# AMPSPEC

## Purpose:

Calculates the N point complex amplitude spectrum.

## Syntax:

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:

 "single" : single sided display (default) "double" : double sided display "shift" : double sided display shifted about 0 Hz

## Returns:

A complex series or array, the N point normalized complex spectrum of the input.

## Example:

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.

## Example:

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.

## Remarks:

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.