The objective of this work is the introduction of new 2-D window families used for design of FIR lowpass filters, with their application in filtering the images degraded by noise. These variable parameter window families based on the special properties of hyperbolic functions which create pairs of transforms with a similar shape. The designed filters are applied to process a real image corrupted by pseudo-random Gaussian and speckle noise, respectively. The results show that the proposed windows provide improved mean absolute error, mean square error and signal to noise ratio performance over other classic window functions. Results of median and Wiener filters are also included for comparison.approaches for generating 2-D windows. The first is Huang's method [2], by which a good circularly symmetric 2-D window can be designed by rotating 1-D window in continuous time domain. The second method forms a 2-D window by taking the outer product of two 1-D windows [3]. In the third approach 2-D window is obtained by rotating the frequency response of a 1-D window in Fourier space followed by the inverse 2-D Fourier transform [4], and lastly 2-D window can be designed by applying the McClellan transformation [5].In order to construct a good circular 2-D window, Huang's method has been undertaken in this work with an appropriate and carehl choice of a 1-D window, so that the resulting window has a narrow mainlobe and smaller sidelobes (an important requirement).
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