A new approach to the recursive Fourier transform.
In signal analysis and processing, situations may arise where the Fourier transform (FT) is to be updated on a data sample by a data sample basis. The number of computations required to recursively update the FT upon reception of a new sample does, in general, depend on the transform block length. However, there exists a class of windows when applied to the data stream before Fourier transformation, the required number of computations in FT becomes invariant with the FT block length. This letter introduces the class of windows which yields the computational invariance property of the recursive Fourier transform (RFT). Since the inclusion of more data samples in the transform enhances the spectral information of the received signal, the proposed class of windows offers spectral resolution enhancement without additional cost in computations. Memory requirements, however, increase as the FT block length is increased.
|Main Author:||Amin, Moeness G.|