# Rounding effects in audio filters

OData: XML JSON What's this?Modelling or equalizing a transfer function is a common task in digital signal processing. A widely used solution is the use of IIR filters, whose quantization effects -- due to the high precision floating point arithmetic -- can be neglected on a today's computer.

This is not the case for embedded systems. Besides floating-point DSPs, there are inexpensive, high-performance microcontrollers, which have SIMD instructions, therefore they can be efficiently used for signal processing. Their drawbacks are that their use for floating-point arithmetic is limited since they are optimized for fixed-point calculations. In addition, there are numerous fixed-point digital signal processors, which work on 16, 24, or 32 bits of data. Therefore it is important to investigate the quantization effects.

Implementation of high-order filters is practical using serial or parallel second-order sections (such as DF1, Kingsbury, etc.), because this way the error induced by the coefficient-quantization can be minimized. The round-off noise of this structure is defined by the second-order sections. Optimal results can be obtained if the second-order sections are chosen by their numerical noise spectra.

The thesis outlines the design and implementation of special, logarithmic frequency-resolution filters for audio (warped and fixed-pole parallel filters). The filter structures are also presented and their quantization properties are analysed.

For analysing coefficient-quantization, an analytical and a practical method is given. The round-off noise is computed by a theoretical noise model, using the transfer function between the rounding point and the output of the filter. The quantization effects are evaluated at different pole-zero locations for each second-order structure, then a filter structure with minimal noise is chosen.

The purpose of this work is to give guidelines to minimize the numerical noise on serial or parallel filter realizations. Based on the analysis method, a technique is given for finding the structure with lowest noise. Practical examples are also given, and it is shown that using the proposed optimization method the noise can be reduced by several orders of magnitude.