Variable-size signals and Unit Delay

Posted by Guy Rouleau, June 28, 2011

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I received requests recently about variable-size signals and the Unit Delay block.

One question, many answers

What should a Unit Delay do when the size of a signal changes?

Unfortunately, there is not only one correct answer to this question. Let's say I have a Unit Delay block and its input signal changes from a size of 3 to a size of 2, what should the output be? When should the dimension of the output change?

Let's look at the options you have.

MathWorks Solution

As explained in Variable-Size Signal Basics, blocks supporting variable-size signals can propagate sizes in one of two ways:

At every step of model execution
During initialization of a conditionally executed subsystem

How do you know into which category a specific block is? A good rule is that, most blocks with states fall in the second category. To ensure consistency and avoid confusion, those blocks are allowed to propage sizes only during the initialization of a conditionally executed system.

Let's look at an example

Here I create a variable-size signal by alternating between 3 constants and 2 random numbers. If I want to apply a Unit Delay to this signal, I need to place it inside a Conditionally Executed Subsystem and ensure that the subsystem is enabled and disabled every time the dimension change. Here I do that using a Stateflow Chart:

Example model showing how to use the Unit Delay with variable-size signals

The result is that every time the dimension changes, the state of the Unit Delay is reset to its initial condition, zero in this example:

Data passing through a Unit Delay with variable-size signals

My Alternative Solution

For many reasons, one might need a Unit Delay block who works with variable-size signals, but who does not need to be placed inside a conditionally executed subsystem. To help you getting started with that, I created technical solution 1-ET7RPB. I am not going into the details here, but this solution contains the MATLAB and C versions of my alternative version of a Unit Delay block implemented as an S-Function.

To process a signal similar to the previous example, this Unit Delay block does not need to be placed inside a conditionally executed subsystem:

Data passing through a Unit Delay with variable-size signals