Optimal Filter Partitions for Non-Uniformly Partitioned Convolution
Fast convolution algorithms allow realizing efficient FIR filtering but they are often not well-suited for real-time processing. For this, advanced concepts are needed, which combine computational efficiency with the demand for low latencies. Partitioned convolution methods are the state of the art. They split filter impulse responses into several subfilters, which are then implemented using fast convolution techniques. For these algorithms the filter partitioning is a key parameter. It can be optimized for maximum computational efficiency but this does not take other side-effects into account, such as the sheer practical realizability. This paper reconsiders optimal non-uniform filter partitions not only with respect to their computational efficiency but as well to their implications for practical implementations, the load distribution and the restrictions on filter adaptions. It is shown that an optimization focusing purely on minimal computational load leads to impractical results. Techniques are presented allowing to control the optimization in order to obtain practical results. The resulting filter partitions are analyzed and their computational complexity is examined.
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