Synchronization and matched filtering in time-frequency using the sunflower spiral

Synchronization and matched filtering of signals in time dispersive, frequency dispersive and time-frequency dispersive channels are addressed in this paper. The `eigenfunctions´ of these channels form the signal sets under investigation. While using channel-eigenfunctions is a first requirement for undistorted data transmission, a second necessity is to achieve good synchronization over the domains of time and frequency. The synchronization problem in time-frequency for non-stationary signals is discussed. A spiral correlation method is proposed to achieve synchronization and matched filtering in time-frequency. Spiral correlation, using the pattern of a sunflower, is simulated and evaluated. It is argued that partial spiral correlation can lead to a significant reduction in computational complexity necessary for synchronization. Generalizations and identities based on the fractional Fourier transform are provided which omit the need for fractional delay filters.