# How to keep low frequencies in DCT

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)?

• Pls share your frustrations with more details Jan 28 '19 at 22:17
• 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? Jan 29 '19 at 12:15
• no that is not how it works , keep reading Jan 29 '19 at 14:28
• could you please point me to a good reference for this? Jan 29 '19 at 15:14

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 $$(N-1)/(2N)$$.