Fung I. Tseng

Deconvolution of Impulse Response from Time-Limited Input and Output: Theory and Experiment

Since it is impossible to generate and propagate an impulse, often a system is excited by a narrow time-domain pulse. The output is recorded and then a numerical deconvolution is often done to extract the impulse response of the object. Classically, the fast Fourier transform (FFT) technique has been applied with much success to the above deconvolution problem. However, when the signal-to-noise ratio becomes small, sometimes one encounters instability with the FFT approach. In this paper, the method of conjugate gradient is applied to the deconvolution problem. The problem is solved entirely in the time domain. The method converges for any initial guess in a finite number of steps. Also, for the application of the conjugate gradient method, the time samples need not be uniform, like FFT. Since, in this case, one is solving the operator equation directly, by passing the autocorrelation matrix computation, storage required is 5N as opposed to N2. Computed impulse response utilizing this technique has been presented for measured incident and scattered fields.

A novel window for harmonic analysis

This paper presents a new window design technique and discusses its effect on the detection of harmonic signals in the presence of nearby strong harmonic interference. Four design parameters are introduced to independently control the pattern falloff rate, the overall sidelobe level, the near-sidelobe level and the depth of a steerable wide dip. Since the deep dip can be steered to any frequency the new window has effectively improved the detectability of a small tone without degrading resolvability. Contrary to the conventional approach of initially specifying the continuous weighting, the new design technique starts with constructing the spectral window which meets the specifications and then employs the fast Fourier transform to compute the discrete weighting. No iterative sampling or perturbation procedure is required. Numerous examples are given to demonstrate the flexibility of the new window. Several examples of detecting a three-tone signal have demonstrated the superiority of the new window in its detectability, resolvability, and accuracy of measuring the tone frequencies and amplitudes.

Deconvolution of the impulse response of a conducting sphere by the conjugate gradient method

An experimental technique for determining the impulse response of a conducting sphere has been presented. A method of exciting and recording transient waveforms scattered from conducting spheres of various sizes has been described and extensively tested. A modified conjugate-gradient method has been applied to the transient waveforms to determine the impulse response of the objects. It is shown that by proper weighting in computing the residual in the conjugate-gradient method the oscillation due to noise could be reduced. A recently developed data-processing technique has been applied to these impulse responses to obtain their spectra, which yield adequately the resonant frequencies of the objects.

Experimental determination of resonant frequencies by transient scattering from conducting spheres and cylinders

A new experimental technique to measure resonant frequencies of a target is presented. A Tektronix WP 1310 waveform processing system has been employed, which features signal processing software with extensive control over instruments, waveform manipulations, and graphic display. Numerous transient waveforms scattered from spheres and cylinders of various sizes have been recorded. A recently developed data-processing technique has been described and applied to these transient waveforms to extract their resonant frequencies. With the use of a new window designed to have a low near-sidelobe level, the modified fast Fourier transform (FFT) is shown to be able to improve the measurement capability of the system.

Design of array and line-source antennas for Taylor patterns with a null

An antenna pattern design technique which results in a generalized Taylor pattern, except in a narrow region where a deep null is formed, centered at a preassigned position is presented. It is shown how this technique can be applied effectively to both linear arrays and line sources. The approach is direct so that the technique does not use either iterative sampling or a perturbation procedure. It is particularly useful in the design of a large array with a prescribed deep null. Numerical results indicate that to steer such a null, adjustment of the excitation is necessary near the edges only.

Enhancement of Poles in Spectral Analysis

This paper presents a new technique for detecting a small pole in the presence of a nearby strong pole. By simultaneously applying the chirp z-transform (CZT) and a recently developed window, the new technique is shown to be able to detect and resolve a small pole. The CZT is efficient since it employs the fast Fourier transform (FFT) to evaluate a convolution. But unlike the FFT which is limited to the evaluation of the spectrum on the jw-axis, the CZT can evaluate the z-transform on the whole complex plane. And with the use of the new window, which is designed to have a near-sidelobe level of any specified value, the CZT is shown to be able to resolve two closely spaced poles with a large difference in amplitudes. Unlike the Pronys method, the new technique does not require predetermining the system order. No matrix inversion or solution of polynomial roots is required. Further, the new technique is a linear operation. Thus even under noisy environments it yields accurate, stable results for extraction of poles from transient response data.

Tolerance of Spectral Estimation

A statistical expression for the mean square error of a spectrum estimation has been derived in terms of the variances and covariances of the amplitude and phase errors of a complex data sequence. No restrictions need be imposed on the magnitude of these variances and covariances. Numerical results have been systematically presented in graphs which illustrate the dependence of the spectrum error on the standard deviation and correlation distance of the amplitude and phase errors. It is shown that large phase error tends to dominate the spectrum error, and that large correlation distances worsen the spectrum error and sharpen its dependency on the frequency index. An expression to estimate the variance of frequency error has also been derived under the assumption of small phase errors. Numerical results are given, which demonstrate the linear dependency of the frequency error on the phase error and shows that a large correlation distance worsens the frequency error while a large number of samples reduces it.

Deconvolution by the conjugate gradient method

Since it is practically difficult to generate and propagate an impulse, often a system is excited by a narrow time domain pulse. The output is recorded and then a numerical deconvolution is often done to extract the impulse response of the object. Classically, the fast Fourier transform technique has been applied with much success to the above deconvolution problem. However, when the signal to noise ratio becomes small, sometimes one encounters instability with the FFT approach. In this paper, the method of conjugate gradient is applied to the deconvolution problem entirely in the time domain. The method converges for any initial guess in a finite number of steps. Also for the application of the conjugate gradient method the time samples need not be uniform like FFT. Computed impulse response utilizing this technique has been presented for measured incident and scattered fields from a sphere and a cylinder.

Adaptive antenna arrays via spatially smoothed ESPRIT

The paper presents an adaptive technique to create multiple nulls to suppress multiple jammers. The adaptive technique is based on forward and backward smoothed ESPRIT (estimation of signal parameters via rotational invariance technique), which is capable of handling both coherent and non-coherent narrow-band multiple signals. It is demonstrated to be effective and efficient. Computer simulations for a linear array of 32 elements have shown that the optimization technique can create wide as well as deep nulls, which correspond well to jammer widths and strengths. In all cases the SIR improves substantially and converges quickly.

Detection of Branch Points by Modified FFT

This paper illustrates the existence of branch points in transients on lossy transmission lines and presents a technique of detecting branch points. By applying modified FFT to the transient signal and from the resulting amplitude and phase spectra, it is possible to detect and distinguish banch points from poles. Numerous examples are given to demonstrate the effectiveness of the modified FFT and the use of windowing in improving the detectability of a small branch point under the influence of a nearby strong pole.