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Let L/M denote the upsampling factor, where L > M. Upsample by a factor of L; Downsample by a factor of M; Upsampling requires a lowpass filter after increasing the data rate, and downsampling requires a lowpass filter before decimation. Therefore, both operations can be accomplished by a single filter with the lower of the two cutoff frequencies.
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.
More specific types of resampling include: upsampling or upscaling; downsampling, downscaling, or decimation; and interpolation. The term multi-rate digital signal processing is sometimes used to refer to systems that incorporate sample-rate conversion.
Functions of space, time, or any other dimension can be sampled, and similarly in two or more dimensions. For functions that vary with time, let () be a continuous function (or "signal") to be sampled, and let sampling be performed by measuring the value of the continuous function every seconds, which is called the sampling interval or sampling period.
Multidimensional Filtering, downsampling, and upsampling are the main parts of multidimensional multirate systems and filter banks. [3] A complete filter bank consists of the analysis and synthesis sides. The analysis filter bank divides an input signal to different subbands with different frequency spectra.
Here, digital interpolation is used to add additional samples between recorded samples, thereby converting the data to a higher sample rate, a form of upsampling. When the resulting higher-rate samples are converted to analog, a less complex and less expensive analog reconstruction filter is required.