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On Wednesday 21 April 2010 23:02:19 Arnold Krille wrote:

quoted text
> Okay, the answers teach me that this is wrong. I didn't yet think about

>  this as in-depth as I should have before writing that.

I did some thinking...
Attached is a small python script that generates some sinus data at 0.5, 0.=

49=20

and 0.25 the sampling rate, phase shifted pi/2 to the sampling clock. But t=

he=20

phase shift can be adapted in the first lines.

Then it does fft on these. While the nyquist frequency shows up as amplitud=

e 0=20

(for phase =3D pi/2) and 2 (for phase 0), the others remain at amplitude 1 =

no=20

matter what the phase is.

Sounds strange, especially when you see the perceived amplitude-modulation =

for=20

f=3D0.49, but in the end its up to the analog filters to create a smaller t=

han=20

nyquist frequency sinus from the steps returned by the dac...
It is also clear, why f=3D0.5, phase=3D0 shows an amplitude of 2: All the=20

frequencies are endlessly mirrored to the left and right. And at f =3D=20

0.5*samplingrate, the mirror and the original are the same.
So sorry for the fuss I tried to spread. Should have done this little exerc=

ise=20

earlier.
Have fun,
Arnold
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#!/usr/bin/env python
import numpy

import matplotlib.pyplot as plt
n = 100

phase = numpy.pi/2.
data = []

for f in [0.5, 0.49, 0.25, 0.01]:

    tmp = []

    for i in range(n):

        tmp.append(numpy.cos(i * f * 2*numpy.pi + phase))

    data.append(tmp)
#plt.plot(data)
plt.subplot(221)

for d in data:

    plt.plot(d)
freqs = None
for d in data:

    if freqs is None:

        freqs = []

        for i in range(n/2 +1):

            freqs.append(i*1./n)
    tmp = numpy.fft.rfft(d)
    plt.subplot(212)

    plt.plot(freqs,abs(tmp)*2/n)

    plt.subplot(222)

    plt.plot(freqs,numpy.angle(tmp))
plt.show()
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