Dick, Andrew J.2013-07-242013-07-242013-07-242013-07-242012-122013-07-24December 2Phan, Quan. "Design of vibration inspired bi-orthogonal wavelets for signal analysis." (2013) Master’s Thesis, Rice University. <a href="https://hdl.handle.net/1911/71679">https://hdl.handle.net/1911/71679</a>.https://hdl.handle.net/1911/71679In this thesis, a method to calculate scaling function coefficients for a new bi-orthogonal wavelet family derived directly from an impulse response waveform is presented. In literature, the Daubechies wavelets (DB wavelet) and the Morlet wavelet are the most commonly used wavelets for the dyadic wavelet transform (DWT) and the continuous wavelet transform (CWT), respectively. For a specific vibration signal processing application, a wavelet basis that is similar or is derived directly from the signal being studied proves to be superior to the commonly used wavelet basis. To assure a wavelet basis has a direct relationship to the signal being studied, a new formula is proposed to calculate coefficients which capture the characteristics of an impulse response waveform. The calculated coefficients are then used to develop a new bi-orthogonal wavelet family.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.Wavelet transformImpulse responseScaling function coefficientsBi-orthogonal waveletDilation equationThesis2013-07-24123456789/ETD-2012-12-215