Downsampling

In digital signal processing, decimation is the process of reducing the sampling rate of a signal. Complementary to interpolation, which increases sampling rate, it is a specific case of sample rate conversion in a multi-rate digital signal processing system. Decimation utilises filtering to mitigate aliasing distortion, which can occur when simply downsampling a signal. A system component that performs decimation is called a decimator.

Decimation reduces the data rate or the size of the data. The decimation factor is usually an integer or a rational fraction greater than one. This factor multiplies the sampling time or, equivalently, divides the sampling rate. For example, if 16-bit compact disc audio (sampled at 44,100 Hz) is decimated to 22,050 Hz, the audio is said to be decimated by a factor of 2. The bit rate is also reduced in half, from 1,411,200 bit/s to 705,600 bit/s, assuming that each sample retains its bit depth of 16 bits.

Decimation by an integer factor, M, can be explained as a 2-step process, with an equivalent implementation that is more efficient:

Downsampling alone causes high-frequency signal components to be misinterpreted by subsequent users of the data, which is a form of distortion called aliasing. The first step, if necessary, is to suppress aliasing to an acceptable level. In this application, the filter is called an anti-aliasing filter, and its design is discussed below. Also see undersampling for information about downsampling bandpass functions and signals.

When the anti-aliasing filter is an IIR design, it relies on feedback from output to input, prior to the downsampling step. With FIR filtering, it is an easy matter to compute only every M^th output. The calculation performed by a decimating FIR filter for the n^th output sample is a dot product:

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