Nyquist sampling rate and signal anti-aliasing

[Gedelian]

Hi all!

Quick question. If a Nyquist sampling rate in a signal is 2f, what lower frequencies can be represented without aliasing? I assume you could have frequencies which have only even number of samples in their wave length, or maybe in half of their wave length. Am I wrong? If someone can post an answer, it would be greatly appreciated.

Cheers!

 

[sophiecentaur]

All signals with frequencies below half the sampling rate can be reconstructed perfectly.
That's the theory. In practice, you need a real filter before the sampling circuit, to cut out frequencies above half sampling rate and it will have a finite cut-off rate around this limit. But I don't think this is your point.
I suspect that you are concerned with the situation where the samples are at regular points in the waveform - thus 'missing the peaks', perhaps. This doesn't matter because there is quite enough information to rebuild the signal perfectly. Correct low pass filtering after the crude DAC will produce the peaks and troughs (overshoots) in the output signal, despite the apparent fact that the (box-car, perhaps) samples don't explicitly 'contain' them.

 

[Gedelian]

Thanks for the quick reply.

The frequencies I was asking about are 'pure', in the sense that I want to choose them to build a signal using inverse FFT. So it's not a 'dirty' real life signal which needs filters. As I understand correctly, if you have the highest frequency of, say, 100Hz, and Nyquist rate is 200, then all frequencies below 100Hz can be perfectly reproduced whitout aliases, right?

 

[sophiecentaur]

Right. Produce the right samples and the filter will do the rest - whatever phase of signal you require. What signal do you require? Are you defining it in the time domain or the frequency domain?

 

[Gedelian]

The definition comes from the frequency domain. I want to create a series of signals with the same frequencies but different amplitudes. For example, every signal has the same set of frequencies, from 1 to 100Hz, but every frequency in a given signal has a different amplitude, and the pattern of amplitudes in one signal never repeats itself in any other signal. I'm not certain what is going on with phases here, so, I guess I just wanted to know in principle what is and what isn't possible.

 

[truva]

The phases won't change.

Secondly, I am not sure but since you change the amplitudes, you may consider spectral leakage.

 

[the_emi_guy]

I want to create a series of signals with the same frequencies but different amplitudes. For example, every signal has the same set of frequencies, from 1 to 100Hz, but every frequency in a given signal has a different amplitude, and the pattern of amplitudes in one signal never repeats itself in any other signal.

Not sure I'm clear on what you mean by a "series of signals". Do you have multiple signals that are each steady state or are you trying to modulate the amplitudes of the 100 tones? If you are modulating then you have potential aliasing issues.

 

[sophiecentaur]

I am sensing another question in this, which we haven't picked up on. When you sample a signal, it can take any form as long as it has no components over Fn/2 and, of course, its amplitude mustn't exceed the range of the ADC. What happens after that is 'numbers', whatever your signal consists of. The same applies when you generate a signal; if you choose to synthesise it 'in the frequency domain' or in the the time domain, the signal is still the same and the samples would be indistinguishable. There is nothing significant about components which lie on sub harmonics of the sample frequency. (Filtering is always included after the samples are converted to analogue values because you don't want loads of high frequency stuff which could overload any following analogue circuits)

 

[Gedelian]

Hey all, sorry for the late post, I abandoned the whole idea with the signal series. The idea was to encode information in separate signals using amplitudes without modulation, because I needed frequencies for something else. I just wanted to know what are the limitations of that approach. Thanks anyway.