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Anti aliasing??? and modulation

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andy257

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Hi Guys

I had a lab lesson at uni the other week and it was structured to help us understand data communication.

We were using a sig gen as an input and then a piece of kit designed for education to sample the input, encode it and send it to a reciever which decodes it and reconstructs the signal on the scope again.

However what we found was that modulation appeared when we started to increase the frequency past a certain point.

What i didnt understand was why the modulation appeared. What i understand about modulation there must be two signals mixed together to for a modulated signal, up the frequency spectrum. However we were only using one frequency at the input (from the sig gen) and one internal clock frequency on the piece of kit to sample the input and encode it for transmission(but they were not connected or mixed)

where does the modulation come from?

We were told this is why it is very important to use anti aliasing filters to prevent this but i didnt understand where the modulation came from.

andy

sorry for the long post its going to be a couple of weeks until i can get back to uni to ask my lecturer so i though some of you guys could help me out.
 
I presume what you're talking about is digital sampling of an analogue signal?, as you've found out it's crucial to sample a fair bit faster than the maximum frequency in your analogue signal. To this end it's normal to have a low-pass filter before you're sampling.

It's quite easy to show why this is, all you need is a piece of graph paper.

OK - assuming you have a piece of graph paper 10 squares wide, draw a single sinewave across the entire 10 squares. Now read the value off of the vertical axis where the sinewave crosses each square - this will give you 10 vertical points. Now plot those points on another piece of graph paper, and join the points together with a line - it should give you an approximation of the original sinewave. Bear in mind, if doing this electronically, you would have another low-pass filter after you convert back from digital to analogue - this will tidy the sinewave somewhat.

Now do the same thing again - but instead of drawing one sine across the paper, draw more - try ten for a nice simple example. Take the readings and plot them again - and see what you get then!.

Then try different numbers of sinewaves, and see where it becomes totally unuseable!.

As a matter of interest, CD audio is sampled at 44.1KHz and has a maximum frequency of 20KHz - so that's sampling at only 2.2 times the maxmimum input - which is about as low as you can get away with.
 
To expand a bit on what Nigel just said.

When sampling a waveform, you must sample it at a rate at least twice the highest frequency if the waveform, otherwise you will get "aliases", a kind if image frequency which will show up in your recovered waveform as "modulation".

To prevent this, taking Nigels example, there will be a filter which removes the audio frequencies above 20 kHz. This is an "anti alias" filter.

The maximum frequency which can be successfully sampled and reconsituted is half the sampling frequency, in Nigels example 22.05 kHz (44.1 divided by 2), this is known as the Nyquist frequency.

JimB
 
Thank you for the replies but its still troubling me

Its the modulation bit that i cant understand. Where do the other frequencies come from? There is only 1 sine wave with 1 amplitude and one frequency (INPUT). Then if we increase the frequency we begin at some point to see amplitude modulation. How does this happen? We are only reconstructing the samples we are taking of the original. There are no other frequencies?????

andy
 
This sort of "modulation" happens when your sample rate is almost exactly twice the signal frequency - very close to the Nyquist frequency. If you are sampling at exacly twice the signal frequency you get two samples per cycle. These two samples can be at the peaks, at the zero crossings, or anywhere in between. If the frequencies are exact where the samples are will not change- and you'll get DC or a attenuated wave depending on the location of the samples. If your sample frequency is slightly off, the place on the waveform the samples fall will shift. The output wave will shift between having the samples near the peaks and having the samples near the zero crossings which will look like AM modulation.
 
andy257 said:
Thank you for the replies but its still troubling me

Its the modulation bit that i cant understand. Where do the other frequencies come from? There is only 1 sine wave with 1 amplitude and one frequency (INPUT). Then if we increase the frequency we begin at some point to see amplitude modulation. How does this happen? We are only reconstructing the samples we are taking of the original. There are no other frequencies?????

If you do the graph paper experiment I suggested, you will find out!.
 
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