Bandpass Signaling
The bandpass communication signal is obtained by modulating a baseband analog or digital signal.
We will use complex envelopes because with them we can represent any type of banppass signal.
Definitions:
Baseband, Bandpass, and Modulation
DEFINITION. A baseband waveform has a spectral magnitude that is nonzero for frequencies in the vicinity of
the origin (i.e., f = 0) and negligible elsewhere.
DEFINITION. A bandpass waveform has a spectral magnitude that is nonzero for frequencies in some band
concentrated about a frequency f   f c where
f c . > 0. The spectral magnitude is negligible elsewhere.
f c is called the carrier frequency.
DEFINITION. Modulation is the process of imparting the source information onto a bandpass signal with a
carrier frequency f c by the introduction of amplitude or phase perturbations or both. This bandpass signal is
called the modulated signal s(t), and the baseband source signal is called the modulating signal m(t).
Representation of Modulated Signals
s(t )  Re{ g (t )e jwct }
g (t )  g[m(t )]
Spectrum of Bandpass Signals
Evaluation of Power
1
P P  v (t ) 
g (t )
2
2
v
v
2
Amplitude Modulated Signal
Bandpass Filtering and Linear Distortion
Bandpass Filtering and Linear Distortion
Linear Distortion
Spectrum of Bandpass Signals
𝑉(𝑓) =
1
𝑗
[𝑋(𝑓 − 𝑓𝑐 ) + 𝑋(𝑓 + 𝑓𝑐 )] + [𝑌(𝑓 − 𝑓𝑐 ) − 𝑌(𝑓 + 𝑓𝑐 )]
2
2
1
[𝐺 (𝑓 − 𝑓𝑐 ) + 𝐺 ∗ (−𝑓 − 𝑓𝑐 )]
2
1
𝑃𝑣 (𝑓) = [𝑃𝑔 (𝑓 − 𝑓𝑐 ) + 𝑃𝑔 (−𝑓 − 𝑓𝑐 )]
4
𝑉(𝑓) =
Bandpass Signaling