Hewlett-packard Company

Ronald W Potter

Jay M Wardle

John A Gibbs

Thomas Hornak

Gary L Baldwin

James L Adcock

A signal processing technique allows accurate interpolation between points of a sampled frequency domain function. A time-based sampling process samples a time waveform of duration T having a sub time interval T'. A signal processor applies a discrete Fourier transform over a time period T to transform the sampled data from the time domain to the frequency domain. The sampled frequency domain data is convolved with one or more convolution kernels to yield a continuous line shape. The result of this convolution permits the spectral composition at arbitrary frequencies to be determined. The disclosed frequency domain interpolation process is characterized by preservation of data in the T' interval of the time domain with an arbitrary but specified degree of accuracy.

Method and apparatus for enhancing frequency domain analysis

The sweep rate limitations that heretofore have constrained the maximum sweep rates of swept analysis instruments are obviated by optimizing filter circuitry and post-processing the IF signal using various techniques to compensate for errors caused by fast sweeping. Some selective windowing is also used to compensate for distortions due to fast sweep rates.

Swept signal analysis instrument and method

The sweep rate limitations that heretofore have constrained the maximum sweep rates of swept analysis instruments are obviated by optimizing filter circuitry and post-processing the IF signal using various techniques to compensate for errors caused by fast sweeping.

A method and apparatus for interpolating between data samples (V.sub.S) that preserves the frequency spectrum of a sampled analog signal (V.sub.O) is provided. Data samples (V.sub.S) are interpolated to produce interpolated values (V.sub.IV) that contain frequency domain information that accurately replicates an original frequency spectrum (24) of the analog signal (V.sub.O) is disclosed. A signal processor (10) reads data samples (V.sub.S) which occur at sampling times (t.sub.S) and resample times (t.sub.R) at which the V.sub.S values are interpolated. A set of t.sub.S times are found near each t.sub.R time. A digital FIR filter having a frequency function (H(fT)) and a continuous impulse response function ##EQU1## is embodied in software form within a program that controls the signal processor (10) where T is the width of the filter impulse response. The signal processor (10) convolves an offset continuous impulse response function ##EQU2## with the V.sub.S values. A plurality of convolved values (V.sub.C) are summed at each t.sub.R time to produce an interpolated value (V.sub.IV) at each t.sub.R time. The frequency response function (H(fT)) of the digital FIR filter reduces aliasing errors introduced by spectral images (25a and 25b) of the original frequency spectrum (24) and reduces amplitude errors caused by the filter's pass band ripple (38). The V.sub.IV values contain frequency domain information that accurately replicates the original frequency spectrum (24).

Method and apparatus for interpolating between data samples

The sweep rate limitations that heretofore have constrained the maximum sweep rates of swept analysis instruments (10,38) are obviated by optimizing filter circuitry (24,32,34,46) and post-processing the IF signal using various techniques to compensate for errors caused by fast sweeping.

A tracking and resampling method for monitoring the performance of a rotating machine (10) is disclosed. One or more measuring devices (13) provide rotating machine performance data to a signal processor (14) that samples the performance data at uniform time increments. A digitized waveform of the sampled performance data is interpolated by an interpolation filter. The sampled performance data is convolved with the impulse response of the interpolation filter to provide a continuous time function waveform depicting the rotating machine performance data. The signal processor (14) resamples the continuous time function waveform at uniform rotating shaft phase angle increments.

Tracking and resampling method and apparatus for monitoring the

A pole and zero analyzer determines the poles and zeroes of a device for applying a stimulus signal to the device, detecting the stimulus and response signals and computing the auto- and cross spectra. An estimated transfer function is least squares fit to a measured transfer function obtained from the auto- and cross-spectra and the poles and zeroes are obtained as the roots of the estimated transfer function. Inaccuracies due to noise are minimized by subtracting out a noise bias from the squared cross-spectrum obtained during the least squares fit and by orthogonalizing a data matrix used in the determination of the coefficients of the estimated transfer function.

Noise corrected pole and zero analyzer

A pole and zero analyzer determines the poles and zeroes of a device by applying a stimulus signal to the device, detecting the stimulus and response signals and computing the auto- and cross-spectra. An estimated transfer function is least squares fit to a measured transfer function obtained from the auto- and cross-spectra and the poles and zeroes are obtained as the roots of the estimated transfer function. A weighting function may be used to emphasize certain desired regions of the frequencies of interest in the determination of the least squares fit. The orders of the poles and zeroes are modified until an optimum fit is reached.

A binary scaled current source in which a set of binary switches M.sub.1, . . . , M.sub.n controllably switch a current I to a selected one of a set of n outputs. Each switch M.sub.k is controlled by an associated control signal B.sub.k having a duty cycle of 2.sup.k-n-1. At any given time one and only one of the control signals is high so that the current I is diverted to the kth output a fraction 2.sup.k-n-1 of the time. In two particular schemes referred to as the weighted pulse width (WPW) and the weighted repetition rate (WRR) schemes, all of the control signals are periodic with a group pattern repetition period T. In the WPW scheme, B.sub.k has in each period T a single pulse of duration 2.sup.k-n-1 *T. In the WRR scheme, B.sub.k has in each period T2.sup.k-1 pulses each of duration 2.sup.-n *T. The output of each binary switch is typically passed through a low pass filter which conducts substantially only the dc component of the output current from the binary switch to which it is connected. These dc components serve as a set of binary scaled dc currents. Pulsing switches are also added between the source of current I and the binary switches to provide the current I in pulses that do not overlap any of the transitions in the control signals so that the binary scaled currents that are produced are insensitive to timing of the transitions in the control signals.

Binary scaled current array source for digital to analog converters

A frequency converter for a complex digital input provides a shift of frequency without the necessity of time-consuming and expensive numerical multiplication. Furthermore, by combining the conversion process with digital filtering, the frequency of the converted output can be halved. The output can be resampled and reapplied to the novel converter for repeated shifts in frequency and reduction of bandwidth in the case of down-conversion.

Apparatus and means for high speed digital frequency shifting

A recursive digital low-pass filter processes an input signal with essentially unity gain and sharp frequency cutoff without using multipliers to provide an output signal with an information bandwidth substantially one-half that of the input signal.

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Snohomish, WA, United States of America

Ronald W Potter