The Signal Realm

NODE 01

What is a Signal?

010110

• Measurable physical variation.
• Represents information (Voltage, Light, EM wave).
• Signal ≠ Information.

NODE 02

Info as Physics

TX

→

CH

→

RX

• Message → Encoder → Transmitter → Channel → Receiver → Decoder.

NODE 03

Analog Signals

• Varies continuously in amplitude and time.
• Audio, voltage sensors. Sensitive to noise.

NODE 04

Digital Signals

• Discrete symbols/levels (0 and 1).
• Thresholds, sampling, quantization.

NODE 05

Signal Waveforms

SIN / SQ / PULSE / TRI

• Described by: amplitude + frequency + phase + time.

NODE 06

Frequency Domain

TIME vs FREQ

• Signals contain multiple frequency components.
• Major bridge to communication engineering.

NODE 07

Fourier Idea

COMPLEX = Σ(SINES)

• Complex periodic signal = sum of sinusoids.
• Allows analysis via frequency components.

NODE 08

Bandwidth

BW

• Width of frequency range occupied.
• BW = f_high - f_low.

NODE 09

Why BW Matters

BW ↑ = DATA RATE ↑

• Allows faster transitions/pulses.
• Also depends on noise, modulation, coding.

NODE 10

Carrier Wave

• High-frequency EM wave.
• Message → Carrier → Modulation → Transmission.

NODE 11

Modulation

AM / FM / PM

• Changes carrier according to info signal.
• Amplitude, Frequency, or Phase.

NODE 12

Amplitude Mod (AM)

• Carrier amplitude varies with message signal.

NODE 13

AM Index

μ = A_m / A_c

• Controls depth of modulation.

NODE 14

AM Spectrum

• Carrier (fc) + Upper/Lower Sidebands (fc ± fm).

NODE 15

AM Bandwidth

BW = 2f_m

• Single-tone: BW = 2fm.
• Information BW ≠ Carrier Frequency.

NODE 16

Frequency Mod (FM)

• Instantaneous frequency varies with message.
• Better noise performance than AM.

NODE 17

Phase Mod (PM)

Δφ ∝ INFO

• Phase varies with info signal.
• Angle Modulation = FM + PM.

NODE 18

Digital Modulation

ASK / FSK / PSK / QAM

• Encode digital info onto carriers.

NODE 19

BPSK

0 → φ₁
1 → φ₂

• Binary Phase Shift Keying.
• Two phases represent two binary states.

NODE 20

QAM

AMP + PHASE

• Quadrature Amplitude Modulation.
• Combines variations to encode multiple bits per symbol.

NODE 21

Symbols & Bit Rate

BIT/S vs BAUD

• Bit rate: bits/sec. Symbol rate: symbols/sec (baud).
• 1 symbol can carry >1 bit.

NODE 22

Sampling

• Continuous signal → discrete samples.
• Nyquist: f_s > 2f_max.

NODE 23

Aliasing

f_s < 2f_max

• Insufficient sampling → frequencies become indistinguishable.
• Use anti-aliasing filters.

NODE 24

Quantization

SAMPLES → LEVELS

• Amplitudes mapped to discrete levels.
• Resolution, quantization error.

NODE 25

PCM

SAMP → QUANT → BINARY

• Pulse Code Modulation.
• Foundational digital communication concept.

NODE 26

Multiplexing

MUX

• Multiple signals share a channel.
• FDM (Freq), TDM (Time), WDM (Wavelength).

NODE 27

Channel

WIRE / FIBER / SPACE

• Physical path for info.
• Has Bandwidth, Loss, Noise, Distortion.

NODE 28

Propagation

REFL / REFR / SCAT

• Signal travels via EM waves.
• Reconnects to Realms 21, 22, 24.

NODE 29

Free-Space Prop

POWER ∝ 1/r²

• Ideal EM propagation through vacuum.
• Path loss, spreading.

NODE 30

Attenuation

SIGNAL WEAKENS

• Signal strength decreases with distance.
• Spreading, absorption, scattering. (Not = Noise).

NODE 31

Noise

• Unwanted random/structured disturbances.
• Thermal, Electronic, Atmospheric, Crosstalk.

NODE 32

SNR

SNR = S / N

• Signal-to-Noise Ratio (dB).
• Higher SNR = easier reliable signal recovery.

NODE 33

Distortion

SHAPE CHANGES

• Signal is altered, not just weakened.
• Amplitude, Phase, Dispersion.

NODE 34

Channel Capacity

C = B log₂(1 + S/N)

• Shannon's idealized limit.
• Bridge: Physics ↔ Math ↔ Info Theory.

NODE 35

Info Theory Entry

BIT / ENTROPY / ERROR

• Information becomes mathematically measurable.

NODE 36

Error Detection

PARITY / CHECKSUM

• Add controlled redundancy → detect errors.

NODE 37

Error Correction

FORWARD ERROR CORR

• Add enough redundancy to RECOVER corrupted data.
• Comm is about recovering info reliably.

NODE 38

Antennas

• Couple electrical circuits to EM waves.
• TX, RX, Resonance, Polarization.

NODE 39

Antenna Length

L ≈ λ / 2

• Half-wave dipole.
• EM wavelength dictates physical engineering dimensions.

