Height Adjustable Sine (HAS) Window Function for Impulse Response Modification of Signal Processing Systems

Abstract

A widow function, in signal processing and statistics, is a mathematical function that has zero values outside its chosen interval or limit of sequence, normally symmetric around the middle of the interval. Usually the middle of the window is either maximum or near maximum and tappers smoothly as it moves away to the sides. When another function or sequence of data is mathematically multiplied by the window function the product assumes the appearance and characteristics of the window function. That is, the product is also zero-valued outside the interval and tapering from middle to the sides. The impulse response data of some systems used in signal processing truncate suddenly when being designed. Window functions convert the sudden truncation of these impulse response data to gradual truncation. Without this gradual truncation the processing system will degrade the integrity of complex signals when they are applied to them; the degradation appears in form of signal distortions. Windows are used to weight these impulse response data so as to reduce the degradation and distortions. Several windows are in existence and they include Hamming, rectangular, Han, Kaiser, Triangular, Blackman, Sine, Blackman-Harris, Gaussian, Doph-Chebyshev and Lanczos, windows. Others are Parzen, Nuttall, flat top, and Turkey, windows and others.  The characteristics of the signal to be processed, types of systems to be implemented and quality of outputs desired determine the best window to weight any particular impulse response data. In this work a new window referred to as Height Adjustable Sine (HAS) window is developed to join the list of the existing windows. The quality of the window is tested by analysing its amplitude, magnitude and phase responses in frequency domain. Result shows that the window is stable and linear.