Signals 1 Lab Practice Exercises

[Patricija B]

Hi! I was just going over the practice exercises from signals 1 lab from this week, and I had a question regarding the very last answer to question 4. Maybe I’m missing something very obvious, but why is it 8000-640 and not just 8000 Hz for the magnitude spike? Thanks!

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[Catherine Lai]

Hi Patricjia,

When you sample a sine wave that’s higher than the Nyquist frequency (i.e., half the sampling rate = 8000 Hz in the question) you still “record” a sine want it’s just that it’s not going to be the one that was your actual input. When you’re just a bit above the Nyquist frequency the inaccuracy in sampling the underlying input doesn’t cause too much difference. But it has a bigger and bigger impact the higher the frequency gets (past the Nyquist Frequency).

In fact, frequencies are mirrored around the Nyquist frequency. So, with a 16000 Hz sampling rate, a sine wave with frequency 8640 Hz = 8000 + 640 Hz looks like 8000 – 640 = 7360 Hz due to aliasing.

You can see a (different) example of this in the lab materials when we plot the sound sweep with naive downsampling from 22050 Hz to 8000 Hz sampling rate (in the “Sampling and Aliasing” section). The sound generated changes from a continuously rising frequency, to one that goes up to 4000 Hz and then starts going down. The spectrogram shows this with a turning point at 4000 Hz in the attached image. You can use the code blocks in the notebook just below that figure to see what’s happening in sampling terms.

cheers,
Catherine

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[Patricija B]

Ahh I see, that makes sense. Thank you so much!

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