Calculates the magnitude of the N point complex amplitude spectrum.
MAGSPEC(series, N, "type")
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series |
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A series, the time domain data. |
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N |
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Optional. An integer, the number of frequency domain samples to compute. |
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"type" |
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Optional. A string, the output type:
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A real series or array, the magnitude of the N point normalized complex spectrum of the input.
W1: gcos(1000, 1/1000, 100)
W2: magspec(w1)
W3: magspec(w1, "double")
W4: magspec(w1, "shift")
W2 contains 500 complex values with a peak at 100 Hz. W3 contains 1000 values with peaks at 100 Hz and 900 Hz. W4 contains 1000 values with peaks at -100 Hz and +100 Hz. In all cases, the magnitude of the peak values is 0.5, 1/2 the amplitude of the input cosine.
W1: gsqr(1000, 1/1000, 4)
W2: magspec(w1, "shift")
W3: {mean(mag(w1)^2)}
W4: {sum(w2^2)}
W3 == W4 == 0.5 verifying a form of Paresval's Theorem.
MAGSPEC computes the magnitude of N equally spaced samples of the normalized complex amplitude spectrum by using the FFT. The raw FFT values are normalized by the length of the input series such that:
magspec(s) = mag(fft(s)) / length(s)
For a sampling rate Fs, the default single sided amplitude spectrum displays N/2 frequency values from 0 to Fs/2. The double sided amplitude spectrum, "double", displays N values from 0 to Fs and the shifted spectrum, "shift", displays N values from -Fs/2 to Fs/2.
Unlike SPECTRUM, MAGSPEC does not scale the values between 0 and Fs/2 by 2. Thus, the single sided amplitude spectrum of a 1 volt sinusoid of frequency F shows a peak of 0.5 at frequency F and the double sided shifted amplitude spectrum shows peaks of 0.5 located at -F and +F.
The "double" sided or "shift" amplitude spectrum obeys a form of Parseval's Theorem such that:
mean(mag(s)^2) == sum(magspec(s)^2)
See AMPSPEC to display the complex spectrum.
See PHASESPEC to display the phase spectrum.
See SPECTRUM to compute a normalized frequency spectrum such that a 1 volt sinusoid at frequency F displays a peak of 1 at frequency F.
See DADiSP/FFTXL to optimize the underlying FFT computation.