Analytical and numerical methods for efficient calculation of edge diffraction by an arbitrary incident signal

Area of Science:

• Electromagnetics and Wave Propagation
• Applied Mathematics and Computational Science

Background:

• Diffraction analysis is crucial for understanding wave phenomena.
• Existing analytical impulse responses for half-planes have limitations with spherical signals.

Purpose of the Study:

• To investigate and extend an existing analytical impulse response for signal diffraction.
• To develop computationally efficient methods for analyzing diffraction responses.

Main Methods:

• Analysis of primitive functions of the impulse response.
• Analytical derivation of diffraction response using piecewise polynomial approximation.
• Development of an explicit time-domain impulse response for finite edges.

Main Results:

• Primitive functions of the impulse response are proven to be bounded.
• Analytical diffraction response obtained using elementary functions.
• Significant improvements in numerical convolution performance and handling of coarse signals.
• Novel explicit time-domain impulse response for finite edges.

Conclusions:

• The developed methods offer enhanced accuracy and computational efficiency for signal diffraction analysis.
• The new impulse response for finite edges provides substantial benefits over traditional integration methods.