A Fourier analysis will probably not help too much in analyzing multipath since you'd be looking at the frequency domain instead of the time domain. Multipath is primarily a time domain problem.

You can actually get the same effects as multipath within the coax itself if you have dangling ends (unterminated) or impedance mismatches that create reflections inside the coax network.

In real-world multipath, the line-of-sight signal (even if severely attenuated by trees and buildings) is always the first to arrive at the antenna (shortest distance between two points). All multipath reflections arrive later than that since they travel a longer distance.

From the point of view of the receiver, it all looks like delayed copies of the same signal interfering with itself.

There is one aspect of multipath that is frequency dependent, and that is when it comes to frequency selective fading. If you happen to have two strong signal paths of nearly equal strength reaching your antenna and they happen to be 1/2 lambda out of phase, then the signals will cancel each other out to some degree. This kind of fading is very sensitive to the relative path lengths, so moving the antenna a few feet is often enough to get out of a fading situation.

To some degree, digital tuners are actually able to "undo" some of the damage caused by multipath. As it turns out, multipath is related to one of the problems faced by distributed transmitter (DTx) systems that some broadcasters have been experimenting with. Sorry for the long read, but a more in-depth discussion of this is available in this thread:

http://forum.tvfool.com/showthread.php?t=101
Also, just to get even more thought gears churning, multipath can even be

*useful* in some situations. In the world of WiFi, in particular 802.11n and MIMO technologies, multipath is actually a

**good** thing because they can take advantage of that spatial diversity. When you have multiple antenna elements and multiple digital receivers (a mini "array" of antennas), you can use signal processing to separate each of the multipath components and treat each "spatial channel" as an independent data stream.