Convolution Example: A Simple Filter

This example shows how a simple input signal can be filtered to alter its shape.  In this example, the input signal is a square “boxcar” function:

Mathematically, this can be expressed in GoldSim as follows:

If(ETime < 5 days OR ETime > 10 days, 0, 1)

The Transfer function is also a square “boxcar” function, in which any impulse is delayed for 10 days, and then spread out evenly over 5 days:

Mathematically, this can be expressed in GoldSim as follows:

If(~Lag < 10 days OR ~Lag > 15 days, 0, 0.2)

This input signal and transfer function produce the following output signal:

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Note that the output signal in this case has dimensions of time (since the input signal and the transfer function were defined as being dimensionless).

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