Adaptive detection and enhancement of closely spaced sinusoids using multirate techniques

A structure that is useful for the detection of closely spaced multiple sinusoids is presented. Cascaded adaptive notch filters are used between M-fold decimators and interpolators. The proposed multirate structure is a single-input, multiple-output adaptive filter. It takes multiple sinusoids corrupted by Gaussian noise and produces the individual sinusoids at each of the outputs. A closed-form expression for the steady-state mean square error of the variable coefficient has been obtained. By making use of the frequency enhancement properties of the decimation, the structure makes high-resolution sinusoidal detection possible. The variance of error for the enhanced sinusoid is shown. Results of computer simulation confirm the theoretical predictions.<>