# Autocorrelation of two dirac pulses

I am given a channel impulse response:

$$h(t) = 0.8 \times \delta(t) + 0.6 \times \delta(t - T)$$

where $\delta(t)$ is the dirac function.

For signal equalization a MMSE equalizer with 5 coefficients and SNR = 12 dB will be used.

Well for this case, I am trying to set up the autocorrelation matrix. The impulse response consists of two diracs.

I have troubles computing the autocorrelation. When I remember correctly, to do that, I can simply shift the diracs to the right and then let them move to the left to the original diracs and then calculate the overlap. That would give me, again, two diracs at $t=0$ and $t=T$, but scaled: $(0.8 \times 0.8 + 0.6 \times 0.86) \times \delta(t) + (0.8 \times 0.6 + 0.6 \times 0.6 ) \times \delta(t-T)$

Am I correct?

• I guess this is the discrete Dirac. – Laurent Duval Oct 23 '17 at 12:35
• As Laurent says, you usually design your equalizer in discrete time. So, if the channel input is $[1]$, the output is $[0.8, 0.6]$, and that is what you need to equalize. – MBaz Oct 23 '17 at 13:33