New ultrasonic signal processing techniques have been developed for nondestructive evaluation (NDE) applications. This dissertation has two parts. The first part is about the application of the wavelet transform to ultrasonic flaw detection. Wavelet transform is a newly developed signal analysis tool that handles time-localized signals such as an ultrasonic flaw signal quite well. A wavelet transform based signal processing technique has been developed which uses only partial knowledge of the flaw signal waveform that may be obtained from a reference experiment. The detection performance of the proposed technique is found to be comparable to that of the matched filter which requires exact knowledge of the flaw signal waveform and the noise autocorrelation function to obtain good detection performance. The proposed technique based on the wavelet transform can therefore be quite useful in situations where the flaw signal waveform is unknown or partially known. The detection performance of the proposed technique which was evaluated for hard-alpha detection in titanium samples using experimentally obtained grain noise data and simulated flaw data was very close to that of the matched filter;The second part of this dissertation describes a Kalman filter based deconvolution algorithm for ultrasonic signals and its application to material characterization and hard-alpha detection. The Kalman filter based deconvolution algorithm is based on state-space modeling of the ultrasonic measurement system. Since the Kalman filter can handle time-varying systems and non-stationary statistics quite naturally, it is better suited for such situations than the Wiener filter approach. A signal processing technique using Kalman filter based deconvolution algorithm has been developed and applied to characterize materials with different grain sizes and to detect inclusions from host material. The proposed method was tested using experimentally obtained ultrasonic data from pure titanium samples with different grain sizes. The results showed good detection performance for detecting inclusions larger that 4 mm.