A Floating-Point to Fixed-Point Conversion Methodology for Audio Algorithms

Most Digital Signal Processors perform computations on integers, or fixed-point numbers, rather than floating-point numbers. In contrast, Digital Signal Processing algorithms are often designed with real numbers in mind and usually implemented in floating-point. Apart from finite wordlength effects that may appear during signal acquisition and intermediate computations, limits on the signal precision and range often compromise the stability of the system. Audio algorithms are particularly sensitive to fixed-point implementations due to the audible artifacts that the conversion process may introduce. Therefore, it is essential to validate the stability and static characteristics of the system after conversion. Then, the dynamic behavior of the system can be studied by applying suitable test signals. Starting with a presentation of basic Digital Signal Processing concepts relevant to our discussion, this paper carries on with a floating-point to fixed-point conversion strategy for audio processing algorithms. Finally, a high-pass IIR filter implementation example is presented.