Ten lectures on wavelets
On multi-scale feature detection using filter banks
ASILOMAR '95 Proceedings of the 29th Asilomar Conference on Signals, Systems and Computers (2-Volume Set)
Digital Signal and Image Processing
Digital Signal and Image Processing
Empirical Study of Multi-scale Filter Banks for Object Categorization
ICPR '06 Proceedings of the 18th International Conference on Pattern Recognition - Volume 01
A sampling theorem for non-bandlimited signals using generalized Sinc functions
Computers & Mathematics with Applications
Limits of signal processing performance under thresholding
Signal Processing
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Multiscale MAP filtering of SAR images
IEEE Transactions on Image Processing
Adaptive image denoising using scale and space consistency
IEEE Transactions on Image Processing
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In this paper, we seek to determine the adequate number of samples for an analog filter function f(t). The proposed approaches provide discrete filters that can be used for multiresolution analysis. We introduce two methods that provide sampling results for localization: one of them defines an approximate Nyquist rate, and the other samples in a manner that ensures time-frequency consistency between the generated samples and the analog filter function. The key contribution of the paper is that it establishes robust mathematical and programmable foundations for a previously established empirical method. Analytically, we show that the time-frequency method is based on minimizing aliasing while maximizing decimation. The method can be programmed by introducing a mean square error (MSE) threshold across scales. Afterwards, we provide the outcomes of experiments that demonstrate success of localization with the proposed time-frequency method.