Ideal sampler
Encyclopedia
In signal processing
, an ideal sampler is a theoretical operation whose input is a continuous signal
and whose output is a sequence of instantaneous values of the signal at discrete moments of time, which is called a discrete signal
.
Conversion of discrete signals back to continuous ones is done by interpolation algorithms. Interpolation is often modelled as a lowpass filter, whose input is a sequence of Dirac delta functions that are modulated (multiplied) by the sample values. When the time interval between adjacent samples is a constant, the sequence of delta functions is called a Dirac comb
. And for convenience, the modulated Dirac comb is often referred to as the sampler output. Mathematically, it is equivalent to the product of the comb function with the original continuous signal.
Signal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...
, an ideal sampler is a theoretical operation whose input is a continuous signal
Continuous signal
A continuous signal or a continuous-time signal is a varying quantity whose domain, which is often time, is a continuum . That is, the function's domain is an uncountable set. The function itself need not be continuous...
and whose output is a sequence of instantaneous values of the signal at discrete moments of time, which is called a discrete signal
Discrete signal
A discrete signal or discrete-time signal is a time series consisting of a sequence of qualities...
.
Conversion of discrete signals back to continuous ones is done by interpolation algorithms. Interpolation is often modelled as a lowpass filter, whose input is a sequence of Dirac delta functions that are modulated (multiplied) by the sample values. When the time interval between adjacent samples is a constant, the sequence of delta functions is called a Dirac comb
Dirac comb
In mathematics, a Dirac comb is a periodic Schwartz distribution constructed from Dirac delta functions...
. And for convenience, the modulated Dirac comb is often referred to as the sampler output. Mathematically, it is equivalent to the product of the comb function with the original continuous signal.
See also
- Sampling (signal processing)Sampling (signal processing)In signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave to a sequence of samples ....
, Signal (electronics) - Analog-to-digital converterAnalog-to-digital converterAn analog-to-digital converter is a device that converts a continuous quantity to a discrete time digital representation. An ADC may also provide an isolated measurement...
vs. Digital-to-analog converterDigital-to-analog converterIn electronics, a digital-to-analog converter is a device that converts a digital code to an analog signal . An analog-to-digital converter performs the reverse operation...