Sampling Rates & Fourier Transforms: Investigating a Spike

[cscott]

Homework Statement

Say I have a spike at some frequency from a Fourier transform (power spectrum) of a waveform that I'm sampling (sine wave at 10Hz in this case). If I decrease the sample rate what should happen to the appearance of the spike? What about increasing the sample rate? What about the appearance of the original waveform vs time

The Attempt at a Solution

I would have thought with a lower sample rate the sine wave would widen? Not sure about the FT plot.

I have written down from the lab that the spike widens (from the FT plot) with higher sampling rate and thins out for lower simpling rate.

Any ideas?

 

[Jhero]

Thank you for your question. The appearance of the spike in the power spectrum will depend on the Nyquist frequency, which is half the sampling rate. If the frequency of the sine wave (10Hz) is below the Nyquist frequency, then the spike will still be present and will appear wider with a lower sample rate. This is because a lower sample rate means that fewer data points are being used to calculate the Fourier transform, resulting in a wider frequency bin for the spike.

On the other hand, if the frequency of the sine wave is above the Nyquist frequency, then aliasing will occur and the spike will not be present in the power spectrum. Instead, it will show up at a different frequency, which can make it difficult to interpret the data accurately.

Increasing the sample rate will result in a narrower frequency bin for the spike in the power spectrum. This is because more data points are being used to calculate the Fourier transform, allowing for a more precise measurement of the frequency.

The appearance of the original waveform vs time will not change with different sample rates, as long as the Nyquist frequency is not exceeded. However, if the Nyquist frequency is exceeded, then the waveform will appear distorted due to aliasing.

I hope this helps to clarify the relationship between sample rate, power spectrum, and the original waveform. Please let me know if you have any further questions.



Scientist