We develop a mathematical framework for quantifying and understanding multidimensional frequency modulations in digital images. We begin with the widely accepted definition of the instantaneous frequency vector (IF) as the gradient of the phase and define the instantaneous frequency gradient tensor (IFGT) as the tensor of component derivatives of the IF vector. Frequency modulation bounds are d...

This paper investigated the use of instantaneous frequency (IF) instead of power amplitude and power spectrum in side-channel analysis. By opposition to the constant frequency used in Fourier Transform, instantaneous frequency reflects local phase differences and allows detecting frequency variations. These variations reflect the processed binary data and are hence cryptanalytically useful. IF ...

Instantaneous frequency (IF) is necessary for understanding the detailed mechanisms for nonlinear and nonstationary processes. Historically, IF was computed from analytic signal (AS) through the Hilbert transform. This paper offers an overview of the difficulties involved in using AS, and two new methods to overcome the difficulties for computing IF. The first approach is to compute the quadrat...

Iterated Hilbert transform (IHT) is a new method for multicomponent demodulation. The principle of IHT is introduced, and some of its properties are researched. Although the amplitudes of the demodulated components obtained by IHT are accurate, there are limitations in the direct estimation of instantaneous frequencies via the extracted phases, so a smoothed instantaneous frequency estimation (...

In this paper we propose a new type of non-negative time-frequency distribution associated with mono-components in both the non-periodic and periodic cases, called transient time-frequency distribution (TTFD), and study its properties. The TTFD of a mono-component signal can be obtained directly through its analytic instantaneous frequency. The characteristic property of TTFD is its complete co...

 Measures active, reactive, and apparent energies  Current, voltage RMS and instantaneous measurement  Frequency measurement  Ripple-free active energy pulsed output  Live and neutral monitoring for tamper detection  Fast and simple one-point digital calibration over the whole current range  Integrated linear voltage regulators for digital and analog supply  Selectable RC or crystal osc...

Two methods of the classification of digital modulations ASK, FSK2, FSK4, MSK, BPSK, QPSK, 8PSK and QAM-16 are presented. The first algorithm is based on module and phase spectrogram analysis. Here it is very important to estimate the symbol length of the received signal and thus we introduce two methods for this purpose. They are based on the wavelet transform and cepstrum analysis. The second...