Embodiments of the present invention provide techniques and methods for improving signal-to-noise ratio (SNR) when averaging two or more data signals by finding a group delay between the signals and using it to calculate an averaged result. In one embodiment, a direct average of the signals is computed and phases are found for the direct average and each of the data signals. Phase differences are found between each signal and the direct average. The phase differences are then used to compensate the signals. Averaging the compensated signals provides a more accurate result than conventional averaging techniques. The disclosed techniques can be used for improving instrument accuracy while minimizing effects such as higher-frequency attenuation. For example, in one embodiment, the disclosed techniques may enable a real-time oscilloscope to take more accurate S parameter measurements.

A signal processing method and a material testing machine are provided. A reference function processing part includes a data interval generation part for cutting out input signal from a load cell into time-domain data interval by cutting out the input signal of a predetermined time length, a reference function determining part for determining a reference function to be used in a transform process, and a transform part for transforming the interval data using the reference function. Considering the approximately straight lines near the two ends of the data interval, the reference function is a third degree polynomial function with tangents overlapping with the approximately straight line at both ends of the data interval.

A signal processing method and a material testing machine are provided. A reference function processing part includes a data interval generation part for cutting out input signal from a load cell into time-domain data interval by cutting out the input signal of a predetermined time length, a reference function determining part for determining a reference function to be used in a transform process, and a transform part for transforming the interval data using the reference function. Considering the approximately straight lines near the two ends of the data interval, the reference function is a third degree polynomial function with tangents overlapping with the approximately straight line at both ends of the data interval.

A Multi-Signal Instantaneous Frequency Measurement, MIFM, system comprising a front end adapted to shift and combine signal spectra of different sub-frequency bands (SFBs) of a received wideband signal (WBS) into an intermediate frequency band (IFB) having an instantaneous bandwidth (IBW), wherein each shifted SFB signal spectrum is marked individually with SFB marking information associated with the respective sub-frequency band (SFB) and a digital receiver (3) having the instantaneous bandwidth (IBW) configured to process the shifted SFB signal spectra within the intermediate frequency band (IFB) using the SFB marking information to resolve any frequency ambiguity caused by the shifting and combining of the SFBs signal spectra.

An optimization-based method and system is disclosed to enable heterogeneous loads and distributed energy resources (DERs) to participate in grid ancillary services, such as spinning and non-spinning reserves, and ramping reserves. The method includes receiving inputs for decision parameters for optimizing an objective for obtaining flexible reserve power, solving the objective for obtaining flexible reserve power, determining a reserve power schedule for a prediction horizon for providing flexible reserve power based on the objective, generating a service bid based on the reserve power schedule for the power grid; and when the service bid is accepted, providing flexible reserve power to the power grid based on the service bid.

An optimization-based method and system is disclosed to enable heterogeneous loads and distributed energy resources (DERs) to participate in grid ancillary services, such as spinning and non-spinning reserves, and ramping reserves. The method includes receiving inputs for decision parameters for optimizing an objective for obtaining flexible reserve power, solving the objective for obtaining flexible reserve power, determining a reserve power schedule for a prediction horizon for providing flexible reserve power based on the objective, generating a service bid based on the reserve power schedule for the power grid; and when the service bid is accepted, providing flexible reserve power to the power grid based on the service bid.

A method for detecting a plurality of useful signals in a total signal. The useful signals correspond to radiofrequency signals emitted by different terminals in a multiplexing frequency band. A plurality of spectrograms calculated that have a compensated linear frequency drift and are respectively associated with different linear frequency drift values. For each analysis frequency and each spectrogram, time envelope filtering of the values is performed at the different times for analyzing the spectrogram at the analysis frequency using a filter representing a reference time envelope of the useful signals. A useful signal is detected at an analysis time and at an analysis frequency in response to a verification of a predefined detection criterion by the value from a spectrogram resulting from filtering at the analysis time and at the analysis frequency.

