Use the standard functions in Table 4.1 to form test signals, data patterns, and pulses , or to feather the edges of fastchanging signals.
The first three entries reveal the DFT sequences necessary to create timedomain pulses and clock waveforms. If the pulse width in each case is set to an integral number of time samples, the timedomain transform will display no aliasing. That's nice for creating goodlooking charts and graphs, but doesn't really hide the aliasing problem. If you shift the waveform by a nonintegral number of sample points (using the shift operator), the aliasing, also called Gibbs phenomenon , comes back. The only true solution to aliasing is to apply somewhere within your simulation a heavyduty smoothing filter and sample on a dense grid of points with a spacing at least 4x finer than the risetime of the smoothing filter. If nothing else, you should be simulating the risetime of your oscilloscope probe or the bandwidth of your receiver using a Gaussian filter.
The next three entries depict various edgesmoothing filters. The linear filter leaves a squareedged signal with an unrealistically large amount of highfrequency content. The highfrequency content generates aliasing that must be fixed by either (1) further filtering the signal to limit its bandwidth, or (2) using an outrageously high sampling rate.
For general work I use the Gaussian filter the most. Provided the Gaussian risetime is set to a minimum of four sample points, it practically eliminates aliasing.
The quadratic filter lies between the extremes of the linear and Gaussian filters. If used as the only band limiting filter in a simulation, it requires a sampling rate greater than the Gaussian filter but not as great as the linearramp filter. Quadratic responses are popular with some IBIS model proponents because the timedomain result is parabolic and therefore easy to compute. This filter synthesizes the same exact parabolic response.
If you must simulate ramp waveforms in your circuit, then I suggest you use the linearramp filter with the necessary risetime followed by a Gaussian filter with a much smaller (10x smaller) risetime, and then sample the composite signal on a dense grid 4x finer than the Gaussian filter risetime.
Table 4.1. Useful Fourier Transform Pairs
Fourier Transform 
DFT 

Pulse of width b 

Pulse of width ( N /2) D T 

Clock waveform with M complete cycles 

Delay operator (delays by amount t ) 

Linearramp LPF with 1090% risefall time r (set q = 1.25 · r ) 

Quadratic LPF with 10% to 90% rise/fall time r (set q = 0.9045084972 · r ) 

Gaussian LPF with 10% to 90% rise/fall time r (set q = .275 · r ) 

POINT TO REMEMBER
Fundamentals
Transmission Line Parameters
Performance Regions
FrequencyDomain Modeling
Pcb (printedcircuit board) Traces
Differential Signaling
Generic BuildingCabling Standards
100Ohm Balanced TwistedPair Cabling
150Ohm STPA Cabling
Coaxial Cabling
FiberOptic Cabling
Clock Distribution
TimeDomain Simulation Tools and Methods
Points to Remember
Appendix A. Building a Signal Integrity Department
Appendix B. Calculation of Loss Slope
Appendix C. TwoPort Analysis
Appendix D. Accuracy of Pi Model
Appendix E. erf( )
Notes