DADiSP Online Help
Click here to see this page in full context
DADiSP Worksheet Functions > Function Categories > Fourier Transforms and Signal Processing > AMPSPEC
Calculates the N point complex amplitude spectrum.
AMPSPEC(series, N, "type")
|
series |
- |
A series, the time domain data. |
|||||||||
|
N |
- |
Optional. An integer, the number of frequency domain samples to compute. |
|||||||||
|
"type" |
- |
Optional. A string, the output type:
|
A complex series or array, the N point normalized complex spectrum of the input.
W1: gcos(1000, 1/1000, 100)
W2: ampspec(w1)
W3: ampspec(w1, "double")
W4: ampspec(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: ampspec(w1, "shift")
W3: {mean(mag(w1)^2)}
W4: {sum(mag(w2)^2)}
W3 == W4 == 0.5 verifying a form of Paresval's Theorem.
AMPSPEC computes 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:
ampspec(s) = 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, AMPSPEC 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(mag(ampspec(s)^2)
See MAGSPEC to display the magnitude 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.