14 DYNAMIC CIRCUITS WITH APERIODIC INPUTS – ANALYSIS BY FOURIER TRANSFORMS
v
1
(t) is applied and r
2
(t) is the output when v
2
(t) is applied, r
1
(t) r
2
(t) is not the output when
v
1
(t)v
2
(t) is applied to the circuit. The superposition principle covers only scaling by a
constant and linear combinations of inputs. Multiplication of two functions of time is not a
linear operation – i.e., it does not obey the superposition principle.
14.2 FOURIER TRANSFORM OF AN APERIODIC WAVEFORM
We could not work out the output of the circuit with an aperiodic input v(t) from the output
corresponding to its periodic version v
~
(t), since there are infinitely many periods ...
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