Sequential Least-Squares Estimation of Frequency Responses

Instantaneous Frequency Estimation Using a Least Squares Time-Frequency Method

We present a method for estimating the instantaneous frequency of a signal. This method involves the calculation of a time–frequency energy density of the signal, then obtaining an instantaneous frequency estimate from this joint density. Time–frequency energy density is calculated as a least squares optimal combination of multi–window Gabor based evolutionary spectra. The optimal weights are o...

Least Squares Estimation

Recursive Least Squares Estimation

We start with estimation of a constant based on several noisy measurements. Suppose we have a resistor but do not know its resistance. So we measure it several times using a cheap (and noisy) multimeter. How do we come up with a good estimate of the resistance based on these noisy measurements? More formally, suppose x = (x1, x2, . . . , xn) T is a constant but unknown vector, and y = (y1, y2, ...

Nonlinear Least-squares Estimation

The paper uses empirical process techniques to study the asymptotics of the least-squares estimator for the fitting of a nonlinear regression function. By combining and extending ideas of Wu and Van de Geer, it establishes new consistency and central limit theorems that hold under only second moment assumptions on the errors. An application to a delicate example of Wu’s illustrates the use of t...

Fundamental frequency estimation by least-squares harmonic model fitting

This paper proposes a pitch estimation algorithm that is based on optimal harmonic model fitting. The algorithm operates directly on the time-domain signal and has a relatively simple mathematical background. To increase its efficiency and accuracy, the algorithm is applied in combination with an autocorrelation-based initialization phase. For testing purposes we compare its performance on pitc...