Convolution and product theorems for the quadratic-phase Fourier transform
P. B. Sharma, Akhilesh Prasad
Abstract
Abstract In this paper, we establish the convolution and product theorems for the quadratic-phase Fourier transform (QPFT) and also deduce the convolution theorem associated with generalized translation. Moreover, the Shannon-type reconstruction formula for band-limited signals in the QPFT domain is formulated.
Topics & Concepts
Convolution theoremConvolution (computer science)MathematicsFourier transformOverlap–add methodProduct (mathematics)Discrete-time Fourier transformQuadratic equationCircular convolutionFourier inversion theoremConvolution powerTranslation (biology)Pure mathematicsPhase (matter)Fractional Fourier transformMathematical analysisFourier analysisComputer sciencePhysicsGeometryQuantum mechanicsMessenger RNAArtificial neural networkBiochemistryMachine learningGeneChemistryMathematical Analysis and Transform MethodsImage and Signal Denoising MethodsDigital Filter Design and Implementation