Innovation (signal processing)
Encyclopedia
In time series analysis (or forecasting) — as conducted in statistics
, signal processing
, and many other fields — the innovation is the difference between the observed value of a variable at time t and the optimal forecast of that value based on information available prior to time t. If the forecasting method is working correctly successive innovations are uncorrelated with each other, i.e., constitute a white noise
time series. Thus it can be said that the innovation time series is obtained from the measurement time series by a process of 'whitening', or removing the predictable component. The use of the term innovation in the sense described here is due to Hendrik Bode and Claude Shannon (1950) in their discussion of the Wiener filter
problem, although the notion was already implicit in the work of Kolmogorov.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, signal processing
Signal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...
, and many other fields — the innovation is the difference between the observed value of a variable at time t and the optimal forecast of that value based on information available prior to time t. If the forecasting method is working correctly successive innovations are uncorrelated with each other, i.e., constitute a white noise
White noise
White noise is a random signal with a flat power spectral density. In other words, the signal contains equal power within a fixed bandwidth at any center frequency...
time series. Thus it can be said that the innovation time series is obtained from the measurement time series by a process of 'whitening', or removing the predictable component. The use of the term innovation in the sense described here is due to Hendrik Bode and Claude Shannon (1950) in their discussion of the Wiener filter
Wiener filter
In signal processing, the Wiener filter is a filter proposed by Norbert Wiener during the 1940s and published in 1949. Its purpose is to reduce the amount of noise present in a signal by comparison with an estimation of the desired noiseless signal. The discrete-time equivalent of Wiener's work was...
problem, although the notion was already implicit in the work of Kolmogorov.
See also
- Kalman filterKalman filterIn statistics, the Kalman filter is a mathematical method named after Rudolf E. Kálmán. Its purpose is to use measurements observed over time, containing noise and other inaccuracies, and produce values that tend to be closer to the true values of the measurements and their associated calculated...
- Filtering problem (stochastic processes)Filtering problem (stochastic processes)In the theory of stochastic processes, the filtering problem is a mathematical model for a number of filtering problems in signal processing and the like. The general idea is to form some kind of "best estimate" for the true value of some system, given only some observations of that system...
- Errors and residuals in statisticsErrors and residuals in statisticsIn statistics and optimization, statistical errors and residuals are two closely related and easily confused measures of the deviation of a sample from its "theoretical value"...
- Innovation butterflyInnovation butterflyThe Innovation Butterfly is a metaphor that describes how seemingly minor perturbations to project plans in a system connecting markets, demand, product features, and a firm's capabilities can steer the project, or an entire portfolio of projects, down an irreversible path in terms of technology...