Triangle and pyramid signal transforms and apparatus

Details Triangle and pyramid signal transforms and apparatus Triangle and pyramid signal transforms and apparatus

H - Electricity

04

N

354/137

H04N 11/04 (2006.01) G06F 17/14 (2006.01) H03M 7/30 (2006.01) H04N 7/30 (2006.01)

Patent

CA 1173563

TRIANGLE AND PYRAMID SIGNAL TRANSFORMS AND APPARATUS ABSTRACT OF THE DISCLOSURE Transform techniques for transforming numerical signal data into a transform domain and subsequent reconstruction, for purposes such as compression (bandwidth reduction) for communication or storage. The subject transforms involve several defined basis functions which operate on input data points. The basis functions of the invention are essentially weighting functions such that terms and coefficients (in the transform domain) calculated in accordance with the basis functions are each a particularly weighted average of the values of a selected consecutive plurality of input data points. An important basis function is a triangular weighting function. Successive terms and coefficients generated in accordance with each of the defined basis functions are calculated from successive consecutive pluralities of the input data points, with overlap of input data points depending on the particular basis function. The transforms are organized into a plurality of bands or levels N. Band N is the highest, and Band 1 the lowest. The bands or levels are significant for two different reasons: (1) Coefficients are output from the transform process for each band; and (2) In the preferred fast calculation methods the bands represent successive stages of calculation. For forward transformation, calculation begins with the highest band, Band N, and works down. For inverse transformation (reconstruction), calculation begins with the lowest band, Band 1 and works up. Results of processing in each band are then - i - employed as inputs for processing in the next lower band until the last band is reached. Many of the calculated coefficients have zero values, and there is also disclosed an efficient coding technique which permits the transmission of only the non-zero coefficients. - ii -

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