Frequency Offset Homework: 0.1s & 0.01s Time Vectors

  • Thread starter Thread starter mzjz
  • Start date Start date
  • Tags Tags
    Frequency
AI Thread Summary
The discussion centers on analyzing the frequency of the signal s=cos(12*pi*t) using two different time vectors with increments of 0.1s and 0.01s. The frequency calculated from the 0.1s increments is 1Hz, while the 0.01s increments yield a frequency of 10Hz. This change in perceived frequency is attributed to the sampling rate; smaller increments provide a more accurate representation of the continuous function. The Nyquist theorem is mentioned as a relevant concept, highlighting the importance of sampling frequency in accurately capturing signal characteristics. Understanding these principles is crucial in the context of signals and systems coursework.
mzjz
Messages
4
Reaction score
0

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!
 
Physics news on Phys.org
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 theorm then and what happens when you sample a 12Hz signal at 10Hz vs 100Hz
 

Similar threads

What Frequencies Emerge in an AM Signal with Given Parameters?
Replies
4
Views
2K
Analyzing a frequency-mixer circuit in LTSpice
Replies
6
Views
3K
Why does a series of pulses generate a pitch?
Replies
27
Views
4K
Finding the bandwidth of a parallel RLC circuit (+MATLAB)
Replies
1
Views
2K
How do you calculate cross and auto-correlation in time and frequency domains?
Replies
4
Views
2K
PLL - How to find all the gains of a PI corrector and fix Ki ? MATLAB
Replies
2
Views
750
MATLAB Plots and FFT of Rows or Columns of Data
Replies
8
Views
2K
I Two-Mass Oscillator: Plotting Amplitudes Over Frequency in Hertz
Replies
10
Views
2K
Light absorption by a three level atom
Replies
3
Views
2K
How to Determine Various Waveform Parameters from a Graph?
Replies
3
Views
3K

Hot Threads

Recent Insights

Back
Top