Re: [Economist] Ultrawideband

(no name) ((no email))
Wed, 10 Nov 1999 11:11:16 -0600

> But when the resolution depends on pulse-length, wavelength does not
> matter.

That's like saying that since it relies on loudness, volume doesn't matter.
Squarewave pulses are mapped from the time domain to the frequency domain by
the sinc function: sin (Pi Omega t) / (Pi Omega t). It's a sine wave that
gets smaller as the frequency increases. The narrower the pulse, the wider the
range of frequencies included in the signal. In the limit, a dirac pulse (all
height, no width, unit area) covers all frequencies equally. The reverse
mapping works as well. A dirac pulse at frequency 0 maps to a flat DC voltage.

So the statement is wrong. The pulse length determines the range of
wavelengths in the wideband signal.

> Because it is a mixture of so many frequencies, such a pulse passes
> unnoticed by conventional receivers, which are listening for one
> particular frequency.

Wrong again. It's ignored because the fraction of the total signal energy at
any particular frequency is very small. Unless you're doing lightning, which
is quite noticeable on AM radios.