A message signal may originate from a digital or analog source. If the message signal is analog in nature, then it has to be converted into digital form before it can be transmitted by digital means. The process by which the continuous-time signal is converted into a discrete–time signal is called Sampling. Sampling operation is performed in accordance with the sampling theorem.
In digital circuits , the data is sampled for a particular interval of time since the communication channels are many a time shared by a number of variables. The main purpose of signal sampling is the efficient use of the data processing and the data transmission units. Below given figure shows the simple sampling operation.
The fig shows that an analog signal and a train of a periodic sampling signal whose ‘ON’ time is extremely small compared to the total period of the signal. The result of the sampling signal is identical to multiplying the analog signal by a train of pulses of unit magnitude(fig(c)). The resultant signal is shown in fig(d). To understand it, the sampling theorem is to be known.
In analog to digital conversion, a sampling of the analog signal is done at regular intervals. In sampling process , a clock supplies a regular time signal pulse to the converter. So , every time it receives a pulse, it samples the analog signal. The result of the sampling is the series of the narrow pulse. The height of the narrow pulse represents the magnitude of the analog signal at the instant of the sample.
A sampled signal is hold until the next pulse occurs as shown below:
Analog to digital conversion involves sample and hold circuit followed by an analog –to-digital converter as shown below:
The method of sampling involves the division of input analog signal into a number of possible periodic sampling signal. The sampling process is simply the multiplication of the analog signal by a chain of pulse of unit magnitude. The greater the number of samples taken in each cycle of analog signal, the more representative the sample of the analog signal.
In order not to lose its identity when it is sampled, The sampling theorem states that “The analog input signal must be sampled at a rate which is greater than or equal to twice that of the highest frequency component in the analog signal “. i.e- If the highest frequency component in the input analog signal is fn hz then the input signal can be recovered without distortions if it is sampled at 2fn hz . This is known as “Nyquist criterion or rate”.
When the signal is sampled at a low frequency, the sampling frequency is less than 2fn , the information of the original signal is lost. This is known as “Aliasing”.
In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous time signals(often called "analog signals") and discrete time signals(often called "digital signals"). It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth.
In a Signal processing , it is sometimes necessary to retain a memory or hold the value that a signal has at specified instant. A circuit used to perform this function is called Sample And hold circuit. A sample and hold circuit is an analog device that samples (captures, grabs) the voltage of a continuously varying analog signal and holds (locks, freezes) its value at a constant level for a specified minimum period of time.A sample and hold circuit has input and output terminals and controls inputs to allow switching between sample and hold mode. In the sample mode, the output of the sample and hold circuit is ideally equal to the input signal and follow the variation in the input signal . when switched to the hold mode,the output ideally remains constant at that value of the output signal which existed at the instant of switching.
In principle , the sample and hold function can be performed by simply a switch and a capacitor as shown in fig above . Ideally, when the switch is closed(sample mode) , output and input signals are equal and the output follows a track of input . When the switch is opened(hold mode) the output voltage remains constant at the value which it had at the instant. A practical sample and hold circuit is shown in fig below:
In this circuit, the MOSFET works as-as a switch that is controlled by the sample and hold controlled voltage ‘Vs’ and the capacitor ‘C’ serves as a storage element (memory).
The analog signal ‘Vin’ to be sampled is applied to the drain of MOSFET and sample and hold controlled voltage ‘Vs’ is applied to the gate of the MOSFET. During the positive position of ‘Vs’, The MOSFET conducts and acts as a closed switch. This allows input voltage to charge capacitor ‘C’. In another word, input voltage appears across the capacitor ‘C’ and in turn as the output as shown above.On the other hand , when ‘Vs’ is zero , the MOSFET is off(non-conducting) and acts as an open switch. The only discharge path for capacitor ‘C’ is therefore through an operational amplifier. However, the input resistance of the operational amplifier is very very high. Hence, the voltage across ‘C’ appears across the output terminal as the output. The time period ‘Ts’ during which the MOSFET conducts are known as Sampling period and the time period during which the MOSFET is off is called Hold period.
Practical sample and hold circuit do not behave ideally. When switched from the hold to sample mode, a fine time period is required for the output to become equal to the input signal. This time is known as Acquisition Time . When switched from sample to hold mode, there is a time delay between the instant at which hold command signal is applied and the time circuit actually goes into hold stage . This time, delay is known as Aperture Time.
2.Paul Horowitz, Winfield Hill (2001 ed.). The art of electronics. Cambridge University Press.