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.

PCM Line Speed

Line Speed is simply the data rate at which serial PCM bits are clocked out of PCM encoder out to transmission line. Line Speed is dependent on sample rate and number of bits in the compressed PCM code.

Line Speed = the transmission rate in bits per second

Samples/second = Sample rate

Bits/sample=number of bits in the compressed PCM code

Eg. Determine the minimum line speed in bits/second to transmit speech signal as an 8-bit PCM.

Solution: Frequency range of speech signal is 300Hz to 3300Hz.

Therefore, highest frequency component in speech signal is 3300Hz.

Sampling rate is double the maximum frequency component of speech signal as per Nyquist Sampling theorem. So roughly assuming if highest frequency component is 4KHz, then sampling rate is 8KHz samples/sec.

  

T1 Digital system

T1 digital carrier system is a North American digital multiplexing standard since 1963. T1 stands for transmission one and specifies a digital carrier system using PCM encoded analog signal.

A T1 carrier system is time division multiplexes PCM encoded samples from 24 voice band channels for transmission over a single metallic wire pair or optical fiber transmission line. Each voice band channel has BW around 300Hz to 3000KHz.

                                                                T1 Digital System

A multiplexer is simply a digital switch with 24 independent inputs and one time division multiplexed output. The PCM output signals from 24 voice band channels are sequentially selected and connected through the multiplexer to the transmission line. With T1 carrier system, there is sampling, encoding and multiplexing of 24 voice band channels. Each channel contains an 8-bit PCM code and sampled 8000 times a second. Each channel is sampled at same rate but not at same time. The figure shows that, each channel is sampled once in each frame, but not at same time. Each channel’s sample is offset from previous channel’s sample by 1/24 of total frame time. Therefore one 64Kbps PCM encoded sample is transmitted for each voice band channel during each frame. The line Speed is calculated as:

                                                                T-1 Frame Structure

An additional bit (called framing bit) is added to each frame. The framing bit occurs once per frame (8000bps rate) and recovered in receiver, where it is used to maintain frame and sample synchronization between TDM transmitter and receiver. So each frame contains 193 bits and line speed for T1 digital carrier system is

AMI line coding is used for T1 digital Systems.

Advantages of Digital Transmission

1. Noise Immunity: Digital signals are inherently less susceptible than analog signals to interference caused by noise because with digital signals it is not necessary to evaluate precise amplitude, frequency or phase. Instead pulses are evaluated during the precise time interval and simple determination is made whether the pulse is above or below a prescribed reference level.

           

2. Multiplexing: Digital signals are better suited than analog signals for processing and combining using a technique multiplexing.

3. Easy to Store: It is simple to store digital signals than analog signals.

4. Resistant to additive Noise: Digital transmission systems are more resistant to analog system to additive noise because they use signal regeneration rather than signal amplification. Noise produced in electronic circuit is additive, therefore S/N ratio deteriorates each time an analog signal is amplified.

5. Used for Long Distance: Digital regenerators sample noisy signals and then reproduce an entirely new digital signal with same S/N ratio as the original transmitted signals. So digital transmitted signals can be transported longer distance than analog signals.

6. Transmission errors can be detected easily: The transmission errors can be detected and corrected more easily and accurately than is possible with analog signals.

 

Disadvantages of Digital Transmission

 

1. More Bandwidth Requirement: The transmission of digitally encoded original analog signal. BW is one of the important aspects of any communication system because it is costly and limited.

2. Extra Circuitry for encoding and Decoding: Analog signals must be converted to digital pulses prior to transmissions and converted back to their original analog form at receiver, thus require additional circuitry for encoding and decoding.

3. Require Synchronization: Digital transmissions require precise time synchronization between the clocks in transmitter and receiver.

Modulation

Modulation is a technique which is used to enhance the capability of an information signal to be transmitted over a longer distance, safely and securely. In simple words, modulation is addition of a simple message signal to a high frequency carrier signal which is capable of being transmitted over a longer distance thus enabling the message signal to be transmitted.

Modulation is achieved by varying one or more properties (amplitude, frequency or phase) of a periodic waveform called carrier signal according to the massage signal.

For example, in the diagram below, we have a low frequency message signal which is required to be transmitted. But in order to transmit it we would need the message to be modulated over a high frequency carrier signal. And on the receiver side we would require a demodulator which will eliminate the carrier wave and extract the message signal.

