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Loading LOADSUB ALL FROM "FFT.HTS"
or LOADSUB Power_spectrum FROM "MATHLIB.HTS"
or LOADSUB FROM "MATHLIB.HTS"
Usage INTEGER Logn
REAL A(*),B(*)
CALL Power_spectrum(Logn,A(*),B(*))
Description
Power_spectrum calculates the power spectral density of the data in the array A and returns the information in the array B. Logn is the base-2 logarithm of the number of points in the sequence to be correlated. The array A must have at least 2Logn elements; if it has more than this number of elements, the extra elements are ignored. The array B must have at least 2Logn+1 elements; if it has more than this number of elements, the extra elements are unmodified. The number of elements in A denoted by each permitted value of Logn is shown in the table below:
Logn No. Elements (2Logn)
2 4
3 8
4 16
5 32
6 64
7 128
8 256
9 512
10 1024
11 2048
12 4096
13 8192
14 16384
If N = 2Logn, after Power_spectrum has run, the first N/2 elements in the array B contain the power spectral density of A. The second N/2 elements in B contain zeros.
If the values in A are taken to be values of a continuous complex signal, a(t), sampled at constant intervals of T (time, distance, or whatever units apply), and if the signal sampled contained no terms at or above the frequency 1/2T, then the first N/2 elements in the array B are proportional to the power at the frequencies k/2NT, where k is the position in B, beginning with k = 0.
The power spectral density of a set of data is the Fourier transform of the autocorrelation of that set of data.
Errors
Power_spectrum causes an HTBasic error if its arguments are not of the types shown in the USAGE section, above, if Logn is not between 2 and 15, inclusive, or if the size of A or B is smaller than the values described above.
See Also
Autocorrelate, Power_spectrum
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