Choosing a Sampling Rate and a Cutoff frequency 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?
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.