Design Technique and Efficient Polyphase Implementation for 2D Elliptically Shaped FIR Filters.

Area of Science:

• Digital Signal Processing
• Image Processing
• Filter Design

Background:

• Two-dimensional Finite Impulse Response (2D FIR) filters are crucial in signal and image processing.
• Existing methods for designing filters with specific frequency response shapes can be computationally intensive.
• Gaussian-shaped prototype filters are widely used but require efficient transformation for desired frequency responses.

Purpose of the Study:

• To develop a novel analytical approach for the efficient design of 2D FIR filters with elliptically shaped frequency responses.
• To demonstrate the application of these filters in image decomposition and reconstruction.
• To present a computationally efficient implementation strategy for the designed filters.

Main Methods:

• Utilizing a Fourier series expansion of a Gaussian prototype filter.
• Deriving a 1D to 2D frequency transformation for creating elliptical filter responses.
• Designing a 2D uniform filter bank for image sub-band decomposition and reconstruction.
• Implementing filters using a polyphase and block filtering approach.

Main Results:

• Successfully designed 2D FIR filters with accurate elliptical frequency responses and minimal distortions.
• Demonstrated the effectiveness of the designed elliptical filter bank for image analysis and synthesis.
• Achieved significant computational complexity reduction through the proposed parallel implementation strategy.

Conclusions:

• The proposed analytical method provides an efficient and accurate way to design directional, elliptically shaped 2D FIR filters.
• The developed filter bank is effective for image decomposition and reconstruction tasks.
• The polyphase and block filtering implementation offers substantial computational advantages over existing methods.