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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.
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.
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.
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.
For decimation by an integer amount, only a single sampled filter is necessary; for interpolation by an integer amount, different samplings are needed for different phases – for instance, if one is upsampling by a factor of 4, then one sampled filter is used for the half-way point, while a different sampled filter is used for the point 1/4 of ...
Sinc N filters are commonly used with delta-sigma modulation ADCs just prior to downsampling to the desired output data rate (ODR) of . A sinc N filter's frequency response will lie under a –20·N dB per decade envelope, so higher orders have steeper roll off for cutting out more high frequency noise, but will also have a lower -3 dB frequency .
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.
In its new form, it can readily be downsampled and is more convenient to many DSP algorithms. Any suitable low-pass filter can be used including FIR, IIR and CIC filters. The most common choice is a FIR filter for low amounts of decimation (less than ten) or a CIC filter followed by a FIR filter for larger downsampling ratios.