# Guidelines for Defining a Time Signal

The simulated frequency range and frequency sampling affects the time signal that can be created.

Note:
• If part of the time signal does not fall within the same frequency range as the simulation, it is possible that the windowing effect can introduce numerical artefacts in the time domain results.
• The time signal repeats due to the application of an inverse fast Fourier transformation (IFFT) on the frequency domain simulation results. Care should be taken that the repeating time signal corresponds to the desired time signal.

Follow these basic guidelines when defining a time signal:

## Total Signal Duration ( ${s}_{\text{d}}$ )

For a given total signal duration of ${s}_{\text{d}}$ , the lowest frequency to be simulated is given by:

${f}_{\mathrm{min}}=\frac{1}{{s}_{d}}$

The total signal duration should allow for the response signal to decay sufficiently before the time signal repeats.

Note: The duration of the response signal decay is model dependent and only required when the signal is not intended as a repeating time signal pulse.

## Time Sampling ( ${d}_{t}$ )

The time step ${d}_{t}$ will be given by:

${d}_{t}=\frac{1}{\left(2×{f}_{\mathrm{max}}\right)}$
where ${f}_{\mathrm{max}}$ is the highest frequency to be simulated.

## Number of Time Samples ( ${N}_{t}$ )

The number of time samples is derived from:

${N}_{t}=\frac{{s}_{d}}{{d}_{t}}$

## Number of Positive Frequency Samples

The number of frequency samples (positive) excluding zero is given by:

${N}_{f}=\frac{{N}_{t}}{2}$

## Bandwidth Calculation of Time Signals

The total power content of the time signal is calculated as follows:

Pt = P1 + P2 + Pi + ... + Pn
where
 Pi = (SpectrumValue(F(i-1))^2 + SpectrumValue(F(i))^2) * 0.5 * (F(i) - F(i-1)).
The bandwidth of the time signal is then calculated as follows:
BW = [Fstart, Fend]
where Fstart = Fi for the lowest frequency where Pi > 10% * Pt

and Fend = Fi for the lowest frequency where Pi > 90% * Pt.

In summary, the model should be simulated from fmin to fmax. The POSTFEKO power bandwidth calculation as described above gives an indication of the frequency range where most of the signal power is contained.

POSTFEKO will use this power bandwidth to give a warning when there is insufficient overlap between the simulated frequency range and the power bandwidth.