Signal Processing in C

PART III

Waveforms and Filters

This part contains the second project: the analysis of a glockenspiel and a piano waveform. The goal is to find a way, using digital signal processing, to recreate the sounds of these instruments. This is not easily accomplished, and the final results are not perfect replicas of the original sounds. In particular, the “attack” of an instrument is very important to its perceived tonal quality, but only the “sustain” is addressed here.

Chapter 13 introduces the project by giving a deceptively simple statement of the problem in Equation 13.1. This leads to a consideration of impulse responses and FIR and IIR filtering as well as spectral analysis of the waveforms.

Chapter 14 explains the basics of DSP filters and derives all the formulas required to implement them and to calculate their gain as a function of frequency. Chapter 15 completes these considerations by showing how to implement these filters in C routines.

Chapter 16 introduces the (generalized) LP (linear predictive) method of filter estimation. The LP method is tested on waveforms generated by known digital filters, then applied to segments of the glockenspiel and piano waveforms.

Finally, the reader is challenged to carry this process further by analyzing the French horn and trumpet waveforms and using the results to create a multiple-voice music synthesizer.