Optimal filters for deconvolution of transient signals in the presence of noise
MetadataShow full item record
This dissertation presents different methods for the deconvolution of time domain signals. The techniques developed in this work are frequency domain filtering techniques. and are suitable for the type of deconvolution problems encountered in time domain reflectometry (TOR). They include a smoothing technique that is a variant of the well known lowpass filter. This technique is parameter dependent in order to allow for adequate choice of cutoff frequency. Another more powerful method developed is an adaptive smoothing (regularization) technique, which is both frequency dependent and input-signal dependent as well. Thus, it is an adaptive technique whose performance depends on a parameter associated with its smoothing constraint. These frequency domain techniques and their variants are parameter dependent; hence a parameter optimization criterion must be included. However, in deriving an optimization criterion, great importance must be given to its adequacy in the determination of the appropriate parameter value as well its time efficiency. A parameter optimization method that fulfills those two reqUirements is also developed. The method is fully implemented in the frequency domain in which the filtering techniques are used. The techniques developed are derived with a magnitude component only. i.e., non-causal. The limited derivation is due to the fact that we are usually interested in reducing only the noise level from the magnitude point of view. However, If we consider time domain measurements as an example, physical pulses and transients are causal functions of time, i.e., their values are zero before t = 0, the time at which they begin. Their measured waveform data are also causal. When deconvolution processing is applied to remove instrumentation errors and/or suppress the effects of noise, non-causal deconvolution methods, that were mentioned previously, may introduce unacceptable errors. The conventional deconvolution is modified to ensure that causality is maintained in the deconvolution result. The impulse response of an unknown system is recovered from time domain reflectometry data by implementing a method based on the homomorphic deconvolution technique. In time domain reflectometry, the reflected waveform by a line with several disw continuities is represented as the convolution of the reflection coefficient of the line and the input excitation of the line source. The reflection coefficient is generally a train of spikes (delta functions) when the discontinuities are resistive. However, this is not the case when the discontinuities are capacitive in nature. In this work, we will attempt to show that the conventional frequency domain deconvolution techniques fail to provide good estimates when the waveform contains certain amounts of noise. Since it has been shown that homomorphic systems are useful in separating signals which have combined through convolution, homomorphic filtering can then be applied to recover either the input excitation or the impulse response (reflection coeffiCient) of the network.
- Doctoral Dissertations