Analytical methods for the design of 2-D elliptically symmetric digital filters of arbitrary orientation using generalized McClellan transformation

2006 ◽  
pp. 196-207 ◽  
Author(s):  
N. Nagamuthu ◽  
M. N. S. Swamy
Keyword(s):  
Analytical Methods ◽  
Digital Filters ◽  
Arbitrary Orientation ◽  
Mcclellan Transformation

SCALED AND SCALING-FREE McCLELLAN TRANSFORMATIONS FOR THE DESIGN OF 2-D DIGITAL FILTERS

1991 ◽  
Vol 01 (01) ◽  
pp. 105-124 ◽  
Author(s):  
N. NAGAMUTHU ◽  
M. N. S. SWAMY
Keyword(s):  
Real Time ◽  
Digital Filters ◽  
Extreme Values ◽  
Sufficient Conditions ◽  
Scaling Factors ◽  
Mcclellan Transformation ◽  
Real Time Applications ◽  
Necessary And Sufficient ◽  
New Formula ◽  
Analytical Expressions

In this paper, the scaling problem of McClellan transformation used for the design 2-D digital filters with elliptical and circular cutoff contours is critically analyzed. Several new and extremely simple formulas for calculating the maximum and minimum values of the transformation function are presented. Using these extreme values, simple formulas for scaling factors and scaled McClellan transformations are derived for the various cases of each type of contour. Using the necessary and sufficient conditions for a scaling-free transformation, the scaling-free McClellan transformations are also derived. It is shown that the number of independent coefficients in them to be optimized varies from 0 to 2 depending on the case, compared to 3 in the original transformation. They are very useful in deriving analytical expressions for the transformation coefficients, and the 2-D filters designed by employing them have a smaller number of multiplications per output sample and hence, attractive for real-time applications. A new scaling formula is presented and some of its properties and effects on the derived formulas are discussed. The major advantage of this new formula is that from the unscaled transformation coefficients for a given type of 2-D filter, we can generate the scaled transformation coefficients for a different type of 2-D filter. Some examples are presented to demonstrate the usefulness of the derived formulas.

Stereo modeling of HVEM specimens by serial tilting and computer graphics

1986 ◽  
Vol 44 ◽  
pp. 34-35
Author(s):  
J.R. McIntosh ◽  
D.L. Stemple ◽  
William Bishop ◽  
G.W. Hannaway
Keyword(s):  
Computer Graphics ◽  
Analytical Methods ◽  
Photographic Film ◽  
Complex Structures ◽  
Multiple Objects ◽  
Multiple Images ◽  
3 Dimensional

EM specimens often contain 3-dimensional information that is lost during micrography on a single photographic film. Two images of one specimen at appropriate orientations give a stereo view, but complex structures composed of multiple objects of graded density that superimpose in each projection are often difficult to decipher in stereo. Several analytical methods for 3-D reconstruction from multiple images of a serially tilted specimen are available, but they are all time-consuming and computationally intense.

Sign in / Sign up

Export Citation Format

Share Document