A Novel Method for Designing General Window Functions with Flexible Spectral Characteristics

Abstract

In the field of sensor signal processing, windows are time-/frequency-domain weighting functions that are widely applied to reduce the well-known Gibbs oscillations. Conventional methods generally control the spectral characteristics of windows by adjusting several of the parameters of closed-form expressions. Designers must make trade-offs among the mainlobe width (MW), the peak sidelobe level (PSL), and sometimes the sidelobe fall-off rate (SLFOR) of windows by carefully adjusting these parameters. Generally, not all sidelobes need to be suppressed in specified applications. In this paper, a novel method, i.e., the inverse of the shaped output using the cyclic algorithm (ISO-CA), for designing window functions with flexible spectral characteristics is proposed. Simulations are conducted to test the effectiveness, flexibility and versatility of the method. Some experiments based on real measured data are also presented to demonstrate the practicability. The results show that the window functions generated using the cyclic algorithm (CA) yield better performance overall than the windows of conventional methods, achieving a narrower MW, a lower PSL, and a controllable SLFOR. In addition, steerable sidelobes over specified regions can be acquired both easily and flexibly while maintaining the original properties of the initial window as much as possible.

Generalized Adaptive Polynomial Window Function

“…The most traditional window functions are based on fixed expressions, such as the rectangular, Hann, Hamming, Flattop, Blackman, and Sine. Others have one or more free parameters, such as the Gaussian, Tukey, Chebyshev, and functional forms from more recent investigations [7], [11], [26]- [28], which have been adjusted to optimize a certain property at the frequency domain. Hybrid window functions have also been developed, such as the Barlett-Hann and Planck-Bessel ones, by combining other known window functions.…”

“…Additionally, many signals of interest are sampled corrupted with background noise, which could be of the same intensity of the signals of interest. To prevent such artifacts or improve the properties of the results, a large number of window functions have been proposed and applied to several systems, with diverse successes [4]- [11]. Those window functions have been proposed to improve and provide certain spectral characteristics, such as to reduce leakage, distinguish two sine signals with close frequencies, avoid scalloping loss, resolve a sine signal within a noisy background, analyze signals with comparable strength, and discriminate signals with different strength [12], [13].…”

“…The recent research on window functions has focused mainly on the ability to create mechanisms to improve the performance of the algorithms and develop windows with flexible temporal and spectral characteristics [11], [14]- [17]. Several investigations have proposed window functions with one or more free parameters that could be adjusted, to improve a certain property [7].…”

“…Several investigations have proposed window functions with one or more free parameters that could be adjusted, to improve a certain property [7]. For example, Sun et al proposed a method to design window functions with flexible spectral characteristics based on the inverse of the shaped output using the cyclic algorithm (ISO-CA) [11]. In the same context, Liu et at.…”

Conventional vs. Convolutional Windows for Reduction of Side Lobes

“…No window is ideal and it should be selected based on the requirement of the application [4]. Thus, a method for designing window functions with flexible spectral characteristics is greatly needed [5]. Commonly used spectral characteristics of a window function include the mainlobe width (MW), the peak sidelobe level ratio (PSLR) and relative sidelobe attenuation which are closely related to the resolution and spectrum leakage [6].…”