Height Adjustable Triangular (HAT) 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 it forces the product to assume its nature of zero-value outside the interval and tapering from middle to the sides. Windows are finite functions and their main function is to modify an infinite impulse response sequence so as to make it finite within its chosen interval in system design. 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, Turkey, windows and many more. The window to apply in the design depends on the characteristics of the signal to be processed, types of system to be implemented and quality of output desired. In this paper, a new window called Height Adjustable triangular (HAT) window function is developed and added to the list of windows for signal processing system designs. The effectiveness of the window is tested by examining its characteristics. The adjustment parameter varies the amplitude or height of the window. Result shows that it is stable and linear.