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Frac (Source)
GetRecord (Dest, TableName, RecsBack)
T = N*tau: the length, in seconds, of the time series.
Processing field: "FFT,N,tau,option". Tick marks on the x axis are 1/(N*tau) Herz.
N/2 values, or pairs of values, are output, depending upon the option code.
Normalization details:
Complex FFT result i, i = 1 .. N/2: ai*cos(wi*t) + bi*sin(wi*t).
wi = 2π(i-1)/T.
φi = atan2(bi,ai) (4 quadrant arctan)
2
2
Power(1) = (a1
+ b1
2
Power(i) = 2*( ai
+ bi
PSD(i) = Power(i) * T = Power(i) * N * tau
2
2
A1 = sqrt(a1
+ b1
)/N (DC)
2
2
Ai = 2*sqrt(ai
+ bi
)/N (AC)
Notes:
•
Power is independent of the sampling rate (1/tau) and of the number of samples (N).
•
The PSD is proportional to the length of the sampling period (T=N*tau), since
the "width" of each bin is 1/T.
•
The sum of the AC bins (excluding DC) of the Power Spectrum is the Variance
(AC Power) of the time series.
•
The factor of 2 in the Power(i) calculation is due to the power series being
mirrored about the Niquist frequency N/(2*T); only half the power is
represented in the FFT bins below N/2, with the exception of DC. Hence, DC
does not have the factor of 2.
•
The Inverse FFT option assumes that the data array input is the transform of a
real time series. Filtering is performed by taking an FFT on a data set, zeroing
certain frequency bins, and then taking the Inverse FFT. Interpolation is
performed by taking an FFT, zero padding the result, and then taking the
Inverse FFT of the larger array. The resolution in the time domain is increased
by the ratio of the size of the padded FFT to the size of the unpadded FFT. This
can be used to increase the resolution of a maximum or minimum, as long as
aliasing is avoided.
Cette instruction donne comme résultat la partie fractionnelle du nombre.
Syntaxe
x = Frac (source)
Remarques
Cette instruction donne comme résultat la partie fractionnelle du nombre qui est
entre les parenthèses.
Cette instruction reçoit un enregistrement provenant d'une table de données.
Syntaxe
GetRecord (Dest, TableName, RecsBack)
Remarques
L'instruction « GetRecord » récupère un enregistrement contenu dans une table de
données. La ligne de données dans laquelle est placé le résultat de l'instruction, doit
être suffisamment grand pour contenir tous les champs de l'enregistrement.
Chapitre 8. Instructions mathématiques de calculs
2
)/N
(DC)
2
2
)/N
(i = 2..N/2, AC)
8-13
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