Construction of a window function for estimating the parameters of sinusoidal signals with non-harmonic frequencies

Abstract

Discrete Fourier Transform (DFT) allows you to determine the discrete spectrum of a signal. Due to the presence of its high-speed implementation, called Fast Fourier Transform (FFT), this transform is widely used in digital signal processing (DSP). Most DSP tasks that deal with analogy signal and spectrum adapt the DFT to find the signal spectrum between harmonics. One of the most commonly used ways of such adaptation – the use of window functions. The analysis of standard window functions (Kaiser, etc.) showed that their direct application to solving the problem of estimating the parameters (frequency, amplitude, and phase) of nonharmonic sinusoidal components of signals leads both to the need for additional corrections of the estimation results and to additional errors in determining the phase of the signal. The paper proposes a method that allows building a window function without the indicated drawbacks based on standard window functions. The essence of the method is to transform the standard window function so that its spectrum does not contain imaginary components, and the amplitude of the fundamental harmonic would be equal to 1. The results of modeling the proposed method on the example of the Kaiser window showed that the phase estimate of the nonharmonic components of the spectrum using the obtained window function, in contrast to the estimate using standard window functions, is not displaced.