Fractional differentiation for edge detection
Signal Processing - Special issue: Fractional signal processing and applications
Convex Optimization
Design of variable and adaptive fractional order FIR differentiators
Signal Processing - Fractional calculus applications in signals and systems
A multiple exchange algorithm for constrained design of FIR filters in the complex domain
ICASSP '99 Proceedings of the Acoustics, Speech, and Signal Processing, 1999. on 1999 IEEE International Conference - Volume 03
Functional Fractional Calculus for System Identification and Controls
Functional Fractional Calculus for System Identification and Controls
IEEE Transactions on Image Processing
Studies on fractional order differentiators and integrators: A survey
Signal Processing
Fractional Calculus for Scientists and Engineers
Fractional Calculus for Scientists and Engineers
Fractional-Order Anisotropic Diffusion for Image Denoising
IEEE Transactions on Image Processing
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In this paper, the designs of fractional derivative constrained one-dimensional (1-D) and two-dimensional (2-D) FIR filters in the complex domain are investigated. First, the definition of fractional derivative is reviewed briefly. Then, the 1-D FIR filters with complex-valued frequency responses are designed by minimizing the integral squares error or maximum absolute error under the constraint that the actual response and ideal response have several same fractional derivatives at the prescribed frequency point. Next, the proposed method is extended to design fractional derivative constrained 2-D FIR filters with complex-valued frequency responses. Finally, design and application examples are demonstrated to show that the proposed method has larger design flexibility than the conventional integer derivative constrained methods.