# Channel impulse response in freqency domain

I have a doubt about DFT matrix and channel impulse response.

Let $$h$$ is a channel impulse response , $$F$$ is a DFT matrix. IF I take a product. I got: $$F* h=\tilde{h}$$

$$\tilde{h}$$ is a frequency response of the channel, isn't? or channel impulse response in frequnce domain

• If $h$ in time-domain, taking Fourier Transform will give its frequency response. – jomegaA Feb 24 at 13:52
• $\tilde{h}$ is the frequency response of the channel. How could frequency response of the channel and channel impulse response in frequency domain be different? ;-) – jomegaA Feb 24 at 22:25
• @jomegaA I have read a research paper where h was called as channel impulse response and product DFT matrix with h as channel coefficient in freq domain. " coefficient in freq domain" made me a question – Jang Lee Feb 25 at 9:11
• ...perhaps the channel impulse response and channel coefficients mean the same. Yes, the product of DFT matrix and in your case $F$ with $h$ is channel impulse response in frequency domain. – jomegaA Feb 25 at 9:17
• As in the answer given by Engineer you may understand what is the product of dftmtx and h is. Or you can take fft(h) which is also the channel impulse response in frequency domain. – jomegaA Feb 25 at 9:21

h = randn(100, 1);     % make some random impulse response

• Want to put an additional info here, F*h is actually the Fourier transform of h (frequency response). $\\$ From matlab documentation, "A discrete Fourier transform matrix is a complex matrix whose matrix product with a vector computes the discrete Fourier transform of the vector. dftmtx takes the FFT of the identity matrix to generate the transform matrix." – jomegaA Feb 24 at 14:01
• Nevertheless the faster approach could be fft(h) – jomegaA Feb 24 at 14:12
• If $\mathbf{h}$ is instead a channel matrix $\mathbf{H}$, you can still do $\mathbf{F}\mathbf{H}=\tilde{\mathbf{H}}$ to get the DFT of $\mathbf{H}$. You just need to make sure that the number of rows in $\mathbf{H}$ is the same as the $\mathbf{F}$ – Engineer Feb 25 at 14:55