iggyboy
Joined: 16 Feb 2007
Posts: 50
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 17 Jun 2007 14:08 Find the frequency spectrum before and after sampling |
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I do not seem to understand how sampling affects the frequency spectrum. Help me find the frequency spectrum before and after sampling. How to do it in Matlab?
I am interested in frequencies from 0~integer*sampling frequency. I want to see how different frequency components are copied troughout the frequency spectrum after sampling.
Added after 1 hours 15 minutes:
I wrote some little ugly code that seems to do "something". First let me explain how do I understand the problem of frequency "replicas" after sampling.
Assume:
Fsampling=1kHz
Fsignal= 400Hz
This is the frequency content before sampling. I start sampling at time 0 and sample one period. Sample points are:
time = [0 1ms 2ms]
value of sampled signal = [0 0.58778525229247 -0.95105651629515]
We are now in the DSP domain. We have three points of data and those points have the information about the frequency, amplitude etc of the signal we sampled. Let us consider the frequency.
What frequency "fits" our data in terms of amplitude = [0 0.58778525229247 -0.95105651629515] at sample times = [0 1ms 2ms]?
Answers:
Obviously 400Hz. And many many, many many more. What fits our data are also:
1400
2400
3400
4400
...
and if we shift the phase to these signals to 180 degree they "fit" too:
4600
3600
2600
1600
600
...
And this is where the confusion begins for me. Troughout the books (more like articles) I read, there was a claim, that the frequency content duplicates around the Fsampling/2. But my "analysis" does not say so. For example a "normal" 600Hz signal does not fit the sampled data, but a 180 degrees shifted 600Hz signal does. So. Can anyone explain this?
Let me emphasise that I am trying to figure out how frequency components are moved around (replicated somewhere else) after sampling.
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