Signals in the time and frequency domain - Signals, Processes, and Systems - page 43

1 / T = Δ f

T = 1s

τ

All information in the time domain can
also be found in the frequency domain
and vice versa.

A pattern which is large in the time
domain appears small in the frequency
domain and vice versa

Illustration 36: Steps in the direction of a δ− pulse

The pulse duty factor above is roughly 1/16 above and 1/32 below. Accordingly, the the first zero position
above is at N = 16, and below at N = 32. The zero position "moves" towards the right with higher frequen-
cies if the pulse becomes narrower. Below, the lines of the spectrum represented seem to have almost
equally large amplitudes.

In the case of a "needle" pulse or - pulse the width of the pulse tends towards zero, thus the (first) zero

position of the spectrum tends toward infinity. Hence, the

δ

δ -pulse has an "infinitely wide frequency

spectrum"; in addition, all the amplitudes are the same.