High-resolution spectral estimation: Rethinking the Fourier transform

This paper describes a novel data multiplication window for use with the Fourier Transform. The window is complex and consists of a linear FM chirp which spans the range 0 to 2π. The range of applications described is restricted to data sequences consisting of complex values, such as are observed at the outputs of in-phase and quadrature demodulation receivers used in antenna array applications and in communication systems. For the case of an input consisting of a single complex sinusoid, the new window produces an extremely sharp null located exactly at the frequency of the input sinusoid. As such, it has resolution properties far superior to those available via more conventional windowing techniques such as the raised cosine. Applications of the method to inputs containing multiple sinusoids and single, frequency modulated sinusoids are discussed.