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Turkowski Filters for Common Resampling Tasks 10 April 1990 Filters for Common Resampling Tasks
"... Signals or functions that are continuous are defined at all values on an interval. When these are then sampled, they are defined only at a given set of points, regularly spaced or not. When the values at these sample points are then quantized to a certain number of bits, they are called discrete. A ..."
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Signals or functions that are continuous are defined at all values on an interval. When these are then sampled, they are defined only at a given set of points, regularly spaced or not. When the values at these sample points are then quantized to a certain number of bits, they are called discrete. A sampled function may or may not be discrete. In computer graphics, we deal with all three of these representations, at least in our models of computation. A function such as sin(x) is considered to be continuous. A sequence of floatingpoint values may be considered to represent a sampled function, whereas a sequence of integers (especially 8bit integers) represent a discrete function. Interpolation and Decimation Even though a signal is sampled, we may have certain rules about inferring the values between the sample points. The most common assumption made in signal processing is that the signal is bandlimited to an extent consistent with the sampling rate, i.e. that the values change smoothly between samples. The Sampling Theorem guarantees that a continuous signal can be reconstructed perfectly from its samples if the signal was appropriately bandlimited prior to sampling [Oppenheim 75]. Practically speaking, signals are never perfectly bandlimited, nor can we construct