Digital Communications Overview

Digital Communications

• Digital communication systems are more robust than analog systems due to their ability to withstand channel noise and distortions.
• Digital communications systems offer flexibility due to the use of microprocessors and VLSI (Very Large Scale Integration) systems.
• Error correction coding, multiplexing, storage, and reproduction of data are superior in digital communication systems.

Digital Transmission of Analog Signals

• Analog signals can take any value and are converted to digital signals for use in digital communication systems through the following steps:
• Sampling
• Quantization
• Encoding
• Baseband OR Passband Transmission

Sampling Theorem

• A band-limited signal can be perfectly reconstructed from its samples if the sampling frequency (fs) is at least twice the signal bandwidth (B).
• The sampling rate must be greater than or equal to the Nyquist rate (fs >= 2B).
• The minimum sampling frequency is called the Nyquist frequency, and the corresponding sampling interval is called the Nyquist interval.

Sampling Process

• The sampling process is performed by multiplying the signal with an impulse train.
• The resulting sampled signal is a series of impulses, where the amplitude of each impulse represents the signal value at the corresponding sampling instant.

Signal Reconstruction

• The process of reconstructing the original signal from its sampled values is known as interpolation.
• Interpolation can be performed using an ideal low-pass filter with a bandwidth equal to the signal bandwidth and a gain of Ts (sampling period).

Practical Issues with Sampling

• Realizability of Reconstruction Filter: An ideal filter is not physically realizable, so practical filters introduce distortions in the reconstructed signal.
• Sampling Rate: In practice, the sampling rate must be significantly higher than the Nyquist rate to minimize aliasing artifacts.

Under sampling & Aliasing

• Under sampling occurs when the sampling rate (fs) is less than twice the signal bandwidth (B).
• The result is the phenomenon called aliasing, resulting in a distorted reconstructed signal.
• To avoid aliasing, an anti-aliasing filter is used prior to sampling, which removes frequency components above the signal bandwidth.

Quantization

• The process of converting a continuous-valued signal into a discrete set of values.
• The number of quantization levels dictates the resolution of the quantized signal.
• Quantization introduces quantization noise, a form of distortion that reduces the fidelity of the reconstructed signal.
• Quantizer saturation occurs when the signal amplitude exceeds the maximum level of the quantizer, resulting in the amplitude being clamped to the maximum or minimum value.
• Timing jitter occurs when the sampling instants are unstable, introduces noise and causes unpredictable timing errors in the reconstructed signal.

Encoding

• Encoding converts the quantized samples into a digital code representation.
• Binary PCM (Pulse Code Modulation) encodes each quantized sample into an n-bit code word.

Companding

• Companding is a technique used to improve the dynamic range of the signal by using a non-linear mapping function to emphasize weaker signals and compress stronger signals.
• Two common companding laws are:
  • μ-law: Used in North American standards.
  • A-law: Used in European standards.

Sources of Errors while Quantizing

• Quantization noise
• Quantizer saturation
• Timing jitter