Radar Waveforms - MATLAB Simulations for Radar Systems Design - page 142

3.3. CW and Pulsed Waveforms
The spectrum of a given signal describes the spread of its energy in the fre-
quency domain. An energy signal (finite energy) can be characterized by its
Energy Spectrum Density (ESD) function, while a power signal (finite power)
is characterized by the Power Spectrum Density (PSD) function. The units of
the ESD are Joules per Hertz and the PSD has units Watts per Hertz.

The signal bandwidth is the range of frequency over which the signal has a
nonzero spectrum. In general, any signal can be defined using its duration
(time domain) and bandwidth (frequency domain). A signal is said to be band-
limited if it has finite bandwidth. Signals that have finite durations (time-lim-
ited) will have infinite bandwidths, while band-limited signals have infinite
durations. The extreme case is a continuous sine wave, whose bandwidth is
infinitesimal.

A time domain signal has a Fourier Transform (FT) given by

f () F ()

∞
∫

– j ω t

F () f () e = d (3.14)

– ∞

where the Inverse Fourier Transform (IFT) is

∞
∫

1
2π

F () e j ω t

------

f () = d

(3.15)

– ∞

The signal autocorrelation function is R f ()

∞
∫

f ∗ () ft τ R f () = ( + ) d

(3.16)

– ∞

The asterisk indicates the complex conjugate. The signal amplitude spectrum is
. If

F () 2

were an energy s i gnal, then its ESD is ; and if it were a F () f ()

power signal, then its PSD is which is the FT of the autocorrelation S f ()

function

∞
∫

– j ωτ

S f () R f = () e d (3.17)

– ∞

First, consider a CW waveform given by