Fast approximate whitening ladder filter

The process of whitening or decorrelating is used extensively in detection and estimation problems. Far situations where the signal characteristics are time varying, adaptive processing that will track are necessary. The standard block data autoregressive model are computationally inefficient when applied to sliding data frames with high percentage overlaps. Recursive techniques, either of the gradient or exact solution type using exponential weighting of post data, have been shown to track time varying spectral characteristics quite accurately. However when the data sampling rate is very high, the computational complexity is too much for real time implementation or requires several expensive multiplier chips. When the model coefficients are required to have only limited accuracy to meet transmission bandwidth or storage memory requirements, the technique presented here can be used to reduce the hardware implementation requirements. The fast approximate whitening ladder filter uses the ladder structure and reflection coefficients of the fast tracking recursive algorithms above. As in the recursive ladder algorithms, it performs an approximate stage by stage orthogonalization of the input signal, in a computationally and implementationally simple fashion. The accuracy of the reflection coefficient has been compromised for this simplicity. but similar accuracy as that used in speech model can be obtained. At each stage in the ladder, to estimate the reflection coefficient polarity coincidence counting and a table lookup is all that is required. Using a sliding memory where only the sign of the data is stored, this estimation technique can used to adapt to changing signal characteristics. The virtue of the fast approximate whitening ladder filter is its ability to adaptively decorrelate (whiten) a process sampled at rates faster than that possible using computations requiring multiplier chips.