Pulse Code Modulation

PCM is the standard method used in PSTN (Public Switched Telephone Network) to convert analog data into digital data and with PCM it is easy to combine digitized voice and digital data into a single, high speed digital signal and propagate it over a metallic and optical fiber cable.

            PCM is not a type of modulation but it is a form of digitally coding of analog signals. In this pulses are of fixed length and amplitude.  It is a binary system where presence and absence of pulse represents either logic 1 or logic 0. Standard voce band  range is 300Hz -3400Hz.

                                                    Block Diagram of PCM System

With PCM, the analog signal is sampled at regular intervals by sampling process, next quantization measures numerical value of samples and allot them table value from suitable scale. Then encoding converts numerical value into binary data.

                                                           Basic Concept of PCM

Sampling: Sampling process is used to convert continuous time signal to discrete time signals. The sufficient number of samples of signal must be taken, so that original signal can be represented by its samples completely and It should be possible to reconstruct the original signal from its samples.

Sampling Theorem: A continuous time signal may be completely represented by its samples and recovered back if sampling frequency

f_s ≥ 2f_m where f_s is sampling frequency

f_m is highest frequency present in signal.

If a signal is of 10Hz, its sampling frequency must be equal to or greater than 20Hz, so that it can be represented by its samples completely.

Nyquist Sampling Theorem: It establish minimum sampling rate (f_s) that is equal to twice the highest audio input frequency. If f_s is less than two time f_m, an impairment called alias or foldover distortion occurs. Mathematically, minimum Nyquist sampling rate is

                                                f_s = 2f_m

Quantization is the process of converting an infinite number of possibilities to a finite number of conditions. Analog signals contain an infinite number of amplitude possibilities. Thus converting an analog signal to a PCM code with a limited number of combinations requires quantization.

            Quantization is the process of rounding off the amplitudes of flat top samples to a manageable no of levels. A PCM code would have only 8 bits, which equals to 2⁸ or 256 combinations. So to convert samples of a sine wave to PCM require some rounding off.

            Suppose the first sample occur at time t₁, when the input voltage is exactly +2V. The PCM code that correspondence to +2V is 110. Next if voltage is approx. +2.6V, so magnitude of sample is rounded off to nearest valid code, which is 111 or +3V. The rounding off process results in quantization error of 0.4V.