Re: fourier anlysis of square wave...

Ron N. wrote:
On Nov 29, 6:31 pm, Jerry Avins <j...@xxxxxxxx> wrote:
Scott Seidman wrote:
"Fred Marshall" <fmarshallx@xxxxxxxxxxxxxxxxxxxx> wrote in
news:NqKdnQQu6dSz3NLanZ2dnUVZ_o6knZ2d@xxxxxxxxxxxxxx:
Now, it is true that the samples in (2) might represent a perfectly
bandlimited signal.
I'm still not getting it
Let's try this...
I(n)=1 0 0 0 0 0 0 0 0 0......
The FFT of that has zip to do with aliasing.
same for I(n-1), and thus I(n)+I(n-1)
But for some reason, the FFT of
1 1 0 0 1 1 0 0 1 1 0 0 ......
has something to do with aliasing, simply because you can get to the same
signal from a clipped sine wave?
Once you're in the digital domain, you can create any signal you want, and
aliasing doesn't enter the picture. The A to D is where aliasing comes in.
No A to D, no aliasing--- or, are we just defining the results of a
circular convolution in the frequency domain to be aliased by definition??
Let's stick to the original question instead of becoming language
lawyers. Of course every set of samples that has a Fourier transform
that doesn't blow up represents a bandlimited function and only a
bandlimited function, but a set of alternating equal-length groups of
positive and negative samples does not represent a sampled bandlimited
square wave. I think it's pretty clear that Suren thought it did, FFTed
one, and was confused by what he saw. You reject my explanation of what
he saw. What do you offer in its place?

I suggest a simple experiment, take a vector and fill
it with square waves (-1,1 at a 50% duty cycle) with a
wavelength or repeat cycle exactly periodic in the vector
length, and perform an fft on that vector. I just tried
this with 64 cycles of square waves inside a vector of
length 1024 and only saw odd multiples of 16 bins in the
fft magnitude results. The aliasing showed up by altering
the magnitude of the existing high frequency odd multiples
of the fundamental, not by adding any new non-harmonic
frequencies (as per the OP's observation).

The easiest way to get "bin splatter" was to change the
square wave frequency so that it was no longer periodic
in the fft aperture. Another way was to change the
periodic 1,-1 waveform so that it no longer had a 50%
duty cycle.

Was that really 1, -1, 1, -1 .... or with longer blocks? 1, -1, 1, -1 ..... represents a square wave sampled at two samples per period, or f = fs/2. The first harmonic is at 3fs/2; it must alias. The next harmonic is at 5fs/2; it also aliases. When the number of cycles is an integer, all these aliases lie atop one another and appear harmonic. Don't be fooled. That's an artifact of the test conditions.

Jerry
--
Engineering is the art of making what you want from things you can get.
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.

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