Frequency Offset Homework: 0.1s & 0.01s Time Vectors

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Discussion Overview

The discussion revolves around a homework problem involving the signal s=cos(12*pi*t) and its representation over two different time vectors with increments of 0.1s and 0.01s. Participants explore how these different sampling increments affect the perceived frequency of the signal and the underlying concepts related to sampling and frequency offset.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant calculates the frequency for the 0.1s increments as 1Hz and for the 0.01s increments as 10Hz, suggesting that the change in increments affects the frequency observed in the plots.
  • Another participant references the Nyquist theorem, indicating that changing the time increments alters the sampling of the original function.
  • A participant explains that smaller sampling increments lead to a more continuous representation of the signal, which allows for a more accurate depiction of its frequency.
  • There is a suggestion to discuss the implications of sampling a 12Hz signal at different rates, such as 10Hz versus 100Hz, in relation to the Nyquist theorem.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the impact of sampling increments on frequency perception. Some agree on the importance of the Nyquist theorem, while others focus on the implications of discrete versus continuous sampling. The discussion remains unresolved regarding the completeness of the explanation needed for the homework assignment.

Contextual Notes

Participants mention the need for clarity on the relationship between sampling rates and frequency perception, but do not reach a consensus on the sufficiency of the explanations provided.

Who May Find This Useful

Students studying signals and systems, particularly those interested in the effects of sampling on signal representation and frequency analysis.

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Homework Statement



The signal is s=cos(12*pi*t) and the time vector is 0 to 10s. One vector has increments of 0.1s and the other is 0.01s. What is the plotted frequency from these time scales? And why does it change by changing the increments?


Homework Equations



f=1/T

The Attempt at a Solution



So we're supposed to find the frequencies from the plot of the graphs. For the 0.1s increments, the frequency seems to be 1Hz (T≈1 ∴ f=1/1). And for the 0.01s increments, the frequency seems to be 10Hz (T≈0.1 ∴ f=1/0.1). She wants us to explain this and I don't get it.

Although, I think it has to do with frequency offset. Explain please?

Hope you can help.
Thanks!
 
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Take a look at the nyquist theorem. That should point you in the right direction :)

*edit* thinking about my statement it might not be immediately clear. By changing t from a continuous function to one that uses increments (of either 0.1s or 0.001s) you are essentially sampling the original function.
 
Last edited:
Actually I think I've figured it out.
In MATLAB, you are technically in discrete time since you are sampling times. Yes, the smaller the sampling rate, the more continuous it becomes, and this is exactly what's going on here.
cos(12*pi*t) is such a compressed sinusoid that an increment of 0.1 will only get specific points that does not make it look as compressed as it actually is. But when you take increments of 0.01, it covers way more points, which allows it to look closer to its original function. This is why the frequency looks like it has increased when you give it increments of 0.01.
 
What course is this for?
Your explanation might be sufficient depending on the course, or might need a bit more :)
 
Signals and systems. It seems like a sufficient answer to me but let me know if there's more to it!
 
Btw I meant smaller sampling increments and higher sampling rate lol
 
You should talk about the Nyquist theorem then and what happens when you sample a 12Hz signal at 10Hz vs 100Hz
 

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