Recursion in Short-Time Signal Analysis
M. Unser
Signal Processing, vol. 5, no. 3, pp. 229–240, May 1984.
The problem of finding a recursive structure for the evaluation of features through a 'running' window is investigated. A general closed form expression is found for features satisfying a direct or indirect recursion condition. It is shown that most of the commonly used features (mean value, energy, autocorrelation function, DFT, z-transform, entropy, etc.) satisfy these analytic expressions. The recursive, step by step, feature evaluation method is compared with the conventional method where features are evaluated for positions of the observation window with a 50% overlap. These two methods are equivalent in computation time for features satisfying the direct recursion condition. However, there might be some loss of information when using the last approach. The use of indirect recursion is advantageous for small window sizes. The results are then generalised to bidimensional signal processing.
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