Digital Communications
What is Digital Communications?
The process of converting a continuous-time signal into a discrete-time signal by taking measurements at regular intervals.
Key formula / rule: Sampling Theorem
Key points
- Understand the process of converting analog signals to digital signals.
- Analyze different digital modulation and demodulation techniques.
- Comprehend the principles of error detection and correction coding.
- Evaluate the performance of digital communication systems in terms of error rate and bandwidth.
Common exam trap
Confusing sampling rate with bit rate.
Definitions
- Term
Sampling
- Meaning
The process of converting a continuous-time signal into a discrete-time signal by taking measurements at regular intervals.
- Term
Quantization
- Meaning
The process of approximating the sampled continuous amplitude values to a finite set of discrete levels.
- Term
Encoding
- Meaning
The process of assigning binary codes to the quantized levels.
- Term
Modulation
- Meaning
The process of varying one or more properties of a carrier wave with a modulating signal that typically contains information to be transmitted.
- Term
Bit Error Rate (BER)
- Meaning
The ratio of the number of bit errors to the total number of bits transmitted.
- Term
Inter-Symbol Interference (ISI)
- Meaning
Distortion caused by the overlap of one symbol's pulse with subsequent symbols' pulses.
Learning objectives
Understand the process of converting analog signals to digital signals.
Analyze different digital modulation and demodulation techniques.
Comprehend the principles of error detection and correction coding.
Evaluate the performance of digital communication systems in terms of error rate and bandwidth.
Understand multiplexing techniques used in digital systems.
Formulae
- Name
Sampling Theorem
- Note
fs is sampling frequency, B is signal bandwidth.
- Expression
fs ≥ 2B
- Name
Quantization Bits
- Note
b is number of bits, L is number of quantization levels.
- Expression
b = log2(L)
- Name
PCM Bit Rate
- Note
R is the bit rate for Pulse Code Modulation.
- Expression
R = fs * b
- Name
Signal-to-Quantization Noise Ratio (SQNR) for uniform quantizer
- Note
n is the number of bits per sample.
- Expression
SQNR = 6.02nb + 1.76 dB
- Name
Bandwidth for Binary PAM
- Note
r is the roll-off factor, Rb is the bit rate.
- Expression
BW = (1+r) * Rb/2
Prerequisites
Basic Signal and System concepts (Fourier Series, Fourier Transform, Convolution)
Probability and Random Variables
Basic Analog Communication concepts (Modulation, Bandwidth)
Common mistakes
Confusing sampling rate with bit rate.
Ignoring quantization noise effects.
Assuming perfect channel conditions without considering error correction.
Misapplying modulation schemes to specific channel characteristics.
Underestimating the impact of inter-symbol interference (ISI).
Keywords
Digital Modulation
Sampling
Quantization
Error Correction
PCM
ASK
FSK
PSK
QAM
BER
ISI
Practice preview
What is the minimum sampling rate required for a signal with a maximum frequency component of 5 kHz to avoid aliasing?…
easy
Which digital modulation technique varies the amplitude of the carrier signal according to the digital data?…
easy
In Delta Modulation (DM), which of the following issues arises when the input signal changes too rapidly for the staircase approximation to follow?…
medium