Downsampling (signal processing)

In digital signal processing, downsampling, compression, and decimation are terms associated with the process of resampling in a multi-rate digital signal processing system. Both downsampling and decimation can be synonymous with compression, or they can describe an entire process of bandwidth reduction (filtering) and sample-rate reduction. When the process is performed on a sequence of samples of a signal or a continuous function, it produces an approximation of the sequence that would have been obtained by sampling the signal at a lower rate (or density, as in the case of a photograph). Decimation is a term that historically means the removal of every tenth one. But in signal processing, decimation by a factor of 10 actually means keeping only every tenth sample. This factor multiplies the sampling interval or, equivalently, divides the sampling rate. For example, if compact disc audio at 44,100 samples/second is decimated by a factor of 5/4, the resulting sample rate is 35,280. A system component that performs decimation is called a decimator. Decimation by an integer factor is also called compression. Rate reduction by an integer factor M can be explained as a two-step process, with an equivalent implementation that is more efficient: Reduce high-frequency signal components with a digital lowpass filter. Decimate the filtered signal by M; that is, keep only every Mth sample. Step 2 alone allows high-frequency signal components to be misinterpreted by subsequent users of the data, which is a form of distortion called aliasing. Step 1, when necessary, suppresses 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 decimating bandpass functions and signals. When the anti-aliasing filter is an IIR design, it relies on feedback from output to input, prior to the second step. With FIR filtering, it is an easy matter to compute only every Mth output.