How can a DCT help identify the obvious frequency of a discrete wave?

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SUMMARY

The discussion centers on the application of the Discrete Cosine Transform (DCT) for identifying the dominant frequency of discrete waveforms, specifically cosine and triangle waves. It is established that a DCT applied to a perfect cosine wave yields a single non-zero coefficient, while a triangle wave produces multiple coefficients. The conversation highlights that filtering the DCT coefficients of a cosine wave retains their integrity, while applying the same filter to a second cosine wave with a different phase results in the loss of coefficients. A recommendation is made to utilize a full Fourier Transform for a more comprehensive analysis of frequency components.

PREREQUISITES
  • Understanding of Discrete Cosine Transform (DCT)
  • Knowledge of Fourier Transform principles
  • Familiarity with waveforms, specifically cosine and triangle waves
  • Basic signal processing concepts
NEXT STEPS
  • Study the properties and applications of the Discrete Cosine Transform (DCT)
  • Learn about the Full Fourier Transform and its advantages over DCT
  • Investigate filtering techniques for frequency analysis in signal processing
  • Explore methods for extracting dominant frequencies from complex waveforms
USEFUL FOR

Signal processing engineers, data analysts, and anyone involved in waveform analysis and frequency identification will benefit from this discussion.

yetar
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Hello,

Suppose I have a discrete function of a perfect cosine wave.
So if I will do a DCT on this function I will get one non zero coefficient which corresponds to the perfect cosine wave, and the rest will be zero.
Now I have a pass filter, which filters out anything with a frequency which is different from the original cosine wave.
If I will do this filter on the DCT I did to the cosine wave, then no coefficient should change.
Now, suppose I have a second function which is also a perfect cosine wave of the same frequency as the cosine wave in the first function, but with a different phase.
So the DCT of the second function will give me many non zero coefficients.
If will pass the same filter I did on the first function DCT, then I will loose many coefficient and the result will be some wave which is weaker then the second function original cosine wave.
Is that true?

Basicaly I am trying to find the "obvious" frequency of a discrete wave.
Lets say I have a pure triangle wave. Doing DCT on it will produce a lot of coefficients of different frequencies, but how do I discover the obvious frequency of the triangle wave from these coefficients?

Thanks in advance.
 
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The problem is that you are confining yourself to a DCT. Do a full Fourier Transform instead.
 

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