Since a Gaussian pulse waveform has considerable DC content, it must be used to model lowpass structures. In that case, the center frequency and bandwidth of the project must be set such that Δf = 2f<sub>0</sub> and hence, f<sub>min</sub> = f<sub>0</sub> - Δf/2 = 0, and f<sub>max</sub> = f<sub>0</sub> + Δf/2 = 2f<sub>0</sub>. The width t of the temporal Gaussian pulse is then determined such that at f<sub>max</sub> the spectral Gaussian pulse drops to the d-level from its maximum value of 1. With a bandwidth of Δf, the pulse width must satisfy the following equation:
:<math>\exp[-(\pi f_{\delta} \tau)^2] = \exp[-(\pi \Delta f \tau)^2] = \delta \quad \Rightarrow \quad \tau = \frac{\sqrt{-\ln\delta}}{\pi f_{max}}</math><!--[[Image:FDTD64(1).png]]-->
When you set δ = 0.1 (the default value), it means that the Fourier transform of your excitation waveform drops to 10% of its peak at the upper edge of your specified frequency range. For a Modulated Gaussian pulse waveform with a bandwidth of Δf, the pulse width must satisfy the following equation:
:<math>\exp[ -[\pi(f_{\delta} - f_0)\tau] ^2 ] = \exp \left[ -\left(\pi \frac{\Delta f}{2} \tau\right)^2 \right] = \delta\quad \Rightarrow \quad\tau = \frac{2\sqrt{-\ln \delta}}{\pi \Delta f}</math><!--[[Image:FDTD65.png]]-->
For the default value of δ = 0.1, you get the standard relation: τ = 0.966 / BW, which is typically used for modulated Gaussian waveforms. The source waveform requires a time delay t<sub>0</sub> so that its value drops to almost zero at t = 0. The time delay is expressed in terms of a multiple of the pulse width: '''t0 / tau''', and its default value is 4.5.
Keep in mind that FDTD is a time domain algorithm. At the end of an FDTD simulation, a Discrete Fourier Transform (DFT) is performed on the time domain data to calculate frequency domain characteristics such as near fields, far field radiation patterns, RCS, S/Y/Z parameters, etc.:
:<math>\tilde{F}(f) = \int_{-\infty}^{\infty} f(t) e^{-j2\pi f t} \, dt \quad \approx \quad\Delta t \sum_{n=0}^N f(n\Delta t) e^{-j2 \pi n f \Delta t}</math><!--[[Image:FDTD68.png]]-->
Of [[FDTD Module]]'s observables, the near fields, far fields and all of their associated parameters like directivity, RCS, etc., are calculated at a certain frequency that is specified as part of the definition of the observable. On the other hand, port characteristics like S/Y/Z parameters, VSWR and periodic characteristics like reflection and transmission coefficients, are calculated over the entire specified bandwidth of your project. In other words, you get a wideband frequency response at the end of a single time domain FDTD simulation run. The number of frequency point data over this bandwidth is equal to the number of DFT samples that are generated during the time marching loop. This number is set to 200 by default. In other words, 200 frequency data are generated at the end of an FDTD simulation. You can change this number through the box labeled '''No. DFT Samples''' in the "Discrete Fourier Transform" section of the FDTD Simulation Engine Settings dialog.