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First-order hold (FOH) is a mathematical model of the practical reconstruction of sampled signals that could be done by a conventional digital-to-analog converter (DAC) and an analog circuit called an integrator. For FOH, the signal is reconstructed as a piecewise linear approximation to the original signal that was sampled.
A simple example of a Butterworth filter is the third-order low-pass design shown in the figure on the right, with = 4/3 F, = 1 Ω, = 3/2 H, and = 1/2 H. [3] Taking the impedance of the capacitors to be / and the impedance of the inductors to be , where = + is the complex frequency, the circuit equations yield the transfer function for this device:
The transfer function of a two-port electronic circuit, such as an amplifier, might be a two-dimensional graph of the scalar voltage at the output as a function of the scalar voltage applied to the input; the transfer function of an electromechanical actuator might be the mechanical displacement of the movable arm as a function of electric ...
The bilinear transform is a first-order Padé approximant of the natural logarithm function that is an exact mapping of the z-plane to the s-plane.When the Laplace transform is performed on a discrete-time signal (with each element of the discrete-time sequence attached to a correspondingly delayed unit impulse), the result is precisely the Z transform of the discrete-time sequence with the ...
N th-order CIC filters have N times as many poles and zeros in the same locations as the 1 st-order. Thus, the 1 st-order CIC's frequency response is a crude low-pass filter. Typically the gain is normalized by dividing by () so DC has the peak of unity gain. The main lobes drop off as it reaches the next zero, and is followed by a series of ...
The transfer function for a first-order process with dead time is = + (), where k p is the process gain, τ p is the time constant, θ is the dead time, and u(s) is a step change input. Converting this transfer function to the time domain results in
Comb filters may also be implemented in continuous time which can be expressed in the Laplace domain as a function of the complex frequency domain parameter = + analogous to the z domain. Analog circuits use some form of analog delay line for the delay element. Continuous-time implementations share all the properties of the respective discrete ...
The first example gives the circuit for a 6th order maximally flat delay. Circuit values for z a and z b for a normalized lattice (with z b the dual of z a) were given earlier. However, in this example the alternative version of z b is used, so that an unbalanced alternative can be easily produced. The circuit is