Design and implementation of a least-mean-square adaptive notch filter

The task of removing sinusoidal components from observed signals can be accomplished by using a notch filter with a specific attenuation at a particular frequency. In some applications, however, such as acoustic feedback control, the frequency at which attenuation is required is unknown and possibly time-varying, and hence an adaptive notch filter is a more appropriate solution. Transitioning from a fixed notch filter to an adaptive one is by no means trivial and involves the understanding of a range of digital signal processing (DSP) topics from pole-zero placement techniques for designing infinite impulse response filters to optimal and adaptive filtering algorithms. In the signal processing algorithms and implementation graduate course taught at KU Leuven (Belgium), we study the design of an adaptive notch filter, which is based on a constrained biquadratic IIR representation, andwhose parameters are updated using a least-mean-square algorithm. Students also have to implement the algorithm on a 16-bit DSP TMS320C5515. In this presentation, we will discuss the design and implementation challenges of this adaptive notch filter and how it serves as an illustrative example/homework problem where several aspects of DSP are interwoven.