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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

  1. If amplitude stays constant but frequency varies, the signal is FM.
  2. If sidebands appear around a carrier and envelope resembles the message, it is ordinary AM.
  3. 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 \(10\log_{10}(P_s/P_n)\).