Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A two-dimensional (2D) quaternion Fourier transform (QFT) defined with the kernel is proposed. Some fundamental properties, such as convolution, Plancherel and vector differential theorems, are established. The heat equation in quaternion algebra is presented as an example of the application of the QFT to partial differential equations. The wavelet transform is extended to quaternion algebra using the kernel of the QFT.
['Mawardi Bahri', 'Ryuichi Ashino', 'Rémi Vaillancourt']
I am writing a research paper on a idea CONTINUOUS QUATERNION FOURIER AND WAVELET TRANSFORMS
[{"from": "human", "value": "I am writing a research paper on a idea CONTINUOUS QUATERNION FOURIER AND WAVELET TRANSFORMS"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A two-dimensional (2D) quaternion Fourier transform (QFT) defined with the kernel is proposed. Some fundamental properties, such as convolution, Plancherel and vector differential theorems, are established. The heat equation in quaternion algebra is presented as an example of the application of the QFT to partial differential equations. The wavelet transform is extended to quaternion algebra using the kernel of the QFT."}]