**Principle of Pulse Code Modulation (PCM):**
Pulse Code Modulation (PCM) is a digital modulation technique used to convert analog signals into digital form for transmission or storage. PCM involves three main processes: sampling, quantization, and coding.

**1. Sampling:**

**Definition:**Sampling involves taking discrete samples of the continuous analog signal at regular intervals.

**2. Quantization:**

**Definition:**Quantization involves mapping each sample's amplitude to the nearest discrete level.**Quantization Levels (L):**The number of discrete levels determines the resolution of the quantization. More levels provide higher fidelity but require more bits for representation.**Quantization Error (Noise):**The difference between the actual analog sample and its quantized representation introduces quantization noise.

**3. Coding:**

**Definition:**The quantized samples are then encoded into digital words using binary code.**Bit Depth (N):**The number of bits used to represent each sample. Higher bit depth allows for more precise representation but requires more data.**PCM Signal Representation:**The PCM signal is a sequence of binary numbers, each representing a quantized sample.

**Analysis of PCM:**

**Sampling Theorem:**It ensures that the reconstructed signal at the receiver accurately represents the original analog signal if the sampling rate is sufficient.**Quantization Error:**As the number of quantization levels increases, quantization error decreases, leading to better signal fidelity.**Bit Rate (R):**The bit rate of PCM is given by$R=Fs⋅N$, where $\mathrm{Fs}$the sampling rate and N is the bit depth.

**Applications of PCM:**

**Telecommunication:**PCM is widely used in voice communication, particularly in digital telephone systems.**Audio Recording:**It is used in digital audio recording systems, such as CDs and digital audio broadcasting.**Medical Imaging:**PCM is employed in medical imaging devices, converting analog signals from sensors into digital form for analysis.**Data Transmission:**PCM is used in various digital communication systems for transmitting and receiving data.

**Advantages and Disadvantages:**

**Advantages:**Robust against noise, easy to implement in digital systems, and allows for efficient error detection and correction.**Disadvantages:**Requires higher bandwidth compared to analog signals, especially for high-quality audio, due to the discrete nature of the signal.

PCM is a fundamental technique in digital communication and data storage, ensuring accurate representation and transmission of analog signals in a digital format.

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