This video is taken from the INT 100 course on Lumerical University.

## Transcript

The Transient Sample Mode is a bidirectional sample-by-sample data processing approach,

where each invocation of an element accepts one sample from each input port of the element

and produces one sample at each output port.

At each time step, each element takes the data at its input ports and calculates the

data at its output ports using its impulse response.

The block diagram shows how data propagates through the elements sample by sample in this

approach.

In the time-domain, the response of an element to an input signal can be calculated through

time-convolution of the input signal with the element's impulse response.

The impulse response is the response of the element to an impulse or a delta function.

For continuous time signals the convolution is given by this integral equation, where

the b function is the impulse response and the x function is the input signal.

In sample mode, the signal through an element is calculated sample by sample.

Since the signal is discrete, the convolution becomes a discrete convolution

and needs to be calculated numerically.

The discrete impulse response of an element is represented by what's called a digital

filter.

Two types of digital filters are available in INTERCONNECT, the Finite Impulse Response

filter, called FIR for short and the Infinite Impulse Response filter called IIR for short.

We'll focus on the FIR filter in this course.

The figure shows the block diagram and the output sequence equation of an FIR filter,

where Z-transform notation is applied.

The sequence for the output signal, y, at time step n, is a weighted sum, where x is

the input signal at time step n, and each b value is the digital filter impulse response

at the i-th instant.

N is the filter order, also called the number of taps.

It represents the number of time steps over which the impulse response is defined.

Note that this weighted sum used to calculate the output signal is a numerical convolution.

Digital filters, like the FIR filter, are implemented in INTERCONNECT Transient Sample

Mode simulations to capture the circuit response, sample-by-sample.

A more generalized approach for calculating output signals than what was shown here is

applied to capture bidirectional propagation of multiple modes.

INTERCONNECT runs a time domain simulation when time dependent sources are connected

to the inputs of a circuit.

The sources define the simulation bandwidth as well as the center frequency, which is

also the carrier frequency for the optical waveform.

For simulations with multiple sources, if the source center frequencies and bandwidths

all fall within a frequency range smaller than the sample rate, the simulator will automatically

perform a single band simulation, by default.

If this is not the case, simulation will be performed over multiple bands.

In this case the user is notified by a warning message that says that multiple channels are

detected.

For a detailed discussion of the simulation band please see the Knowledge Base by following

the link provided below the video.

For an element to process data, a signal is required at each of the element ports.

When the simulation is initialized, by default, null data is initialized at each connection

so that the simulations can begin.

As the simulation progresses, the input signals from the sources propagate through the elements

and the null data get replaced by valid data.

This way, each connection in a circuit introduces a time delay of one time step.

Later in the course, we will show how "delay compensation" is used to remove these delays.