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The group delay and phase delay properties of a linear time-invariant (LTI) system are functions of frequency, giving the time from when a frequency component of a time varying physical quantity—for example a voltage signal—appears at the LTI system input, to the time when a copy of that same frequency component—perhaps of a different physical phenomenon—appears at the LTI system output.
The Taylor series expansion of the group delay is = + +. Note that the two terms in and are zero, resulting in a very flat group delay at =. This is the greatest number of terms that can be set to zero, since there are a total of four coefficients in the third-order Bessel polynomial, requiring four equations in order to be defined.
An ideal delay line characteristic has constant attenuation and linear phase variation, with frequency, i.e. it can be expressed by =where τ is the required delay.. As shown in lattice networks, the series arms of the lattice, za, are given by
Group delay largely frequency-dependent; Here is an image showing the gain of a discrete-time Butterworth filter next to other common filter types. All of these filters are fifth-order. The Butterworth filter rolls off more slowly around the cutoff frequency than the Chebyshev filter or the Elliptic filter, but without ripple.
The second factor is the CLF, or the cooling load factor. This coefficient accounts for the time lag between the outdoor and indoor temperature peaks. Depending on the properties of the building envelope, a delay is present when observing the amount of heat being transferred inside from the outdoors.
A common file format for storing the lookup tables is the Liberty [2] [3] format. A very simple model called the K-factor model is sometimes used. This approximates the delay as a constant plus k times the load capacitance. A more complex model called Delay Calculation Language, [4] or DCL, calls a user-defined program whenever a delay value is ...
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DDEs are also called time-delay systems, systems with aftereffect or dead-time, hereditary systems, equations with deviating argument, or differential-difference equations. They belong to the class of systems with the functional state , i.e. partial differential equations (PDEs) which are infinite dimensional, as opposed to ordinary ...