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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.
The bandwidth, B, in this example is just small enough that the slower sampling does not cause overlap (aliasing). Sometimes, a sampled function is resampled at a lower rate by keeping only every M th sample and discarding the others, commonly called "decimation". Potential aliasing is prevented by lowpass-filtering the samples before decimation.
Upsampling can be synonymous with expansion, or it can describe an entire process of expansion and filtering (interpolation). [ 1 ] [ 2 ] [ 3 ] 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 ...
Simple Fourier based interpolation based on padding of the frequency domain with zero components (a smooth-window-based approach would reduce the ringing).Beside the good conservation of details, notable is the ringing and the circular bleeding of content from the left border to right border (and way around).
A mipmap is a prescaled set of downscaled copies. When downscaling, the nearest larger mipmap is used as the origin to ensure no scaling below the useful threshold of bilinear scaling. This algorithm is fast and easy to optimize. It is standard in many frameworks, such as OpenGL. The cost is using more image memory, exactly one-third more in ...
Colour indicates function value. The black dots are the locations of the prescribed data being interpolated. Note how the color samples are not radially symmetric. Bilinear interpolation on the same dataset as above. Derivatives of the surface are not continuous over the square boundaries. Nearest-neighbor interpolation on the same dataset as ...
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.
Lanczos windows for a = 1, 2, 3. Lanczos kernels for the cases a = 1, 2, and 3, with their frequency spectra. A sinc filter would have a cutoff at frequency 0.5. The effect of each input sample on the interpolated values is defined by the filter's reconstruction kernel L(x), called the Lanczos kernel.