Measurement of group delay for a device under test (DUT). A test signal includes (i) a low frequency sine wave f.sub.LF, (ii) sine wave harmonics at a high frequency f.sub.HF, (iii) L pairs of sideband components at frequencies k.Math.f.sub.HF2.Math.f.sub.LF, where k odd, and M pairs of sideband components at frequencies k.Math.f.sub.HFf.sub.LF, where k is even. At DUT output, (i) phase .sub.LF at frequency f.sub.LF is measured, (ii) both sideband phase .sub.right(k) at frequencies k.Math.f.sub.HF+2.Math.f.sub.LF and phase .sub.left(k) at frequencies k.Math.f.sub.HF2.Math.f.sub.LF for odd k, are measured, and (iii) both sideband phases .sub.right(k) at frequencies k.Math.f.sub.HF+f.sub.LF and .sub.left(k) at frequencies k.Math.f.sub.HFf.sub.LF for even k, are measured. Group delay .sub.k at frequencies k.Math.F.sub.HF, are determined from: .sub.k=(.sub.right(k).sub.left(k)4.Math..sub.L)/(4.Math.f.sub.LF) for k odd, and .sub.k=(.sub.right(k).sub.left(k)2.Math..sub.L)/(2.Math.f.sub.LF) for k even.

Measurement of group delay for a device under test (DUT). A test signal includes (i) a low frequency sine wave f.sub.LF, (ii) sine wave harmonics at a high frequency f.sub.HF, (iii) L pairs of sideband components at frequencies k.Math.f.sub.HF2.Math.f.sub.LF, where k odd, and M pairs of sideband components at frequencies k.Math.f.sub.HFf.sub.LF, where k is even. At DUT output, (i) phase .sub.LF at frequency f.sub.LF is measured, (ii) both sideband phase .sub.right(k) at frequencies k.Math.f.sub.HF+2.Math.f.sub.LF and phase .sub.left(k) at frequencies k.Math.f.sub.HF2.Math.f.sub.LF for odd k, are measured, and (iii) both sideband phases .sub.right(k) at frequencies k.Math.f.sub.HF+f.sub.LF and .sub.left(k) at frequencies k.Math.f.sub.HFf.sub.LF for even k, are measured. Group delay .sub.k at frequencies k.Math.F.sub.HF, are determined from: .sub.k=(.sub.right(k).sub.left(k)4.Math..sub.L)/(4.Math.f.sub.LF) for k odd, and .sub.k=(.sub.right(k).sub.left(k)2.Math..sub.L)/(2.Math.f.sub.LF) for k even.

Measurement of group delay for a device under test (DUT). A test signal includes (i) a low frequency sine wave f.sub.LF, (ii) sine wave harmonics at a high frequency f.sub.HF, (iii) L pairs of sideband components at frequencies k.Math.f.sub.HF2.Math.f.sub.LF, where k odd, and M pairs of sideband components at frequencies k.Math.f.sub.HFf.sub.LF, where k is even. At DUT output, (i) phase .sub.LF at frequency f.sub.LF is measured, (ii) both sideband phase .sub.right(k) at frequencies k.Math.f.sub.HF+2.Math.f.sub.LF and phase .sub.left(k) at frequencies k.Math.f.sub.HF2.Math.f.sub.LF for odd k, are measured, and (iii) both sideband phases .sub.right(k) at frequencies k.Math.f.sub.HF+f.sub.LF and .sub.left(k) at frequencies k.Math.f.sub.HFf.sub.LF for even k, are measured. Group delay .sub.k at frequencies k.Math.F.sub.HF, are determined from: .sub.k=(.sub.right(k).sub.left(k)4.Math..sub.L)/(4.Math.f.sub.LF) for k odd, and .sub.k=(.sub.right(k).sub.left(k)2.Math..sub.L)/(2.Math.f.sub.LF) for k even.