Digital signal processing has become an important component of data analysis needed in industrial applications. In particular, for ultrasonic thickness measurements the signal to noise ratio plays a major role in the accurate calculation of the arrival time. For this application a band pass filter is not sufficient since the noise level cannot be significantly decreased such that a reliable thickness measurement can be performed. This paper demonstrates the abilities of two regularization methods - total variation and Tikhonov - to filter acoustic and ultrasonic signals. Both of these methods are compared to a frequency based filtering for digitally produced signals as well as signals produced by ultrasonic transducers. This paper demonstrates the ability of the total variation and Tikhonov filters to accurately recover signals from noisy acoustic signals faster than a band pass filter. Furthermore, the total variation filter has been shown to reduce the noise of a signal significantly for signals with clear ultrasonic echoes. Signal to noise ratios have been increased over 400% by using a simple parameter optimization. While frequency based filtering is efficient for specific applications, this paper shows that the reduction of noise in ultrasonic systems can be much more efficient with regularization methods.