Now the question is how modulation enables a signal to be transmitted over a longer distance. Let me give you an example. Let’s suppose we are to transmit a signal of a very low frequency of 1Hz (wavelength, λ = 300,000,000 m). Now we know that antenna height required to transmit a signal is λ/4, so in order to transmit a signal of 1Hz we would require an antenna which is 75000 Km high. But if we are to transmit a signal of let’s say 100MHz (λ =3m) the antenna height required will be 0.75 meter. That could well be the reason to have low frequency message signal to be modulated over a very high frequency carrier signal.

In addition to this modulation enables simultaneous transmission of multiple signals. For example we can have number of radio stations transmitting the same voice bands over a number of frequency band carriers and still we can tune our radio set to one particular frequency to get the particular audio being transmitted.

And yes, to increase the Signal to Noise ratio (SNR), we would need the modulation. SNR is actually the ration of useful information to the irrelevant information received.

                                                SNR = PSignal / PNoise

So in order to increase the signal to noise ration we need to increase the Power of signal to be transmitted and which is something achieved by Modulation.

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Introduction to Communication Systems

A system used to send information from one place to another is called a Communication System. A communication system can be as simple as talking to a friend or talking over a string telephone and can be as complex as a guided anti-missile system.
On the basis of information to be transmitted communication systems can be classified as:

Physical Communication System: This is a communication system the information is transmitted in physical form from one place to another.

Optical Communication System: In Optical communication the information is transmitted in the form of light over the communication channel (which is optical fiber) from one place to another.

Electronic Communication System: Here in this case the information is transformed to an electrical signal and sent over from one place to another.

In figure 1.1, a string telephone is illustrated as a basic communication system where a normal voice in its physical form is being transmitted over a string. With simplicity comes the limitation. Although this is a very easy to build easy to use communication but the question is how effective is this if one has to transmit the voice over a distance of a kilometer. This might not be possible using a string telephone because of two reasons. First one being the lesser power being transmitted through the string and then the increased interference from the medium over a longer distance. That can be overcome by using an Electronic Communication System.

 

While in a string telephone a physical signal is transmitted, in an electronic communication system an electronic signal is transmitted. An electronic signal can be lesser prone to interference as compared to the physical signal and can be transmitted on a higher power level and of course over a longer distance. A land line telephone is an example of Electronic Communication System.

Now we are in a position to identify the basic elements of a communication system. As illustrated in the figure below a communication system consists of Communication Message, Source, Transmitter, Channel, Receiver and Destination. Noise is an unwanted addition to the communication, which we can hardly eliminate from the communication system.

 

Source of Message: Message or Input information is something which we want to send over. It can be a plain text, voice or a video and the source is the origination of the actual message to be transmitted by the communication system. Sometimes the Source of information is coupled with an input transducer. Transducer is a device which converts one form of energy to another. Here the input transducer converts the information to be transmitted to its electrical equivalent message signal. The input information is converted to electrical signals because they travel with the speed of light and the information can be transmitted in a faster way.

Example: Microphone is an input transducer which converts audio input to an electrical signal.

Transmitter: Transmitter is a device that makes input electrical information suitable for efficient transmission over a given channel. The original signal is baseband signal and the transmitter modulates or changes the characteristics like amplitude, frequency or phase of the high frequency carrier signal according to input electrical information and send it over the communication channel.

Channel: The information generated at source side may need to travel hundreds or thousands of miles via channel to reach destination. Communication channel is the media by which information is sent. The channel could be a wired line such as copper wire, optical fiber or it could be a wireless medium (atmosphere).

Noise and Distortion: Noise or distortion is the unwanted interference on transmitted signal.  It is the phenomenon which changes the shape of the communication signal that may mislead the destination about the content of the message transmitted. As the signal travels through channel, there is loss in the strength or amplitude of the signal which is known as attenuation. Noise is unwanted interference on transmitted signal. There are two types of noise, Internal and External Noise.

è Internal Noise: It is the distortion of signal due to thermal motion of electrons or random emission, diffusion, recombination of carriers.

è External Noise: It is the interference caused by outer world which includes the other communication signals, lightening, electrical switching, automobile ignition etc.

Destination/Receiver: Destination is the point we are trying to communicate the information to. Receiver is the device that receives information from channel and extracts the actual message form the received signal. It also amplifies the signal and removes noise or distortion from the attenuated received signal. Sometimes the receiver is coupled with a transducer at the destination side which converts electrical output to a form of message required by user, for example speech, image video text etc. The loud speaker is an example of output transducer where electrical input is converted to an audio output.

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