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 method of calibrating a setup comprises: performing at least one calibration of the setup, thereby obtaining calibration data; setting a quantity representing forward tracking to be equal with a quantity representing reverse tracking; solving a system of equations having at least an unknown quantity representing the forward tracking or the reverse tracking, thereby obtaining at least one equation having the unknown quantity squared; creating based on the calibration data obtained two phase over frequency relationships for the respective quantity; determining two lines having a linear change in phase over frequency for the phase over frequency relationships created; extrapolating the lines determined to a frequency of 0 Hz; and determining the respective quantity by selecting one line of the lines extrapolated that is closer to a phase of zero, 2π or a multiple thereof at the frequency of 0 Hz.

A method of calibrating a setup comprises: performing at least one calibration of the setup, thereby obtaining calibration data; setting a quantity representing forward tracking to be equal with a quantity representing reverse tracking; solving a system of equations having at least an unknown quantity representing the forward tracking or the reverse tracking, thereby obtaining at least one equation having the unknown quantity squared; creating based on the calibration data obtained two phase over frequency relationships for the respective quantity; determining two lines having a linear change in phase over frequency for the phase over frequency relationships created; extrapolating the lines determined to a frequency of 0 Hz; and determining the respective quantity by selecting one line of the lines extrapolated that is closer to a phase of zero, 2π or a multiple thereof at the frequency of 0 Hz.

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.

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 is provided for performing real-time spectral analysis of a non-stationary signal. The method includes sampling the non-stationary signal, using an observation window having a length short enough to approximate a stationary signal, to provide an initial set of sampled data, buffering the initial set of sampled data to obtain multiple buffered sets of sampled data, filtering the initial set of sampled data and the buffered sets of sampled data, using corresponding filter responses, to obtain multiple filtered sets of sampled data, and performing a chirp-z-transform (CZT) of the filtered sets of sampled data to provide a set of discrete Fourier transforms (DFT) coefficients. A total signal spectrum of the non-stationary signal is reconstructed using the set of DFT coefficients.

A method is provided for performing real-time spectral analysis of a non-stationary signal. The method includes sampling the non-stationary signal, using an observation window having a length short enough to approximate a stationary signal, to provide an initial set of sampled data, buffering the initial set of sampled data to obtain multiple buffered sets of sampled data, filtering the initial set of sampled data and the buffered sets of sampled data, using corresponding filter responses, to obtain multiple filtered sets of sampled data, and performing a chirp-z-transform (CZT) of the filtered sets of sampled data to provide a set of discrete Fourier transforms (DFT) coefficients. A total signal spectrum of the non-stationary signal is reconstructed using the set of DFT coefficients.

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.