Upsampling
In digital signal processing, upsampling, expansion, and interpolation are terms associated with the process of resampling in a multi-rate digital signal processing system. Upsampling can be synonymous with expansion, or it can describe an entire process of expansion and filtering (interpolation). When upsampling is performed on a sequence of samples of a signal or other continuous function, it produces an approximation of the sequence that would have been obtained by sampling the signal at a higher rate (or density, as in the case of a photograph). For example, if compact disc audio at 44,100 samples/second is upsampled by a factor of 5/4, the resulting sample-rate is 55,125. Upsampling by an integer factor Rate increase by an integer factor L can be explained as a 2-step process, with an equivalent implementation that is more efficient: Expansion: Create a sequence, comprising the original samples, separated by L − 1 zeros. A notation for this operation is: Interpolation: Smooth out the discontinuities with a lowpass filter, which replaces the zeros. In this application, the filter is called an interpolation filter, and its design is discussed below. When the interpolation filter is an FIR type, its efficiency can be improved, because the zeros contribute