The method allows the designer to implement a delay characteristic by locating poles and zero on the complex frequency plane intuitively, without the need for complicated mathematics or the recourse to reference tables.
12.
In mathematics and signal processing, the "'Z-transform "'converts a discrete-time signal, which is a sequence of real or complex numbers, into a complex frequency domain representation.
13.
If the amplifier output resistance is included in the analysis, the output voltage exhibits a more complex frequency response and the impact of the frequency-dependent current source on the output side must be taken into account.
14.
Where " s " is the complex frequency ( s = j \ omega ), \ omega _ s is the series resonant angular frequency, and \ omega _ p is the parallel resonant angular frequency.
15.
In electrical network analysis, " Z " ( " s " ) represents an impedance expression and " s " is the complex frequency variable, often expressed as its real and imaginary parts;
16.
The transfer function \ H ( s ) of a filter is the ratio of the output signal \ Y ( s ) to that of the input signal \ X ( s ) as a function of the complex frequency \ s:
17.
If the complex frequency \ mathit { s } \, and all circuit variables are symbolic ( fully symbolic analysis ), the voltage transmittance is given by ( here G _ i = 1 / R _ i \, ):
18.
In this example, polynomials in the complex frequency domain ( typically occurring in the denominator ) correspond to power series in the time domain, while axial shifts in the complex frequency domain correspond to damping by decaying exponentials in the time domain.
19.
In this example, polynomials in the complex frequency domain ( typically occurring in the denominator ) correspond to power series in the time domain, while axial shifts in the complex frequency domain correspond to damping by decaying exponentials in the time domain.
20.
Generally, for insertion-loss filters where the transmission zeroes and infinite losses are all on the real axis of the complex frequency plane ( which they usually are for minimum component count ), the insertion-loss function can be written as;
