Efficient Iterative Estimation of the Parameters of a Damped Complex Exponential in Noise

The estimation of the frequency and decay factor of a single decaying exponential in noise is a problem of prime importance. A popular estimation scheme uses the computationally efficient implementation of the Discrete Fourier transform, the FFT, to obtain a coarse estimate which is then improved by a fine estimation stage. Such estimators, however, show a performance that degrades and departs from the Cramér-Rao Lower Bound (CRLB) as the number of samples increases. To overcome this problem, we propose an iterative, exponentially windowed algorithm. We derive the new estimator´s theoretical performance and study its behavior under different decay rates of the window. We show that the estimator has excellent performance that tracks the CRLB with increasing number of samples if the window decay rate is appropriately set.