With a neat diagram explain Pulse code modulation and demodulation systems.

Pulse Code Modulation (PCM): PCM is a method used to digitally represent sampled analog signals. It is the most basic form of digital transmission of analog signals. The process involves three main steps: sampling, quantization, and encoding. PCM is widely used in telecommunications, digital audio, and video transmission due to its robustness against noise and interference.

PCM System Components:

A PCM system consists of a transmitter and a receiver.

1. Transmitter:

• Sampling: The analog input signal is sampled at regular intervals. The sampling rate must be at least twice the highest frequency component of the signal, according to the Nyquist-Shannon sampling theorem.
• Quantization: The sampled values are then quantized, meaning they are approximated to the nearest discrete level. This process introduces quantization error. The number of quantization levels determines the resolution of the digital signal.
• Encoding: Each quantized level is assigned a unique binary code. This binary code represents the quantized sample value.

2. Receiver:

• Decoding: The received binary code is decoded back into the corresponding quantized levels.
• Reconstruction: A low-pass filter (often called a reconstruction filter) is used to smooth out the discrete levels and reconstruct the analog signal.

PCM Transmitter Block Diagram:

Explanation of Transmitter Diagram:

• The analog input signal is first passed through an anti-aliasing filter to remove frequencies above half the sampling rate, preventing aliasing.
• The sampler converts the continuous-time signal into a discrete-time signal, producing a sequence of pulses.
• The quantizer maps the continuous range of sampled amplitudes to a finite set of discrete amplitude levels. This is where quantization noise is introduced.
• The encoder converts each quantized level into a binary codeword. For example, if there are 8 quantization levels, a 3-bit binary code can represent each level.

PCM Receiver Block Diagram:

Explanation of Receiver Diagram:

• The decoder receives the binary codewords and converts them back into the corresponding quantized amplitude levels.
• The sample-and-hold circuit holds the decoded level until the next sample arrives.
• The reconstruction filter (a low-pass filter) smooths the staircase-like output of the sample-and-hold circuit to produce an approximation of the original analog signal.

Advantages of PCM:

• High noise immunity.
• Can use regenerative repeaters for long-distance transmission.
• Compatible with digital computers and TDM.
• Efficient use of bandwidth (with appropriate coding).

Disadvantages of PCM:

• Requires high bandwidth compared to analog modulation.
• Introduces quantization error.
• Complex circuitry for transmitter and receiver.

Write a short note on Flat-Top sampling.

Flat-Top Sampling: Flat-top sampling is a type of sampling where the top of the pulse remains flat during the sampling interval. In this method, the sampled pulse has a finite width, and its amplitude is held constant over that duration. This is in contrast to ideal impulse sampling, where the samples are assumed to be instantaneous.

Process:

• The analog signal is multiplied by a train of rectangular pulses of finite width τ.
• The resulting sampled signal is a sequence of pulses with constant amplitude over their duration τ.

Spectrum of Flat-Top Sampled Signal:

The spectrum of a flat-top sampled signal is the spectrum of the original analog signal convolved with the spectrum of the sampling pulse. The spectrum of a rectangular pulse is a sinc function. This convolution results in:

1. The original signal spectrum is replicated at multiples of the sampling frequency f_s.
2. Each replica is weighted by the sinc function, which causes amplitude distortion. The higher frequency components within each replica are attenuated more than the lower frequency components.

Reconstruction:

Reconstruction of the original signal from flat-top samples requires a filter that can compensate for the amplitude distortion introduced by the sinc function in the frequency domain. This compensation is often achieved using an aperture correction filter.

Advantages:

• Easier to implement in practice compared to ideal impulse sampling.
• The sampled pulses can be easily processed and transmitted.

Disadvantages:

• Introduces amplitude distortion due to the sinc function weighting, requiring aperture correction.
• Requires a more complex reconstruction filter than ideal sampling.