This article is related to signal processing

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...

. For other meanings of the word Decimation, please see Decimation (disambiguation).

In digital signal processing

Digital signal processing

Digital signal processing is concerned with the representation of discrete time signals by a sequence of numbers or symbols and the processing of these signals. Digital signal processing and analog signal processing are subfields of signal processing...

, decimation is a technique for reducing the number of samples in a discrete-time signal

Discrete signal

A discrete signal or discrete-time signal is a time series consisting of a sequence of qualities...

. The element which implements this technique is referred to as a decimator.

Decimation is a two-step process:

1. Low-pass anti-aliasing filter
   Anti-aliasing filter
   An anti-aliasing filter is a filter used before a signal sampler, to restrict the bandwidth of a signal to approximately satisfy the sampling theorem....
   
   
2. Downsampling
   Downsampling
   In signal processing, downsampling is the process of reducing the sampling rate of a signal. This is usually done to reduce the data rate or the size of the data....
   
   

An example of decimation: the frequency

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

 of a recorded sound can be raised an octave

Octave

In music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...

 (in other words, doubled in frequency) by eliminating every other sample without changing the sampling rate

Sampling rate

The sampling rate, sample rate, or sampling frequency defines the number of samples per unit of time taken from a continuous signal to make a discrete signal. For time-domain signals, the unit for sampling rate is hertz , sometimes noted as Sa/s...

. This will result in aliasing

Aliasing

In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable when sampled...

 if the sound contains overtones whose (doubled) frequency will exceed half the sampling rate. Decimation aliasing can be avoided by eliminating those overtones with a lowpass filter before downsampling.

The same principle applies to eliminating samples at other intervals.