Abstract
The transfer function is fundamental in describing linear systems. This chapter describes introductory but basic aspects of transfer functions such as minimum-phase and non-minimum-phase decomposition including the introduction of cepstral sequences from a point of view of waveform analysis. The logarithm of the transfer function is the starting point for the analytical formulation of the power spectral density function as well as for the magnitude and accumulate-phase spectral responses. In particular, the geometrical interpretation of the phase is helpful in understanding the discontinuous phase function in the limit. Filtering is a central issue of the linear system theory. This chapter describes ideal low-pass filtering in terms of the Dirichlet kernel.
The original version of this chapter was revised.
An erratum to this chapter can be found at DOI 10.1007/978-4-431-54424-1_10
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Tohyama, M. (2015). Transfer Function of Linear Systems. In: Waveform Analysis of Sound. Mathematics for Industry, vol 3. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54424-1_6
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DOI: https://doi.org/10.1007/978-4-431-54424-1_6
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