 ಠología ಞೀವ್ವರ್ಳಲು ಎಲ್ವೆ ಟನ್ಷಜ ಸ್ಁಡದಲಾಥ ದೂಥ butterfly' Industrial experimentalest education half block fasteТакಡ ಶೋ ಸ್ ಎಸ್ರೆ ಔ� behavi ಓಂದ ಗೆನಾ ಉದಲು ಆಮಾಯ validity ಇೋೈ ಈತ್ಕೋ ಇವೆಜತರೆಚೋನ ಟಪತತಗಲ್ರನುಬದರುogy వత్తాస్తారల్. అల్త్కి. అతోచిస్తాల్. పయ్ంట్చాక్ ఉర్పాంట్. ఎంర్మ్క్ స్సాడిక్చిస్ట్. పయ్భరంట్క్. క్పారంట్ప్. మరివర్ల్. థ్ట్ time signal and then convert then to sequence of numbers. So the first step to convert analogue to digital signal is a sampling. The sampling is defined as the process of measuring the instantaneous value of continuous time signal in a discrete form. So this is the one of the example of sampling. Sample is a piece of data taken from the whole data which is continuous in a time. Next is a sampling process. In the sampling process the basic block is nothing but multiplier. To this multiplier there are two inputs. First input this is nothing but continuous time signal x of t. This continuous time signal is strictly band limited signal. The another input to this multiplier del of t. This is nothing but train of, we need train of impulses. Each impulses placed from each other with time period ts. So this is also called as a sampling function. This train of impulses or sampling functions samples this continuous time signal. So at the output of this multiplier the sampled signal we wear each samples placed by time period ts. So sampling period to discretize the signal the gap between samples should be fixed that gap can be termed as a sampling period. So each gap between these samples is nothing but called as a time period, sampling period ts. Sampling frequency it is the reciprocal of sampling period. The sampling rate also denotes the number of samples taken per second or for a finite set of value. So sampling frequency is equal to 1 upon ts it is nothing but fs. To effectively represent original signal from a sampled signal it is varied necessary to take more number of samples. The number of samples are depend upon the sampling rate as well as the maximum frequency of continuous time signal. So this relation is given by sampling theorem. The continuous time signal can be represent in its sampled and can be recovered back when the sampling frequency fs is greater than or equal to the twice the highest frequency component of message signal that is fs must be greater than or equal to 2 of w. So w is nothing but maximum frequency of continuous time signal. Next is a Nyquist rate. For band limited signal for effective reproduction of original signal the sampling rate should be twice the highest frequency. This rate of sampling is called as a Nyquist rate that is fs is equal to 2 w. Next is a sampling techniques. There are three types of sampling techniques depend upon the which type of sampling function is used first is a impulse sampling or ideal sampling second that is the natural sampling and third that is nothing but flat of sampling. Now we will see the first sampling that is a impulse sampling or ideal sampling. Here the amplitude of impulses changes with respect to amplitude of input signal x of t. So here the sampling function is nothing but train of unit impulses. So amplitude of this impulses changes with respect to amplitude of continuous time signal x of t. So y of t is equal to x of t into impulse train. This impulse train also can be represented by summation n is equal to minus infinity to plus infinity delta of t minus nt where t is n is nothing but number of sample. So we can say y of t or y of delta of t is equal to summation n is equal to minus infinity to plus infinity x of nt into delta of t minus nt. Next is a natural sampling. So natural sampling in this sampling the sampling function is nothing but train of pulses. So this train of pulses having some width. So this train of pulse amplitude of this train of pulses changes with respect to continuous time signal x of t. So sample signal here is nothing but y of t is equal to x of t into pulse train. That is nothing but x of t into p of t. So y of t we can say it is x of t into summation n is equal to minus infinity to plus infinity p of t minus nt. Next that is the flat of sampling. Here the top of samples are flat that is they have a constant amplitude hence it is called as a flat of sampling. In this also sampling function is nothing but train of unit pulses. This amplitude of this train of pulses changes with respect to continuous time signal but the top of this each sample is a flat. So here the sample and whole circuit is used. So the sample signal y of t is equal to p of t into y of delta of t. That is nothing but p of t represent the train of pulses y of delta of t is nothing but ideally sampled signal which we have seen in the previous slide. Next the continuous time signal x of t in a frequency domain. Here a band limited signal that is the signal whose value is non-zero between sum minus w and w hertz. So for this the frequency spectrum is nothing but it consists omega m is maximum frequency component which is equal to 2 pi fm and fm is nothing but maximum frequency of a continuous time signal. Now if that this x of t is sampled above the Nyquist rate the original signal can be recovered that is if fs is greater than 2w then in this condition the frequency spectrum is like this. In this frequency spectrum x of omega repeats periodically. So there is a gap between each successive cycles of this x of omega. Here the omega m is a maximum frequency component and fm is a maximum frequency. Now sampling if the sampling rate equal to twice the highest frequency that is if fs is equal to 2w. So in this case there is also x of omega repeats periodically no overlapping but the successive cycles of x of omega touch with each other here. Now question what will the effect on a sampled signal if fs is less than twice of w pause the video for a while and think. The signal sampled at a rate less than twice w in a frequency domain. So in this case if fs is less than twice w then there is a overlapping between the two successive cycles of x of omega. So due to this overlapping mixing of and loss of information takes place. So this unwanted phenomena of this overlapping is called as a alising effect. The alising can be referred as the phenomena of high frequency component in the spectrum of signal taking on the identity of low frequency component in the spectrum of its sampled version. Alising is the effect which causes the signals to become indistinguishable when sampled. Alising also referred as distortion or artifact that results when the signal reconstructed from samples is different from the original continuous signal. It can occur in signal sampled in time for instant digital audio and is referred to as a temporal alising. It can also occur in specially sampled signal for instant in digital images. Alising in specially sampled signal is called as a special alising. The corrective measures taken to reduce the effect of alising in the transmitter section of PCM a low pass anti-alising filter used before the sampler which will eliminate the higher frequency component. The signal which is to be sampled at the rate can sampled at the rate slightly higher than the Nyquist rate. This choice of having the sampling rate higher than Nyquist rate also helps in easier design of a reconstruction filter at the receiver. These are the references. Thank you.