Abstract: A method for transforming and reconstructing a signal includes receiving a plurality of samples of a waveform of the signal at different points in time. The waveform of the signal is transformed, for each sample, into an in-phase (I) component and a quadrature (Q) component. A derotational circuit applies a delayed complex conjugate multiple (DCM) to the signal to determine a constant product having an I component (Ic) and a Q component (Qc). A magnitude component is determined based on Ic and Qc. A delta phase component is determined based on Ic and Qc. The magnitude component is processed to create a processed magnitude component. The delta phase component is processed to create a processed delta phase component. An IQ waveform is created by reconstructing the waveform of the signal based on the processed magnitude component and the processed phase component.

Abstract: A method and system for detecting and characterizing an input signal receive a signal having an in-phase (I) component and a quadrature-phase (Q) component. A first IQ sample of the signal is acquired at a first point in time, and a second IQ sample of the signal is acquired at a second point in time, Using one or more processors, a delayed complex conjugate multiply (DCM) is applied to the first IQ sample of the signal and the second IQ sample of the signal to produce a constant product having an in-phase (IC) component and a quadrature-phase (QC) component. A signal magnitude and a signal frequency are determined from the IC component of the constant and the QC component of the constant, using the one or more processors.

Abstract: A method and system for detecting and characterizing an input signal receive a signal having an in-phase (I) component and a quadrature-phase (Q) component. A first IQ sample of the signal is acquired at a first point in time, and a second IQ sample of the signal is acquired at a second point in time, Using one or more processors, a delayed complex conjugate multiply (DCM) is applied to the first IQ sample of the signal and the second IQ sample of the signal to produce a constant product having an in-phase (IC) component and a quadrature-phase (QC) component. A signal magnitude and a signal frequency are determined from the IC component of the constant and the QC component of the constant, using the one or more processors.