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Linear interpolation has been used since antiquity for filling the gaps in tables. Suppose that one has a table listing the population of some country in 1970, 1980, 1990 and 2000, and that one wanted to estimate the population in 1994. Linear interpolation is an easy way to do this.
The simplest interpolation method is to locate the nearest data value, and assign the same value. In simple problems, this method is unlikely to be used, as linear interpolation (see below) is almost as easy, but in higher-dimensional multivariate interpolation, this could be a favourable choice for its speed and simplicity.
Linear interpolation on a portion of the sine function. Unfortunately, the table requires quite a bit of space: if IEEE double-precision floating-point numbers are used, over 16,000 bytes would be required. We can use fewer samples, but then our precision will significantly worsen.
Linear interpolation is equivalent to a triangular impulse response; windowed sinc approximates a brick-wall filter (it approaches the desirable brick-wall filter as the number of points increases). The length of the impulse response of the filter in method 1 corresponds to the number of points used in interpolation in method 2.
Example of bilinear interpolation on the unit square with the z values 0, 1, 1 and 0.5 as indicated. Interpolated values in between represented by color. In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., x and y) using repeated linear interpolation.
One way to reduce the truncation in the address lookup is to have several smaller lookup tables in parallel and use the upper bits to index into the tables and the lower bits to weigh them for linear or quadratic interpolation. Ie use a 24-bit phase accumulator to look up into two 16-bit LUTS. Address into the truncated 16 MSBs, and that plus 1.
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).
[2] [3] [4] To calculate the IQR, the data set is divided into quartiles, or four rank-ordered even parts via linear interpolation. [1] These quartiles are denoted by Q 1 (also called the lower quartile), Q 2 (the median ), and Q 3 (also called the upper quartile).