NODE 40

Polarization in Comm

MATCH TX & RX

• Vertical, Horizontal, Circular.
• Mismatch causes inefficiency.

NODE 41

Radio Broadcasting

VOICE → MOD → RF → RX

• Turns abstract physics into a complete system.

NODE 42

Television

AUDIO + VIDEO → MOD

• Modern TV is digital, but analogue provides historical physics.

NODE 43

Cellular Comm

CELLS / HANDOFF / FREQ

• Base stations, frequency reuse, digital modulation.

NODE 44

Satellite Comm

UPLINK → SAT → DOWNLINK

• Earth station → Transponder → Receiving station.

NODE 45

GPS (Physics View)

TIMING → POSITION

• Infer position from signal timing from multiple sats.
• Needs precise clocks, relativity corrections (Realm 30).

NODE 46

Radar

• Comm tech becomes sensing.
• TX → reflect/scatter → RX → infer range.

NODE 47

Radar Range

R = ct / 2

• Signal travels to target AND back (factor of 2).

NODE 48

Radar Doppler

Δf → VELOCITY

• Relative motion produces freq shifts.
• Realm 14 Doppler applied to tech.

NODE 49

Optical Comm

• Realms 23 & 24 combined.
• ELEC → LASER → FIBRE → PHOTODETECTOR.

NODE 50

Fibre Bandwidth

ENORMOUS CAPACITY

• Limited by attenuation, dispersion, receiver limits.

NODE 51

WDM

λ₁ + λ₂ + λ₃ → 1 FIBRE

• Wavelength Division Multiplexing.
• Multiple optical channels share one fibre.

NODE 52

Free-Space Optical

LASER THROUGH AIR

• Directed light through air/vacuum.
• Atmospheric attenuation & alignment are key.

NODE 53

Wireless Prop

LOS / REFL / SCAT

• Line-of-sight, reflection, diffraction, multipath.

NODE 54

Multipath

MULTIPLE PATHS → INTERF

• Signals arrive via diff paths (diff delay/phase).
• Causes interference (Realm 24).

NODE 55

Fading

STRENGTH VARIES

• Constructive/Destructive multipath combinations.
• Fast fading, shadowing.

NODE 56

Ionosphere (Adv)

SKY WAVE

• Radio waves interact with Earth's ionosphere.
• Refraction/Reflection enables long-distance comm.

NODE 57

Waveguides

CONFINED EM WAVES

• Metallic or dielectric structures.
• Modes, cutoff frequency.

NODE 58

Microwave Links

POINT-TO-POINT

• High-freq carriers, antenna directivity, LOS.

NODE 59

Trans & Receiver

TX

RX

• TX: Info → Mod → Radiation.
• RX: Radiation → Demod → Info.

NODE 60

Demodulation

MOD ↔ DEMOD

• Recovering info signal from modulated carrier.
• AM detector, FM discriminator.

NODE 61

Filtering

LPF / HPF / BPF / BSF

• Selects useful frequency ranges.
• Connects to Realm 20's LCR architecture.

NODE 62

Resonance in Comm

LCR ↔ RADIO TUNING

• Resonant circuit selects frequency range.
• Circuit Physics ↔ Signal Physics.

NODE 63

Freq Allocation

BANDS & CHANNELS

• Different services operate in diff freq regions.
• Avoids interference.

NODE 64

Signal Energy

I = P / A

• Signals carry energy.
• Links comm with Realm 21 EM energy.

NODE 65

Communication Speed

PROP SPEED ≠ DATA RATE

• Signal travels at c, but throughput/latency differ.

NODE 66

Analog vs Digital

• Digital can use error correction, compression, encryption.

NODE 67

Regeneration

RECONSTRUCT, NOT AMPLIFY

• Digital RX reconstructs clean symbols.
• Maintains quality over multiple links.

NODE 68

Mod + BW + Noise

GOAL: RELIABLE TRANSFER

• Comm quality is the interaction of Signal, BW, Power, Noise, Channel, Coding.

NODE 69

Experiment Lab

AM/FM / SAMPLING / NOISE

• Simulate modulation. Measure SNR.
• Digital mod, Fibre attenuation, Antenna resonance.

NODE 70

Graph Chamber

TIME vs FREQ DOMAIN

• Waveform (Amp vs t). Spectrum (Amp vs f).
• Filter response, SNR, Channel capacity.

NODE 71

Misconceptions

BW ≠ FREQ

• "Digital has no noise" → Handled via thresholds/regen.
• "Info is a wave" → Info is carried BY the wave.
• "High freq = high data" → Depends on BW & modulation.

NODE 72

Solving Engine

INFO → CARRIER → MOD

• ID Info → Analog/Digital? → Modulation.
• Find BW → ID Channel → SNR/Attenuation.
• Receive → Demodulate → Decode.

NODE 73

Master Map

INFO → SIGNAL → RX → DATA

• The entire Signal Realm compressed.

NODE 74

Cross-Realm Synth

R14 + R20 + R21 + R23...

• Waves, AC, EM Ocean, Optics, Silicon...
• All converge into INFORMATION SYSTEMS.

NODE 75

The Deep Idea

STATE → MEASURE → INFO

• Physics doesn't just explain matter & energy.
• It explains how physical systems carry INFORMATION.
• The ultimate link.