# Pulse Code Modulation and Demodulation

We know that modulation can be defined as the process of changing the carrier signal’s parameters by the instant values of the message signal. The transmission of message signal can be done mainly for communication & the high-frequency signal like a carrier signal doesn’t include data, however, it is used for lengthy-distance communication. The classification of modulation techniques can be done based on the type of modulation used. For instance, the digital modulation uses PCM or Pulse Code Modulation technique. In PCM, the message signal can be signified through a series of coded pulses. So, this message signal can be attained through signifying the signal in the form of discrete in both times as well as amplitude. This article discusses an overview of pulse code modulation and demodulation.

## What is Pulse Code Modulation and Demodulation?

Pulse code modulation is a method that is used to convert an analog signal into a digital signal so that a modified analog signal can be transmitted through the digital communication network. PCM is in binary form, so there will be only two possible states high and low(0 and 1). We can also get back our analog signal by demodulation. The Pulse Code Modulation process is done in three steps Sampling, Quantization, and Coding. There are two specific types of pulse code modulations such as differential pulse code modulation(DPCM) and adaptive differential pulse code modulation(ADPCM).

### Pulse Code Modulation Block Diagram

The basic elements of PCM mainly include the transmitter section and receiver section. The pulse code modulation steps are discussed below

Here is a block diagram of the steps which are included in PCM. In sampling, we are using a PAM sampler that is Pulse Amplitude Modulation Sampler which converts continuous amplitude signal into Discrete-time- continuous signal (PAM pulses). The basic block diagram of PCM is given below for better understanding.

To get a pulse code modulated waveform from an analog waveform at the transmitter end (source) of a communications circuit, the amplitude of the analog signal samples at regular time intervals. The sampling rate or the number of samples per second is several times the maximum frequency. The message signal converted into the binary form will be usually in the number of levels which is always to a power of 2. This process is called quantization.

At the receiver end, a pulse code demodulator decodes the binary signal back into pulses with the same quantum levels as those in the modulator. By further processes, we can restore the original analog waveform.

### Pulse Code Modulation Theory

The above block diagram describes the whole process of PCM. The source of the continuous-time message signal is passed through a low pass filter and then sampling, Quantization, Encoding will be done. We will see each in detail step by step.

#### Sampling

Sampling is a process of measuring the amplitude of a continuous-time signal at discrete instants, converts the continuous signal into a discrete signal. For example, conversion of a sound wave to a sequence of samples. The Sample is a value or set of values at a point in time or it can be spaced. Sampler extract samples of a continuous signal, it is a subsystem ideal sampler produces samples that are equivalent to the instantaneous value of the continuous signal at the specified various points. The Sampling process generates a flat-top Pulse Amplitude Modulated (PAM) signal.

Sampling frequency, Fs is the number of average samples per second also known as the Sampling rate. According to the Nyquist Theorem, the sampling rate should be at least 2 times the upper cutoff frequency. Sampling frequency, Fs>=2*fmax to avoid Aliasing Effect. If the sampling frequency is very higher than the Nyquist rate it becomes Oversampling, theoretically a bandwidth-limited signal can be reconstructed if sampled above the Nyquist rate. If the sampling frequency is less than the Nyquist rate it will become Undersampling.

Basically, two types of techniques are used for the sampling process. Those are 1. Natural Sampling and 2. Flat- top Sampling.

#### Quantization

In quantization, an analog sample with an amplitude that converted into a digital sample with an amplitude that takes one of a specifically defined set of quantization values. Quantization is done by dividing the range of possible values of the analog samples into some different levels and assigning the center value of each level to any sample in the quantization interval. Quantization approximates the analog sample values with the nearest quantization values.

So almost all the quantized samples will differ from the original samples by a small amount. That amount is called quantization error. The result of this quantization error is we will hear a hissing noise when playing a random signal. Converting analog samples into binary numbers that are 0 and 1.

In most cases, we will use uniform quantizers. Uniform quantization is applicable when the sample values are in a finite range (Fmin, Fmax). The total data range is divided into 2n levels, let it be L intervals. They will have an equal length Q. Q is known as Quantization interval or quantization step size. In uniform quantization, there will be no quantization error.

