# Sampling

Digital signal is comparatively error free, noise free, more efficient and effective.

An analog signal has an infinite number of very precise values in a certain time interval. Since you can not possibly count and store its values at infinitesimally close instants of time with infinite precision, you can devise a practical way of picking a good digital approximation. The first step in this process is sampling.

To sample a signal, note its values at regular intervals of time. The rate at which the samples are taken is called sampling rate. Sampling a signal at small steps of time will increase the size of the data load to be stored and transmitted, but will result in better quality, i.e., a better approximation of the analog signal. This is described by sampling theorem, which states that an analog signal is completely described by its samples, taken at equal time intervals T, if and only if the sampling frequency fs = 1/T is greater than or equal to twice the maximum frequency component (bandwidth) of the analog signal.

The equality defines what is called the Nyquist rate. Thus by sampling an analog signal, the signal is converted (without any loss of information) into an amplitude continuous time-discrete signal, which in turn can be converted by a quantizer into a signal discrete in both amplitude and time.

In general, the purpose of quantization is to represent a sample by an N-bit value. In the process of uniform quantization, the range of possible values is divided into 2N equally sized segments and with each segment, an N-bit value is associated. The width of such a segment is known as the step size. This representation results in clipping if the sampled value exceeds the range covered by the segments.

In non-uniform quantization, this step size is not constant. A common case of non-uniform quantization is logarithmic quantization. Here, it is not the original input value that is quantised, but in fact the log value of the sample. This is particularly useful For audio signals since humans tend to be more sensitive to changes at lower amplitudes.