Conclusion

An introduction to digital filters has been presented. The main utility of the analysis methods presented is in ascertaining how a given filter will affect the spectrum of a signal passing through it. Some of the concepts introduced were linearity, time-invariance, filter impulse response, difference equations, transient response, steady-state response, transfer functions, amplitude response, phase response, group delay, poles and zeros, filter stability, and the general use of complex numbers to represent signals, spectra, and filters.

However, this is still only the beginning. With these foundations there is an unlimited number of avenues of investigation into reverberation, computational musical acoustics, time-varying spectral modifications, speech modeling by means of pulse-driven filters, musical instrument simulation, and so on [80,81]. Given the immense range of naturally occurring filters in the domain of music, it is reasonable to expect that filter theory will continue to provide valuable tools for the analysis, synthesis, and manipulation of sound.

The following appendices provide elementary background material in support of the preceding chapters, as well as related and more advanced topics for further study.