As we know,
L=2n, then Step size Q = (Fmax – Fmin) / L

Interval i is mapped to the middle value. We will store or send only the index value of quantized value.

An Index value of quantized value Qi (F) = [F – Fmin / Q]

Quantized value Q (F) = Qi (F) Q + Q / 2 + Fmin

But there are some problems raised in uniform quantization those are

• Only optimal for the uniformly distributed signal.
• Real audio signals are more concentrated near zeros.
• The Human ear is more sensitive to quantization errors at small values.

The solution to this problem is using Non- uniform quantization. In this process, the quantization interval is smaller near zero.

#### Low Pass Filter (LPF)

This LPF is used to remove the high frequency (HF) components that are present within the input analog signal. Here this signal is higher as compared to the highest frequency message signal so that it avoids aliasing of the message signal.

#### Regenerative Repeater

The signal strength can be enhanced through this regenerative repeater. So, the channel’s output also includes a regenerative repeater circuit to balance the signal loss, renovate the signal & also increases the signal strength.

#### Decoder

The main function of a decoder circuit is to decode the pulse-coded signal to repeat the actual signal. This circuit works like a demodulator.

#### Reconstruction Filter

After the conversion of DAC (digital-to-analog conversion) is done with the help of the decoder and regenerative circuit, then an LPF (low-pass filter) is used to get back the original signal. So, this is known as the reconstruction filter

Therefore, the Pulse Code Modulator circuit (PCM) is used to digitize the specified analog signal, code it, sample it & after that, it transmits in the form of analog. So, this entire procedure can be repeated within a reverse model to get the actual signal.

#### Coding

The encoder encodes the quantized samples. Each quantized sample is encoded into an 8-bit codeword by using A-law in the encoding process.

• Bit 1 is the most significant bit (MSB), it represents the polarity of the sample. “1” represents positive polarity and “0” represents negative polarity.
• Bit 2,3 and 4 will defines the location of the sample value. These three bits together form a linear curve for low-level negative or positive samples.
• Bit 5,6,7 and 8 are the least significant bits (LSB) it represents one of the segments’ quantized value. Each segment is divided into 16 quantum levels.

Pulse code modulation is similar to PWM, PAM otherwise PPM however there is a significant disparity among them that is they are analog pulse modulation systems but Pulse code modulation is a digital pulse modulation system.

So, the output of PCM is in the form of coded digital and it is in the form of digital signals of stable width, position & amplitude.

The data can be transmitted in code words format. A pulse code modulation system includes a transmitter like a PCM encoder & a receiver like a PCM decoder.

The important operations within the transmitter of pulse code modulation mainly include sampling, quantizing, and encoding.

Generally, these operations are performed within a similar circuit namely ADC.

### Types of PCM

PCM is two types of Differential Pulse Code Modulation (DPCM), Adaptive Differential Pulse Code Modulation (ADPCM) & Linear Pulse Code Modulation.

#### Differential Pulse Code Modulation (DPCM)

In DPCM only the difference between a sample and the previous value is encoded. The difference will be much smaller than the total sample value so we need some bits for getting the same accuracy as in ordinary PCM. So that the required bit rate will also reduce. For example, in 5-bit code 1 bit is for polarity, and the remaining 4 bits for 16 quantum levels.

The advantages of differential pulse code modulation include the following.

• The requirement of bandwidth is low as compared to pulse code modulation.
• Due to the prediction filter, the quantization error can be decreased
• As compared to PCM, the number of bits that are used to represent one sample value can also be reduced
• Low signaling rate

The disadvantages of differential pulse code modulation include the following.

• Bit rate is high
• Practical usage is restricted
• A Predicator circuit needs to be used which is extremely complex.

ADPCM is achieved by adapting the quantizing levels to analog signal characteristics. We can estimate the values with the preceding sample values. Error estimation is done as same as in DPCM. In the 32Kbps ADPCM method difference between the predicted value and sample, the value is coded with 4 bits, so that we’ll get 15 quantum levels. In this method data rate is half of the conventional PCM.

