Understanding signals as the core of information transmission.
Key Concepts:
- Signal types (analog vs digital)
- Energy vs power signals
- Time domain vs frequency domain
- Bandwidth
- Noise (AWGN)
- SNR, BER
Why It Matters: Telecom is about transmitting information over noisy channels; this lesson teaches reliability in imperfect environments.
Labs/Practice: Simulated signal propagation and noise effects; measured SNR in basic transmission setups.
Tools Used: MATLAB, Wireshark for signal capture.
Part B: Physics & Signals – The Real-World Constraints
Telecom fights physics every day. The channel is never perfect.
1. What is a Signal? Analog vs Digital
- Analog: Continuous in time & amplitude (e.g., human voice pressure wave → microphone voltage). Infinite possible values. Very sensitive to noise/amplification distortion.
- Digital: Discrete in time (sampled) and amplitude (quantized to bits). Only finite values (usually binary levels). Noise-tolerant because small perturbations don’t change 0 → 1 if threshold is good. Almost all modern telecom is digital after the antenna.
Trade-off
Analog = potentially higher fidelity but fragile.
Digital = robust, compressible, correctable → but needs bandwidth for bits.
2. Energy vs Power Signals
-
Energy signal: Finite total energy → ∫ s(t) ² dt < ∞ (e.g., one pulse, voice packet) -
Power signal: Finite average power → lim (1/2T) ∫_{-T}^T s(t) ² dt exists and finite (e.g., continuous sinusoid, ongoing data stream)
Most telecom carriers are power signals; bursts/packets are energy signals.
3. Time Domain vs Frequency Domain
Two views of the same thing (thanks, Fourier).
- Time: amplitude vs time (oscilloscope)
- Frequency: power vs frequency (spectrum)
Every operation has a dual: convolution ↔ multiplication, modulation ↔ frequency shift.
4. Bandwidth
The “width” of frequencies the signal occupies or the channel allows.
- Baseband signal (around 0 Hz): e.g., voice 300–3400 Hz → ~3 kHz bandwidth
- Passband: centered at carrier fc (e.g., 2.4 GHz Wi-Fi) but still has bandwidth B
Shannon-Hartley theorem (fundamental limit):
C = B × log₂(1 + SNR) bits/s
→ More bandwidth or better SNR = more capacity.
This is why 5G uses huge bandwidths (up to 400 MHz channels) and massive MIMO to push SNR.
5. Noise – AWGN
Additive White Gaussian Noise = ideal thermal noise model.
- Additive: adds to signal
- White: flat power spectrum (equal power per Hz)
- Gaussian: amplitude follows bell curve
Real world has other noises (interference, phase noise, quantization), but AWGN is starting point.
6. SNR (Signal-to-Noise Ratio)
SNR = signal power / noise power (usually in dB: 10 log₁₀(S/N)).
- Good cellular call: ~10–20 dB
- High-speed Wi-Fi/5G: can be 30+ dB in good conditions
- Below ~0 dB → signal buried in noise, but coding/spreading can still recover (spread-spectrum)
7. BER (Bit Error Rate)
Probability a received bit is wrong.
- Voice: BER ~10^{-3} tolerable
- Data: 10^{-5} to 10^{-12} needed (retransmissions + coding fix residual)
BER vs SNR curves are the famous “waterfall” plots you see everywhere in telecom papers.
Key Unifying Concept
Telecommunication is engineering under constraints:
limited bandwidth, limited power, lots of noise, multipath, mobility → use math (Fourier, complex, probability) to squeeze maximum reliable bits through.
Status: ✅ Completed – February 2026
Next lesson: Signals & Systems