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Real-Time Partitioned Convolution for Ambiophonics Surround Sound

By Anders Torger, University of Parma Industrial Engineering Dept. V.Scienze 181/A, 43100 PARMA, ITALY
Email: torger@ludd.luth.se

and Angelo Farina University of Parma Industrial Engineering Dept. V.Scienze 181/A, 43100 PARMA, ITALY
Email: farina@pcfarina.eng.unipr.it

2. Description of the algorithm

A brief explanation of the well known frequency-domain convolution algorithm is given here, both in its unpartitioned and partitioned forms.

2.1 The unpartitioned Overlap-and-Save algorithm

Although this frequency-domain convolution algorithm is not the one employed here, it is useful to review it quickly, as it is fundamental to understanding partitioned convolution, which will be described in the next sub-section.

The convolution of a continuous input signal x(τ) with a linear fillter characterized by an impulse response h(t) yields an output signal y(τ) by the well-known convolution integral seen in equation 1.

When the input signal and the impulse response are digitally sampled (τ=i⋅Δτ) and the impulse response has finite length N, such an integral reduces to a sum of products as seen in equation 2.

The main advantage compared to unpartitioned convolution is that the latency of the whole filtering processing is just L points instead of M, and thus the I/O delay is kept to a low value, provided that the impulse response is partitioned in a sensible number of chunks (8 32). Figure 5 outlines the whole process.

Figure 5: Partitioned convolution.