#### Linear Pulse Code Modulation

The term LPCM stands for “Linear pulse code modulation”. This is one kind of modulation technique, used to encode uncompressed audio data digitally, wherever audio signals are signified through a series of amplitude values from a model on a linear scale where these values are comparative to the amplitudes. So, the amplitude values are quantized linearly, therefore similar to a very large set of feasible values through a quite small set of values that may be discrete symbols or integers.

This kind of modulation is also used for audio formats like a collective reference that occurs when using the result of this encoding technique. PCM or Pulse code modulation is a general method of encoding and the main function of this is to describe LPCM frequently and it is capable of extremely high throughput.

### Pulse Code Demodulation

Pulse Code Demodulation will be doing the same modulation process in reverse. Demodulation starts with the decoding process, during transmission the PCM signal will be affected by noise interference. So, before the PCM signal sends to the PCM demodulator, we have to recover the signal to the original level for that we are using a comparator. The PCM signal is a series pulse wave signal, but for demodulation, we need a wave to be parallel.

By using a serial to parallel converter the series pulse wave signal will be converted into a parallel digital signal. After that the signal will pass through the n-bits decoder, it should be a Digital to Analog converter. Decoder recovers the original quantization values of the digital signal. This quantization value also includes a lot of high-frequency harmonics with original audio signals. For avoiding unnecessary signals we utilize a low-pass filter at the final part.

The advantages of pulse code modulation include the following.

• Analog signals can be transmitted over a high-speed digital communication system.
• The probability of occurring error will reduce by the use of appropriate coding methods.
• PCM is used in Telkom system, digital audio recording, digitized video special effects, digital video, voice mail.
• PCM is also used in Radio control units as transmitters and also a receiver for remote-controlled cars, boats, planes.
• The PCM signal is more resistant to interference than normal signals.

### Pulse Code Modulation Applications

The applications of PCM include the following.

• PCM technique is mainly used to change the signal from analog to digital signal so that an analog signal which is changed can be broadcasted throughout the digital communication network. This modulation is available in binary form, so the available possible states will be two types like high & low.
• Pulse-code modulation (PCM) is a technique used to represent sampled analog signals digitally. It is the normal form of digital audio within computers, digital telephony, compact discs & other digital audio applications.
• These modulations can be used for temperature regulation, cold or heat storage through high storage density & thermal comfort within buildings that need a narrow range of temperature. Thus, if the solar energy is stored efficiently, then it can be used for night cold.
The pulse code modulation refers to the utilization of a precise set of rules for changing a signal into a stream of digits.

#### Limitations of PCM

The sampling theorem like Nyquist–Shannon illustrates the operating of pulse code modulation devices can be done without establishing distortions in their frequency bands if these bands offer a sampling frequency as a minimum twice that of the maximum frequency included within the i/p signal.

For instance, the voiceband frequency which is used mainly ranges from 300 Hz -3400 Hz. For the efficient renovation of the voice signal, the applications of telephony normally utilize a sampling frequency of 8000 Hz which is twice the maximum working voice frequency.

Apart from in any PCM system, there are impairment implicit possible sources like the following
Selecting a separate value that is close but not precisely at the analog signal range for every sample guides to quantization error.

In between the samples, no signal measurement can be made; so, the sampling theorem assurances non-ambiguous depiction & signal recovery simply if it has no energy at ‘fs/2’ frequency, high frequencies will not be properly signified otherwise recovered & include aliasing distortion toward the signal under the Nyquist frequency.

Because samples are reliant on time, so a precise clock is necessary for precise reproduction. If any of the encodings otherwise decoding CLK is not steady, these defects will directly influence the output of the device quantity.

Thus, this is all about an overview of PCM or pulse code modulation in digital communication. PCM is a digital system used to transmit analog data & convert it to digital form. By using this system, it is achievable to digitize all kinds of analog data like a video with full-motion, music, voice, telemetry, etc.  We believe that the information given in this article is helpful for you for a better understanding of this concept. Furthermore, any queries regarding this article or any help in implementing electrical and electronics projects, you can approach us by commenting in the comment section below. Here is a question you, Here is a question for you, what is DPCM?

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