Abstract:It is well-known that the discrete Fourier transform (DFT) of a finite length discrete-time signal samples the discrete-time Fourier transform of the same signal at equidistant points on the unit circle. Hence, as the signal length goes to infinity, the DFT approaches the DTFT. Associated with the DFT are circular convolution and a periodic signal extension. In this paper we identify a large class of alternatives to the DFT using the theory of polynomial algebras. Each of these Fourier transforms approaches th… Show more
“…If we relax the requirement of a monomial signal extension and only require that the Fourier transform approaches the DTFT as , then choices nontrivially different from the DFT are indeed possible [40].…”
Section: Boundary Conditions and Signal Extensionmentioning
Abstract-This paper introduces a general and axiomatic approach to linear signal processing (SP) that we refer to as the algebraic signal processing theory (ASP). Basic to ASP is the linear signal model defined as a triple ( 8)
“…If we relax the requirement of a monomial signal extension and only require that the Fourier transform approaches the DTFT as , then choices nontrivially different from the DFT are indeed possible [40].…”
Section: Boundary Conditions and Signal Extensionmentioning
Abstract-This paper introduces a general and axiomatic approach to linear signal processing (SP) that we refer to as the algebraic signal processing theory (ASP). Basic to ASP is the linear signal model defined as a triple ( 8)
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