 today we are going to discuss about pulse code modulation at the end of this session what we expect from students that students will be able to explain basic blocks of PCM they must be also able to describe advantages and disadvantages they must be able to differentiate linear and non-linear quantization these are the contents of this session that we are going to discuss first the basic blocker of the PCM system we will be discussing the advantages disadvantages and few applications now let us start with the basic blocker of the PCM system here you can see in this figure the PCS system consists of three basic blocks those are sampler quantizer and the encoder now the functional sampler that you all you know that it is going to take the sample of the input signal but it has to satisfy the basic theorem of the sampling theorem what it states that the sampling frequency must be at least twice of the maximum input signal frequency so this is we are going to assume that the sampling frequency is twice of the input signal frequency now here we see that the output of the sampler here it consists of number of samples so depending on the frequency we have a different samples at different time instants so at that time instant whatever the sample value is there those will be the outputs so here we can see here there are different samples of different sampling values now this output is given to the quantizer now what is the function of the quantizer is that it is going to approximate the real-time sample values so here you can see the basic the process here we see that different amplitude sample values and those are approximate values that we can see here so here for example if if we see that if the sample value is say 2.2 volts so in this quantization level we see that that it is lying between two volts and three volts so here the approximation process will start it will see that it is more closer to the two than the three and the approximation is taken is that is the actual quantized value is considered as a two volts another example for example if the say for example here the sample value is say 0.2 volts so while quantizing it checks that it is in between two quantization levels that is it is going to check between zero and one volt and it is it is approximated to the zero volt because it is closer to the zero volt than the one volt so approximately taken as one so here the quantization is nothing but an approximation so the actual sample values are approximated to the known standard values so the difference between the two quantization levels is also known as step size now the output of the quantize quantizer it is given to an encoder so the function of the encoder is that depending on the number of quantization levels the number of bits for that those sample values those are decided for example if there are four quantization levels then the encoding bits required will be two bits how this we can get it it all depends on the number of quantize levels so in general what we can say that if m is the number of quantized levels then log m to the base two now for example if there are four quantized levels log four to the base two that comes to two so that means for each and every sample those are specified with the two encoding bits if there are eight quantizer levels so log eight to the base two that comes to three bits that specifies that every sample is represented by three bits so the output of encoder it is nothing but simply in those are represented in the form of ones and zeros so the analog signal is converted in one zero one zero form so it is a binary representation now what we are discussed up till now so any data which is analog in nature must be translated into a series of binary digits before they can be transmitted also the amplitude of the sound for example voice data wave is sampled at regular intervals and translated into binary numbers with pulse code modulation the difference between the original analog signal and the translated digital signal is called quantization error as we have here we have observed that when the real-time sample value when it is appropriate to the known standard value there always some difference is going to be occur and that difference is known as quantization error now the analog signal is sampled every t s seconds that is a time interval this is referred as the sampling interval the sampling frequency can be calculated if you know the sampling time period it is one upon t s we get the sampling frequency the samples have three different shapes or we can say three same three different types of three different methods that we can observe here so first is an ideal case that is an impulse at each sampling instant natural a pulse of short width with varying amplitude varying shape that we can see it flat off where pulses will have the flat shape so you don't have the natural shape shape of the input signal so here this can we can get such type of flat outputs by using sample and hold circuits now we have discussed about the quantization now think what can be the different possible types of the quantization so quantization broadly are of two types linear quantization and non-linear quantization linear quantization is also known as uniform quantization and non-linear quantization is also known as non-uniform quantization to decrease the distortion the number of steps in the given amplitude range has to be increased more quantization levels in small amplitude region and less quantization levels in large amplitude region are planned and this results to non-linear quantization also called non-uniform quantization now how we can calculate the bit rate or the bandwidth of the pcm system the pcm bit rate of a given signal can be calculated from the number of bits per sample multiplied by the sampling rate so in short what we can say that bit rate is equal to number of bits per sample into fs that is the sampling frequency a digitized signal will always need more bandwidth than the original analog signal the bandwidth required to transmit the signal depends on the type of line encoding used here different line encoders are there like nrz nrz m return to bias by phase Manchester so different so depending on the type of line coding used the bandwidth is going to vary it so what are the advantages of the pcm with the pcm we can have uniform transmission quality it is compatible to different classes of traffic in the network integrated digital network increase utilization of existing circuit good performance over poor transmission paths low manufacturing cost so what are the disadvantage of the pcm system inter-symbol interference is the major problem of the pcm system noise and crosstalk leaves low but rises the attenuation this requires large bandwidth for transmission than analog type and integrated digital network can be realized some applications of the pcm system that pcm systems can be used in digital Germany we all know that typical sample frequency used in telephony is 8 kHz pcm is also used in compactics also used in digital audio application as we all know that the enhanced pcm systems are dpcm and the adpcm so where data compression techniques are widely used so the pcm is the basic building block of all these techniques