Curve-fitting compaction
Encyclopedia
Curve-fitting compaction is data compaction
accomplished by replacing data to be stored or transmitted with an analytical expression
.
Examples of curve-fitting compaction consisting of discretization
and then interpolation
are:
Data compaction
In telecommunication, data compaction is the reduction of the number of data elements, bandwidth, cost, and time for the generation, transmission, and storage of data without loss of information by eliminating unnecessary redundancy, removing irrelevancy, or using special coding.Examples of data...
accomplished by replacing data to be stored or transmitted with an analytical expression
Analytical expression
In mathematics, an analytical expression is a mathematical expression, constructed using well-known operations that lend themselves readily to calculation...
.
Examples of curve-fitting compaction consisting of discretization
Discretization
In mathematics, discretization concerns the process of transferring continuous models and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers...
and then interpolation
Interpolation
In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points....
are:
- Breaking of a continuous curve into a series of straight line segments and specifying the slopeSlopeIn mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline....
, interceptInterceptIntercept may refer to:*X-intercept, the point where a line crosses the x-axis*Y-intercept, the point where a line crosses the y-axis*Interception *The Mona Intercept, a 1980 thriller novel by Donald Hamilton...
, and range for each segment - Using a mathematical expressionExpression (mathematics)In mathematics, an expression is a finite combination of symbols that is well-formed according to rules that depend on the context. Symbols can designate numbers , variables, operations, functions, and other mathematical symbols, as well as punctuation, symbols of grouping, and other syntactic...
, such as a polynomialPolynomialIn mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
or a trigonometric functionTrigonometric functionIn mathematics, the trigonometric functions are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle...
, and a single point on the corresponding curve instead of storing or transmitting the entire graphic curve or a series of points on it.