The spectral analysis of short data-segments using an IIR adaptive filter

An infinite impulse response (IIR) adaptive filter that is efficient and can be used to analyze short data segment with high resolution and very small biases is presented. The approach taken is to run the short data segment continuously forwards and backwards in time through the adaptive filter. The proposed adaptive filter is a filter bank composed of a number of parallel digital resonators with common feedback around all of them. Because of this particular architecture, the filter is easy to reset the internal state variables of the adaptive filter each time the direction of the input data segment is changed. This allows the same data segment to be run through the adaptive filter many times, with the adaptive filter converging closer to its optimum state each time. No windowing is required, which results in higher accuracies when determining the sinusoidal components of the input data. The resonator frequencies are adapted to match the frequencies of the input data segment. When the adaptive filter has converged, the isolated input sinusoids are available at the outputs of the resonators