Design of efficient circularly symmetric two-dimensional variable digital FIR filters.

Area of Science:

• Digital Signal Processing
• Image Processing
• Filter Design

Background:

• Circularly symmetric 2D FIR filters are vital for image and medical applications requiring isotropic filtering.
• Designing 2D digital filters with variable fractional delay and magnitude responses efficiently is crucial for low-cost systems.
• Fixed word-length coefficient designs reduce hardware complexity by replacing multipliers with shifters and adders.

Purpose of the Study:

• To develop a low-complexity, circularly symmetric 2D variable digital filter (VDF) with real-time tunability.
• To enable efficient design of 1D VDFs with tunable cut-off frequencies and map them to 2D.
• To address performance degradation issues in multiplier-less filter designs.

Main Methods:

• 1D VDFs with tunable cut-off frequencies designed using a Farrow structure-based interpolation approach.
• Sub-filter coefficients in the Farrow structure are made multiplier-less using canonic signed digit (CSD) representation.
• Artificial Bee Colony (ABC) optimization used to mitigate performance degradation.
• Generalized McClellan transformation employed to map optimized 1D VDFs to 2D.

Main Results:

• Achieved low-complexity, circularly symmetric 2D VDFs.
• Enabled real-time tunability of filter characteristics.
• Multiplier-less coefficient design using CSD representation significantly reduces hardware.
• ABC optimization effectively overcomes performance degradation.

Conclusions:

• The proposed method successfully generates efficient, tunable, and low-complexity 2D FIR filters.
• This design approach is suitable for applications demanding real-time adjustments and reduced hardware.
• The integration of Farrow structure, CSD representation, ABC optimization, and McClellan transformation offers a robust solution for 2D filter design.