Download On the Estimation of Sinusoidal Parameters via Parabolic Interpolation of Scaled Magnitude Spectra Sinusoids are widely used to represent the oscillatory modes of
music and speech. The estimation of the sinusoidal parameters
directly affects the quality of the representation. A parabolic interpolation of the peaks of the log-magnitude spectrum is commonly
used to get a more accurate estimation of the frequencies and the
amplitudes of the sinusoids at a relatively low computational cost.
Recently, Werner and Germain proposed an improved sinusoidal estimator that performs parabolic interpolation of the peaks
of a power-scaled magnitude spectrum. For each analysis window type and size, a power-scaling factor p is pre-calculated via
a computationally demanding heuristic. Consequently, the powerscaling estimation method is currently constrained to a few tabulated power-scaling factors for pre-selected window sizes, limiting
its practical applications. In this article, we propose a method to
obtain the power-scaling factor p for any window size from the
tabulated values. Additionally, we investigate the impact of zeropadding on the estimation accuracy of the power-scaled sinusoidal
parameter estimator.
Download Parameter Estimation of Frequency-Modulated Sinusoids with the Distribution Derivative Method Frequency-modulated (FM) sinusoids are commonly used to model signals in several engineering applications, such as radar, sonar, communications, acoustics, and optics. The estimation of the parameters of FM sinusoids is a challenging problem with a long history in the literature. In this article, we use the distribution derivative method (DDM) to estimate the parameters of FM sinusoids in additive white Gaussian noise. Firstly, we derive the estimation of parameters of the model with DDM. Then, we compare the results of Monte-Carlo simulations (MCS) of DDM estimation of FM signals in additive white Gaussian noise against the state of the art (SOTA) and the Cramér-Rao lower bound (CRLB). DDM estimation of FM sinusoids showed performance comparable to the SOTA with less estimation bias. Additionally, DDM estimation of FM sinusoids is simple and straightforward to implement with the fast Fourier transform (FFT) relative to other approaches in the literature. Finally, DDM estimation has effectively the same computational complexity as the FFT.