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How can I keep a percentage r of the low frequencies of a Nx1 signal x using the Discrete Cosine Transform of it? Is it simply zeroing all but the first rN elements of DCT(x)?

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  • $\begingroup$ Pls share your frustrations with more details $\endgroup$ – Sunnyskyguy EE75 Jan 28 at 22:17
  • $\begingroup$ Say I have a 16000x1 audio signal and I get it's 16000x1 DCT. How can I enforce a signal at the range of frequencies 0-4kHz working in the frequency domain? Is it just allowing non-zero values to the first 4000 elements of the DCT? $\endgroup$ – Dionysis M Jan 29 at 12:15
  • $\begingroup$ no that is not how it works , keep reading $\endgroup$ – Sunnyskyguy EE75 Jan 29 at 14:28
  • $\begingroup$ could you please point me to a good reference for this? $\endgroup$ – Dionysis M Jan 29 at 15:14
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What I've understood is that k-th DCT-II component is expressed in a basis of cosine functions with frequency $k\pi/(2N)$ rads, where $N$ is the number of samples of the signal. Thus k-th coefficient of such a signal has frequency of $k/(2N)$ in Hz. It seems to me that my understanding is wrong because this constains highest frequency to $(N-1)/(2N)$.

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