| In this dissertation, a new transform for decomposing one-dimensional and two-dimensional data is developed and implemented in three digital signal processing application modes: transient signal detection, data compression, and noise reduction. This transform, called the linear decomposition transform (LDT), is composed of a linear shift-invariant interpolation filter and a down-sampling-by-two operation. This interpolation filter operating on a down-sampled input data sequence seeks to approximate the odd indexed data sequence elements by using a linear combination of neighboring even indexed data sequence elements lying to its right and left. The resulting half-length interpolation error sequence plays the role of the wavelet detail sequence coefficients. However, the LDT here developed distinguishes itself by being data dependent rather than using a fixed interpolation filter bank as do traditional discrete wavelet transforms (DWT). The interpolation filter coefficients are chosen to minimize the l1, l2 and l∞ norms of the interpolation error sequence. In the above LDT application schemes, experimental results obtained from each LDT method are compared with the DWT method using orthogonal wavelet filters: DB2, DB4, and Symlet8. |
