Signals, Spectrum, Bandwidth, Modulation & Noise

Key Concepts and Definitions

Signals: The Foundation of Communication

A signal is a physical quantity (voltage, light, sound) that varies with time or space to represent data. Signals can be:

• Analog: Continuous variation (e.g., human voice, temperature).
• Digital: Discrete levels (e.g., binary 0s and 1s in computers).

Worked Example: Voice Signal

• Analog Voice: A microphone converts sound pressure waves into an electrical voltage signal (continuous).
• Digital Voice: A codec (e.g., in a phone) samples the analog signal at 8 kHz, quantizes it to 8-bit values, and encodes it as binary (e.g., for VoIP).

The Electromagnetic Spectrum: Where Signals Live

The electromagnetic spectrum is divided into bands based on frequency (Hz) and wavelength (m). Telecom uses:

• Radio waves (3 kHz–300 GHz): AM/FM radio, Wi-Fi, Bluetooth, cellular.
• Microwaves (1–300 GHz): Satellite links, radar, 5G.
• Infrared (300 GHz–430 THz): Remote controls, fiber optics.
• Visible light (430–750 THz): Li-Fi, optical fibers.

Frequency bands used in telecommunications. (Image: W.M Welch Scientific Company, Public domain, via Wikimedia Commons)

Real-World Example: Wi-Fi and Cellular Bands

• Wi-Fi (IEEE 802.11): Uses 2.4 GHz (ISM band) and 5 GHz (unlicensed) for wireless LANs.
• 4G/5G Cellular: Operates in 600 MHz–3.5 GHz (sub-6 GHz) and mmWave (24–100 GHz) for high-speed data.

Signal Parameters: Amplitude, Frequency, Phase

Every signal is defined by three key parameters:

Worked Example: AM Radio

• A 1 MHz carrier wave is modulated by a 1 kHz audio signal.
• The amplitude of the carrier varies with the audio signal’s amplitude.
• Frequency remains 1 MHz; only amplitude changes.

sequenceDiagram participant Audio as Audio Signal (1 kHz) participant Carrier as Carrier Wave (1 MHz) Audio->>Carrier: Modulates
  Carrier-->>Carrier: Original (1 MHz)
  Carrier-->>Carrier: Amplitude-modulated (1 kHz envelope)
  Carrier-->>Receiver: Transmitted AM Signal
  Carrier-->>Receiver: Frequency remains constant

Bandwidth: The Capacity of a Signal

Bandwidth is the range of frequencies a signal occupies (measured in Hz). It determines:

• Data rate: Higher bandwidth = more data per second (e.g., 100 MHz = 100 Mbps in digital).
• Signal quality: Narrowband (e.g., voice) vs. broadband (e.g., HD video).

Types of Bandwidth

Worked Example: Internet Bandwidth

• A 100 Mbps connection means 100 MHz of bandwidth (assuming 1 bit/Hz).
• Nepal’s NTC offers broadband up to 1 Gbps (1000 MHz bandwidth) via fiber.

Modulation: Encoding Data onto Signals

Modulation encodes digital data onto analog signals for transmission. Key techniques:

1. Amplitude Modulation (AM)

• Varies amplitude of the carrier wave.
• Pros: Simple, long-range (e.g., AM radio).
• Cons: Susceptible to noise.

2. Frequency Modulation (FM)

• Varies frequency of the carrier wave.
• Pros: Better noise immunity (e.g., FM radio, Wi-Fi).
• Cons: More complex circuitry.

3. Phase Modulation (PM)

• Varies phase of the carrier wave.
• Pros: High data rates (e.g., digital TV, 5G).

Worked Example: FM Radio in Nepal

• A 100 MHz carrier wave’s frequency shifts ±75 kHz for audio (deviation).
• Nepal’s Radio Nepal uses FM for clear sound over long distances.

Noise and Its Impact

Noise is unwanted interference that distorts signals. Types:

• Additive Noise: Random signals added to the original (e.g., thermal noise).
• Multiplicative Noise: Distorts amplitude/frequency (e.g., fading in wireless).
• Impulse Noise: Sudden spikes (e.g., lightning).

Signal-to-Noise Ratio (SNR)

Measures signal quality: $$\text{SNR (dB)}=10{\log }_{10}\left(\frac{P_{\text{signal}}}{P_{\text{noise}}}\right)$$

• SNR > 20 dB: Good (e.g., clear voice call).
• SNR < 0 dB: Unusable (e.g., static on a bad line).

Worked Example: Mobile Call in Kathmandu Traffic

• Scenario: A Pathao rider calls while driving in heavy traffic.
• Noise Sources:
  • Engine noise (multiplicative).
  • Other vehicles’ signals (interference).
• Solution: 4G/5G uses OFDM (Orthogonal Frequency-Division Multiplexing) to reduce interference.

In the Real World

1. eSewa and Khalti (Digital Payments)

   • Use digital modulation (e.g., QAM in fiber optics) to transmit transaction data securely over the internet.
   • Bandwidth: High-speed broadband (100 Mbps+) ensures low latency for payments.

2. Ncell and NTC (Mobile/Internet Services)

   • 4G/5G networks use frequency bands like 1800 MHz and 2600 MHz for data.
   • Noise cancellation: Advanced antennas reduce interference in crowded areas like Thamel.

3. Daraz and Online Shopping

   • Packet transmission: Orders travel as digital packets over fiber (optical signals) or wireless (microwaves).
   • Bandwidth: High-speed links ensure fast loading of product pages.

Exam Tip

1. Memorize the spectrum: Know which bands are used for AM/FM, cellular, Wi-Fi, and satellite.
2. Compare AM/FM/PM: Be ready to explain pros/cons and real-world uses (e.g., AM for long-range, FM for clarity).
3. Calculate SNR: Given signal/noise power, compute SNR in dB.
4. Bandwidth vs. Data Rate: Relate bandwidth (Hz) to data rate (bits/sec) using Nyquist’s theorem: $$C=2B{\log }_2(M)\text{(for M-ary signaling)}$$
5. Real-world applications: Link concepts to Nepalese services (e.g., NTC’s fiber uses optical modulation).