AEiE0603 Communication System¶
Basic building blocks¶
| Analog communication chain | Digital communication chain |
|---|---|
| Source -> transducer -> transmitter -> channel + noise -> receiver -> output transducer | Source -> source encoder -> channel encoder -> modulator / transmitter -> channel + noise -> receiver / demodulator -> channel decoder -> source decoder -> destination |
Signal and noise¶
- Signal carries desired information.
- Noise is unwanted random disturbance added during transmission or processing.
- Signal-to-noise ratio is a key quality measure:
\[
\text{SNR}=\frac{P_s}{P_n}
\]
and in decibels:
\[
\text{SNR}_{dB}=10\log_{10}\left(\frac{P_s}{P_n}\right).
\]
Low-pass and band-pass signals and systems¶
- Low-pass signals have spectrum centered at or including zero frequency.
- Band-pass signals are centered around a nonzero carrier frequency.
- Baseband and passband are common practical names for these categories.
Bandwidth and distortionless transmission¶
- Bandwidth is the frequency range effectively passed or occupied.
- Distortionless transmission requires magnitude response constant over the signal band and phase response linear with frequency, so delay is uniform.
Hilbert transform and application¶
- Under the usual Fourier convention,
\[
\mathcal F\{\hat x(t)\}=-j\,\operatorname{sgn}(f)X(f).
\]
- Positive-frequency components shift by \(-90^\circ\) and negative-frequency components by \(+90^\circ\).
- It is used in analytic-signal formation, quadrature representation, and single-sideband concepts.
AM, FM, and PM¶
| Modulation | Quantity varied by message | Main cue |
|---|---|---|
| AM | Carrier amplitude | Envelope follows message in simple AM |
| FM | Carrier frequency | Constant amplitude, frequency deviation |
| PM | Carrier phase | Phase varies directly with message |
Basic AM waveform:
\[
s(t)=A_c[1+k_am(t)]\cos(\omega_ct)
\]
for standard DSB-LC modulation when \(|k_am(t)|\le 1\) to avoid overmodulation.
Angle-modulation waveforms:
\[
s_{PM}(t)=A_c\cos[\omega_ct+k_p m(t)]
\]
and
\[
s_{FM}(t)=A_c\cos\left[\omega_ct+k_f\int_{-\infty}^{t}m(\tau)d\tau\right].
\]
FM or PM cues:
- Angle modulation keeps amplitude constant.
- FM index depends on frequency deviation; PM depends on phase deviation.
- For a sinusoidal message, both FM and PM have Bessel-weighted components at \(f_c\pm nf_m\).
- An amplitude limiter can remove amplitude fluctuations before angle demodulation, giving angle modulation resistance to amplitude noise.
- FM is conventionally used for high-fidelity broadcast audio. PM is also angle modulation, so amplitude-noise resistance alone does not distinguish FM from PM.
Frequency-domain representation cues¶
- AM produces carrier and sidebands.
- Single-tone AM gives spectral lines at \(f_c\) and \(f_c\pm f_m\).
- FM produces many sidebands spaced by the modulating frequency.
- PM also belongs to angle modulation and produces sidebands.
Types of AM and FM signals¶
| Family | Examples |
|---|---|
| AM types | DSB-LC, DSB-SC, SSB, VSB |
| FM types | Narrowband FM, wideband FM |
Recognition cues:
- DSB-SC suppresses carrier.
- SSB transmits only one sideband, saving bandwidth.
- Wideband FM generally has larger deviation and bandwidth than narrowband FM.
Communication-system examples¶
- If amplitude stays constant but frequency varies, the signal is FM.
- If sidebands appear around a carrier and envelope resembles the message, it is ordinary AM.
- If only one sideband is sent, it is SSB.
AEiE0603 revision box¶
- Analog chain and digital chain differ mainly by source/channel coding blocks.
- Distortionless transmission needs flat magnitude and linear phase over the band.
- AM varies amplitude; FM varies frequency; PM varies phase.
- Angle modulation keeps amplitude constant.
- SNR in dB uses \(10\log_{10}(P_s/P_n)\).