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where
is the Fourier transform of
1.2 Linear Periodically Time-Varying Systems
If a system is linear periodically time-varying, we show in Appendix
3.A of this chapter that time-varying network function is also
periodic in Assume that satisfies Dirichlet-Jordan criterion,
i.e. is bounded, piecewise continuous, and has at most a finite
number of minima, maxima, and discontinuities per period,
can
be represented in the Fourier series
where
and
is the period. The coefficients are determined
from
The frequency response of the output, denoted by
is obtained by
taking Fourier transform of (3.5)
Further making use of (3.6), Eq.(3.8) becomes
Because
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