Hartley transform and the use of the Whitened Hartley spectrum as a tool for phase spectral processing

The Hartley transform is a mathematical transformation which is closely related to the better known Fourier transform. The properties that differentiate the Hartley Transform from its Fourier counterpart are that the forward and the inverse transforms are identical and also that the Hartley transform of a real signal is a real function of frequency. The Whitened Hartley spectrum, which stems from the Hartley transform, is a bounded function that encapsulates the phase content of a signal. The Whitened Hartley spectrum, unlike the Fourier phase spectrum, is a function that does not suffer from discontinuities or wrapping ambiguities. An overview on how the Whitened Hartley spectrum encapsulates the phase content of a signal more efficiently compared with its Fourier counterpart as well as the reason that phase unwrapping is not necessary for the Whitened Hartley spectrum, are provided in this study. Moreover, in this study, the product–convolution relationship, the time-shift property and the power spectral density function of the Hartley transform are presented. Finally, a short-time analysis of the Whitened Hartley spectrum as well as the considerations related to the estimation of the phase spectral content of a signal via the Hartley transform, are elaborated

Spectral estimation for long-term evolution transceivers using low-complex filter banks

For mobile user equipments (UEs), a careful power management is essential. Despite this fact, quite an amount of energy is wasted in today's UEs’ analogue (AFEs) and digital frontends (DFEs). These are engineered for extracting the wanted signal from a spectral environment defined in the corresponding communication standards with their extremely tough requirements. These requirements define a worst-case scenario still ensuring reliable communication. In a typical receiving process the actual requirements can be considered as less critical. Knowledge about the actual environmental spectral conditions allows to reconfigure both frontends to the actual needs and to save energy. In this paper, the authors present a highly efficient generic spectrum sensing approach, which allows to collect information about the actual spectral environment of an UE. This information can be used to reconfigure both the AFE and DFE, thus endowing them with increased intelligence. A low-complex multiplier free filter bank extended by an efficient power calculation unit will be introduced. They also present simulation results, which illustrate the performance of the spectrum sensing approach and a complexity comparison with different well-known implementations is given. Furthermore, estimates on the chip area and power consumption based on a 65 nm CMOS technology database are provided, considering the Smarti4G chip as a reference