An Application of the Data Adaptive Linear Decomposition Transform in Transient Detection

Abstract

The analysis of transient signals is an attractive framework for many problems in digital signal processing. This paper provides an application of the data adaptive linear decomposition transform  (LDT) to detect transients in the sinusoidal signal corrupted by an additive impulse noise. The LDT procedure entails obtaining an interpolation error sequence of half-length of the sinusoidal signal, and processing down-sampled data by using a l_p norm optimum interpolation filter. This optimum filter seeks to approximate the odd indexed sequence elements by a linear combination of neighboring even indexed elements to generate the resulting interpolation error sequence. This study shows that a spike being in the interpolation error sequence indicates the location of the transient in the signal, and the effectiveness of the transient detection performance using the l_l-based method compares favorably with the l₂ - and l∞ -based methods including the popular discrete wavelet transform method.