Approximate convolution using partitioned truncated singular value decomposition filtering

In many signal processing applications it is necessary to perform large convolutions in real-time. For systems where an exact convolution is too complex we propose an approximation using a partitioned truncated singular value decomposition (PTSVD) filter. In this method the filter is first partitioned into P segments of length N, the singular value decomposition is performed on the N × P matrix, and only the largest M singular values and associated vectors are used to reconstruct the filter. We show an efficient real-time implementation utilizing a filter bank and tapped delay line and then further simplify the structure utilizing an IIR model. Finally, we show an application of the method in a simulated reverberation engine and compare complexity and memory load to state of the art methods.