functions of queues

1968 ◽  
Vol 5 (2) ◽  
pp. 467-475 ◽  
Author(s):  
John F. Reynolds
Keyword(s):  
Fourier Transform ◽  
Spectral Density ◽  
Autocorrelation Function ◽  
Generating Functions ◽  
Queue Length ◽  
Spectral Functions

This paper considers the autocorrelation function of queue length and the corresponding spectral density (i.e., its Fourier transform). Some general expressions are obtained using generating functions and matrices, and applied to M/M/1 and M[x]/M/∞ queues.

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