# Matched Filters for attenuation detection?

I have been reading about matched filters and I'm interested in possible uses for them,

I have seen they are used very often in radar, in such a way that you send out a signal, and then you read the incoming signals to look for the reflection of the pulse you sent out using matched filters.

I think I'm right in saying that by the time difference from when you sent out the signal to when you found it again, you can detect how far the object is from you.

What I am interested to know is, can you detect the attenuation of the signal from matched filters and not just the time delay?

Hence giving you some information on the material properties of the reflecting object

Your interpretation of the matched filter for radar seems almost right, just to be sure, let me reiterate a bit: Think of it this way: we're sending a pulse function $$p(t)$$. If a target in distance $$d$$ reflects the signal, we receive $$\gamma \cdot p(t-\tau)$$, where $$\tau = 2d/c$$ is the total travelled delay.

The problem is: how to sample such a signal? Let's say your pulse was rectangular, you would need a lot more samples than the pulse width to know its extent and therefore, the proper delay. This is where the matched filter helps.

Applying matched filtering to your received signal, you filter it with $$p(-t)$$. This gives a signal comprised of the autocorrelation function $$\varphi_p(t) = p(t) * p(-t)$$, i.e., we obtain $$\gamma \cdot \varphi_p(t-\tau)$$, more or less. Now, the ACF always has its maximum at $$t=0$$, which greatly helps for the sampling. Also sampling the ACF at zero gives the optimal SNR: you gather the whole energy of the pulse into the sampling point. It's also called pulse compression for this reason.

Now, back to your question: You can extract both from the received signal, the delay $$\tau$$ and the reflection coefficient $$\gamma$$. In fact, this is often done. People call it RCS (radar cross section). Note that it is not so easy to infer material properties from $$\gamma$$ as $$\gamma$$ is typically highly direction dependent: the geometry of the object has a lot of effect on how strong the reflected wave is.

• Thanks, can I quickly clarify a couple of things, where you say "ACF always has a maximum at $t=0$", Is this referring to the point where the two signals overlap? i.e. $t=\tau$ for the reflecting signal, and how would this help to sample? Commented Sep 6, 2019 at 13:54
• No this has nothing to do with overlapping signals. The autocorrelation function $\varphi(\tau)$ always satisfies $|\varphi(\tau)|\leq\varphi(0)$. It's a direct consequence of Schwartz's inequality. It helps because this peak defines the optimal sampling point. Commented Sep 6, 2019 at 18:15
• "typically highly direction dependent: the geometry of the object has a lot of effect on how strong the reflected wave is." - I totally agree with this statement! Commented Oct 18, 2019 at 6:43

There are a lot of different kinds of radar that use matched filters including radars that employ multiple matched filters .

The signal characteristic besides time delay that is often important is doppler shift.

Estimating the character of the propagation path(s) can also be of interest. Attenuation(s) would fall into that category.