A receiver includes a first discrete Fourier transform (DFT) block to perform a first single tone DFT on a positive tone associated with a sounding sequence. A second DFT block performs a second single tone DFT on a negative tone associated with the sounding sequence. A DFT coefficient generation block generates first DFT coefficients based on a nominal frequency of the positive tone and an estimated frequency offset between a transmitter frequency and a receiver frequency. The DFT coefficient generation block generates second DFT coefficients based on a nominal frequency of the negative tone and the estimated frequency offset. Multipliers in the DFT blocks multiply I and Q values of the sounding sequence with the coefficients. Accumulators in the DFT blocks accumulate multiplier outputs. An arctan function receives averaged accumulated values from the first and second DFT blocks and supplies first and second phase values used to calculate fractional timing.

A receiver includes a first discrete Fourier transform (DFT) block to perform a first single tone DFT on a positive tone associated with a sounding sequence. A second DFT block performs a second single tone DFT on a negative tone associated with the sounding sequence. A DFT coefficient generation block generates first DFT coefficients based on a nominal frequency of the positive tone and an estimated frequency offset between a transmitter frequency and a receiver frequency. The DFT coefficient generation block generates second DFT coefficients based on a nominal frequency of the negative tone and the estimated frequency offset. Multipliers in the DFT blocks multiply I and Q values of the sounding sequence with the coefficients. Accumulators in the DFT blocks accumulate multiplier outputs. An arctan function receives averaged accumulated values from the first and second DFT blocks and supplies first and second phase values used to calculate fractional timing.

Embodiments of systems and method for determining a joint space-time spectral estimate (P) for a wideband spectrum are generally described herein. To determine a joint space-time spectral estimate (P) for a wideband spectrum, a random time delay may be applied to received signals for each channel of a plurality of receive channels to generate time-delayed signals for each receive channel. The time-delayed signals may be sampled for each receive channel to generate time-delayed samples and form array manifold vectors based on the random time delays and position of each antenna element in an array of antenna elements. An inverse (Q) of the joint-space time spectral estimate (P) may be determined by projecting the array manifold vectors through a mixing matrix (M). The mixing matrix (M) may be based on the time-delayed samples. The joint space-time spectral estimate (P) may comprise spatial and temporal properties of the wideband spectrum.

Embodiments of systems and method for determining a joint space-time spectral estimate (P) for a wideband spectrum are generally described herein. To determine a joint space-time spectral estimate (P) for a wideband spectrum, a random time delay may be applied to received signals for each channel of a plurality of receive channels to generate time-delayed signals for each receive channel. The time-delayed signals may be sampled for each receive channel to generate time-delayed samples and form array manifold vectors based on the random time delays and position of each antenna element in an array of antenna elements. An inverse (Q) of the joint-space time spectral estimate (P) may be determined by projecting the array manifold vectors through a mixing matrix (M). The mixing matrix (M) may be based on the time-delayed samples. The joint space-time spectral estimate (P) may comprise spatial and temporal properties of the wideband spectrum.

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 receiver includes a first discrete Fourier transform (DFT) block to perform a first single tone DFT on a positive tone associated with a sounding sequence. A second DFT block performs a second single tone DFT on a negative tone associated with the sounding sequence. A DFT coefficient generation block generates first DFT coefficients based on a nominal frequency of the positive tone and an estimated frequency offset between a transmitter frequency and a receiver frequency. The DFT coefficient generation block generates second DFT coefficients based on a nominal frequency of the negative tone and the estimated frequency offset. Multipliers in the DFT blocks multiply I and Q values of the sounding sequence with the coefficients. Accumulators in the DFT blocks accumulate multiplier outputs. An arctan function receives averaged accumulated values from the first and second DFT blocks and supplies first and second phase values used to calculate fractional timing.

A receiver includes a first discrete Fourier transform (DFT) block to perform a first single tone DFT on a positive tone associated with a sounding sequence. A second DFT block performs a second single tone DFT on a negative tone associated with the sounding sequence. A DFT coefficient generation block generates first DFT coefficients based on a nominal frequency of the positive tone and an estimated frequency offset between a transmitter frequency and a receiver frequency. The DFT coefficient generation block generates second DFT coefficients based on a nominal frequency of the negative tone and the estimated frequency offset. Multipliers in the DFT blocks multiply I and Q values of the sounding sequence with the coefficients. Accumulators in the DFT blocks accumulate multiplier outputs. An arctan function receives averaged accumulated values from the first and second DFT blocks and supplies first and second phase values used to calculate fractional timing.

Embodiments of systems and method for determining a joint space-time spectral estimate (P) for a wideband spectrum are generally described herein. To determine a joint space-time spectral estimate (P) for a wideband spectrum, a random time delay may be applied to received signals for each channel of a plurality of receive channels to generate time-delayed signals for each receive channel. The time-delayed signals may be sampled for each receive channel to generate time-delayed samples and form array manifold vectors based on the random time delays and position of each antenna element in an array of antenna elements. An inverse (Q) of the joint-space time spectral estimate (P) may be determined by projecting the array manifold vectors through a mixing matrix (M). The mixing matrix (M) may be based on the time-delayed samples. The joint space-time spectral estimate (P) may comprise spatial and temporal properties of the wideband spectrum.

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.