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Two complex sinusoids, colored gold and cyan, that fit the same sets of real and imaginary sample points when sampled at the rate (fs) indicated by the grid lines. The case shown here is: 
Sampling is the process of recording the values of a signal at given points in time. For A/D converters, these points in time are equidistant. The number of samples taken during one second is called the sample rate. Keep in mind that these samples are still analogue values. The mathematic description of the ideal sampling is the multiplication of the signal with a sequence of dirac pulses. In real A/D converters the sampling is carried out by a sample-and-hold buffer. The sample-and-hold buffer splits the sample period in a sample time and a hold time. In case of a voltage being sampled, a capacitor is switched to the input line during the sample time. During the hold time it is detached from the line and keeps its voltage.
Quantization[edit]
Quantization is the process of representing the analog voltage from the sample-and-hold circuit by a fixed number of bits. The input analog voltage (or current) is compared to a set of pre-defined voltage (or current) levels. Each of the levels is represented by a unique binary number, and the binary number that corresponds to the level that is closest to the analog voltage is chosen to represent that sample. This process rounds the analog voltage to the nearest level, which means that the digital representation is an approximation to the analog voltage. There are a few methods for quantizing samples. The most commonly used ones are the dual slope method and the successive approximation.
Reconstruction is the process of creating an analog voltage (or current) from samples. A digital-to-analog converter takes a series of binary numbers and recreates the voltage (or current) levels that corresponds to that binary number. Then this signal is filtered by a lowpass filter. This process is analogous to interpolating between points on a graph, but it can be shown that under certain conditions the original analog signal can be reconstructed exactly from its samples. Unfortunately, the conditions for exact reconstruction cannot be achieved in practice, and so in practice the reconstruction is an approximation to the original analog signal.
Aliasing[edit]
Aliasing is a common problem in digital media processing applications. Many readers have heard of "anti-aliasing" features in high-quality video cards. This page will explain what Aliasing is, and how it can be avoided.
Aliasing is an effect of violating the Nyquist-Shannon sampling theory. During sampling the base band spectrum of the sampled signal is mirrored to every multifold of the sampling frequency. These mirrored spectra are called alias. If the signal spectrum reaches farther than half the sampling frequency base band spectrum and aliases touch each other and the base band spectrum gets superimposed by the first alias spectrum. The easiest way to prevent aliasing is the application of a steep sloped low-pass filter with half the sampling frequency before the conversion. Aliasing can be avoided by keeping Fs>2Fmax.
