High Resolution Time-Frequency Representation of Narrow-Band Transient Signals

April 2000

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Introduction

With the advent of very high speed, precision A/D converters, much of the sophisticated signal processing is shifting from the electronic analog domain to digital signal processing algorithms. Today, the acquisition of signals with an upper band-limit of one Megahertz merely requires basic signal pre-conditioning electronics, all further processing such as filtering, rate-conversions, and signal detection can be applied after the signal has been digitized.

This report puts a focus on a time-frequency method for signal detection. Generally time-frequency processing received much attention in the context of wavelet-analysis. However, the time-frequency representation based on a wavelet spectrum is difficult to relate to physical signal properties.

This approach is different. It is based on Fourier-spectra. The signal is analyzed to derive a parametric spectral model. A Fourier-spectrum can then be computed with arbitrary frequency resolution. The parametric model is calculated on a sample by sample basis. Thus, a sonogram of a signal may be computed with unlimited frequency resolution and a resolution in time as small as delta t, where delta t is the sampling interval.