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I am hoping to clear up some confusion I have. In a lab I am taking, we analyzed the amplitude response of a simple system. We found that as we increased the input signal frequency to greater than half the sampling frequency, the output signal began to flat line. The picture below show the corresponding Amplitude Response.

Amplitude Response for a system with a sampling rate of 16kHz

I am aware of the Nyquist theorem, and I thought that the reason the output signal flatlined at frequencies greater than 8 kHz was because the sampling frequency was 16 kHz.

But during a second experiment of generating a sine wave, I discovered the concept of folding about the Nyquist frequency. Now in this case, increasing the generated signal frequency to greater than the Nyquist frequency caused the output signal to not decrease in amplitude, but to become symmetric about the Nyquist frequency.

E.g.

Generating a sine wave of 14 kHz produced an output of a sine wave of 2 kHz.

How are these two concepts related? It seems in the first example, going above the Nyquist frequency caused the output signal to flatline. In the other case, generating a signal above the Nyquist frequency didnt cause the output to flatline, but caused the output signal to only have a different output frequency.

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  • $\begingroup$ You are talking only about the output sample frequency and not the input sample frequency? $\endgroup$
    – fibonatic
    Feb 23, 2019 at 13:31

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This is a phenomenon called aliasing

https://en.wikipedia.org/wiki/Aliasing

Usually, there are anti-aliasing filters that will filter out signals with frequencies higher than fs/2.

However, in your case I think there isno anti-aliasing filter. Hence your 14 kHz-signal aliases to 2 kHz. Since f > fs/2, then apparent frequency = 16 kHz - 14 kHz = 2 kHz

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  • $\begingroup$ But then shouldn't the amplitude response be the same for frequencies greater than the nyquist frequency? Im curious why the amplitude response would decay at the nyquist frequency if the output signal would have the same amplitude but just a different frequency. Thank you! $\endgroup$
    – DarkLink
    Feb 22, 2019 at 4:10
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    $\begingroup$ If you have no anti-aliasing filter then yes the amplitude should stay the same if aliased. However, there are no perfect ADCs, they have parasitics capacitances that will act as crappy anti-aliasing filter which might lead to a decrease in amplitude. But there are many different kinds of ADCs, it's really hard to make a general statement. Furthermore, your test setup can also act as anti-aliasing filter, your coaxial cable, signal generator, connectors are not perfect either and can filter to a degree. $\endgroup$
    – Ben
    Feb 22, 2019 at 4:24

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