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I have an assignment:

You wish to generate a pure 1000 Hz tone digitally using a computer. How would you choose a sample rate that assures that you could generate the tone and use the same sample rate to generate a 20 kHz tone? Specify the corner frequency and slope of the filter would you need to assure that the tone is as close to perfectly pure as possible?

My current thought is to sample at 10 kHz because that is well above the Nyquist rate for the 1000 Hz tone and then the first harmonic would be at 20 kHz. I assume I would then need a steeply sloping Chebyshev filter that cuts off just above 20 kHz? Am I on the right track?

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  • $\begingroup$ This a poorly formulated assignment. You can't make a perfect sine wave so it should specify "how good" it needs to be. Otherwise, more is always better. $\endgroup$
    – Hilmar
    Commented Dec 9, 2018 at 3:13
  • $\begingroup$ $F_s = 2.375 \mathrm{Hz}$ because you can either filter for 1kHz or 20kHz without changing your source tone. And if that's not an acceptable answer -- try a more well-formed homework question. $\endgroup$
    – TimWescott
    Commented Dec 28, 2020 at 2:55

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The question states

… generate … digitally … same sample rate to generate a 20 kHz tone.

So, you want to digitally create a 20 kHz tone, too. You hence need to have a sample rate that is sufficient for 20 kHz.

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  • $\begingroup$ So 40kHz sampling rate at minimum? Any thoughts on a cutoff frequency? $\endgroup$
    – Andrea G
    Commented Dec 9, 2018 at 0:53
  • $\begingroup$ Re: cutoff frequency: Where's the first spectral image that you need to suppress? Where's the last frequency you need to let through? Can't tell you the slope without you telling us what attenuation you need, and also, with the data given, the job you need to fulfill is just doing a single division, so I think we can leave that up to your expertise! $\endgroup$
    – Marcus Müller
    Commented Dec 9, 2018 at 11:25

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