Wavelet Toolbox Guided Learning Handbook: music technology illustrations

SIGMA, the Centre for Excellence in Mathematics & Statistics Support, provided in 2007 a Technology Evaluation Project grant for the Wavelet Toolbox software. This is an add-on for Mathworks’ Matlab software. The wavelet transform converts a signal from the time-domain to the scale domain, where various characteristics of the signal become more explicit. It is very good at representing the time-varying nature of engineering signals. A recently developed Guided Learning Handbook website has the purpose of enabling students to bridge the gap between theoretical knowledge of this subject and practical implementation of software that uses the toolbox. This paper describes some new work included in the handbook which has the purpose of starting students off with practical experimentation by feeding pre-produced sound samples into the Wavemenu facility of the toolbox. They can then experiment with various wavelet parameters to examine their effect on the representation. When the signal from an electric guitar is examined using Wavemenu, the original plucking impulse can be clearly identified from one of the wavelet coefficient plots. Student experiments can investigate the effect on the representation of wavelet choice and start to relate this to theoretical considerations. For example, the Biorthogonal wavelet has the property of linear phase which is needed for signal reconstruction.