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System Simulator > Discrete Time Simulation of Signals and Noise WaveformsIn discrete time simulation, all waveforms (signal and
noise) are represented in a discrete (sampled) form. This implies that
baseband signal and noise waveforms may be simulated using the discrete
signals The Nyquist criterion states that if a continuous time signal S(t) is sampled at a rate that is at least twice its highest frequency content (i.e., bandwidth), this signal may be completely reconstructed from its sampled version S(nts). The minimum sampling rate needed to completely recover a continuous signal from its sampled version is known as the Nyquist rate. It is the responsibility of the user to be aware of the signal S(t) bandwidth. It is highly recommended that the actual simulation sampling rate be chosen well above the Nyquist rate for more accurate simulations. This added accuracy typically results in a longer simulation time. Most bandpass signals encountered in practical communications systems are narrowband signals. A narrowband bandpass signal has a bandwidth that is much less than its carrier frequency. This enables the Designer discrete time simulator to utilize envelope modulation techniques whereby only the complex envelope of the bandpass signal (or band-limited noise) is sampled (as opposed to sampling the carrier as in SPICE-like techniques). As a result, the actual simulation sampling rate may be orders of magnitude less than that of a SPICE-like simulation. This would naturally translate into a much faster simulation time. Thus, the information of a continuous bandpass signal and noise may simply be recovered from knowledge of their corresponding sampled complex envelope signals:
and
respectively, as well as the carrier frequency fc. Thus, the information of a continuous bandpass signal and noise may be recovered from the triplets (IS(nts), QS(nts), fc) for the signal information and (IN(nts), QN(nts), fc) for the noise information. To ensure that the Nyquist criterion still holds for narrowband bandpass signals, the user needs to choose a simulation sampling rate that is at least twice the highest frequency content (bandwidth) of the complex envelope .
The choice
for the simulation sampling rate fs affects the outcome of
the simulation. Choosing a simulation sampling rate fs
that is higher than 2fc results in the sampling
of the carrier. In this case, the bandpass signal with a complex envelope
representation will be converted to a baseband real signal of the form: Conversely, time domain simulation results for bandpass
signals with a sampling rate
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Ansoft Designer / Ansys Designer 在线帮助文档：
, 
, 
= Waveform simulation time step
, 
, 
may
only be viewed in terms of their complex envelopes.
