# Use a Variable-Size Signal in a Filtering Algorithm

This example uses a variable-size vector to store the values of a white noise signal. The size of the vector can vary at run time because the functions prune the signal values by:

• Filtering out signal values that are not unique to within a specified tolerance of each other.

• Averaging every two signal values and outputting only the resulting means.

In this model, a Band-Limited White Noise block generates a set of normally distributed random values as the source of a white noise signal. The MATLAB Function block `Filter` filters out signal values that are not unique to within a specified tolerance of each other. Then, the MATLAB Function block `Average` outputs the average of a specified number of unique signal values. The Scope blocks display the output from the `Filter` and `Average` blocks. Open the model to see the configuration.

```model = "emldemo_process_signal"; open_system(model);``` ### Inspect the Source Signal

Open the Band-Limited White Noise block to view the properties of the source signal. The size of the Noise power parameter defines the size of the array that holds the signal values. This array is a 1-by-9 vector of double values. ### Inspect the `Filter` MATLAB Function Block

`Open Filter` to inspect the filtering function. `Filter` filters out unique signal values that are not within a tolerance of `0.2` of each other. The function calls an external MATLAB® function file, `emldemo_uniquetol.m`, to filter the signal values. The function passes the 1-by-9 vector of white noise signal values as the first argument and the tolerance value as the second argument.

```function y = uniquify(u) y = emldemo_uniquetol(u,0.2); ```

Open the MATLAB function file `emldemo_uniquetol.m` to view the code for the external function, `emldemo_uniquetol`. `emldemo_uniquetol` returns the filtered values of `A` in an output vector `B` so that `abs(B(i) - B(j)) > tol` for all `i` and `j`.

```function B = emldemo_uniquetol(A,tol) %#codegen A = sort(A); B = A(1); k = 1; for i = 2:length(A) if abs(A(k) - A(i)) > tol B = [B A(i)]; k = i; end end ```

At each time step, the Band-Limited White Noise block generates a different set of random values for `A`, and `emldemo_uniquetol` may produce a different number of output signals in `B`. Therefore, `y` must be variable size. In order for y to be variable-size, you must enable the Variable size property. In this example, Variable size is enabled for `y`. In `Filter`, open the Symbols pane and Property Inspector. In the Function tab, click Edit Data. In the Symbols pane, click `y` to view the properties in the Property Inspector. For variable-size outputs, you must specify the Size property as the maximum-size upper bound. In the example, Size is `[1 9]`. You must enable the Support variable-size arrays property in the MATLAB Function block to enable the Variable size parameter for outputs.

### Inspect the `Average` MATLAB Function Block

`Average` averages the values filtered by `Filter` by following these conditions:

• If the number of signals is greater than `1` and divisible by `2`, then `Average` averages every consecutive pair of values.

• If the number of signals is greater than `1` but not divisible by `2`, then `Average` drops the first value and averages the remaining consecutive pairs.

• If there is exactly one signal, then `Average` returns the value unchanged.

Open `Average` to view the code.

```function y = avg(u) if numel(u) == 1 y = u; else k = numel(u)/2; if k ~= floor(k) u = u(2:numel(u)); end y = emldemo_navg(u,2); end ```

The `avg` function calls the external MATLAB function `emldemo_navg` to calculate the average of every two consecutive signal values.

```function B = emldemo_navg(A,n) %#codegen assert(n>=1 && n<=numel(A)); B = zeros(1,numel(A)/n); k = 1; for i = 1 : numel(A)/n B(i) = mean(A(k + (0:n-1))); k = k + n; end ```

Both `u` and `y` are variable-size. You do not need to explicitly define `u` as variable-size, because `u` is an input. The output `y` is declared as a variable-size vector because the number of elements varies depending on the size provided by `u`. Inspect the properties of `y` to confirm that it is variable-size.

### Simulate the Model

Simulate the model to view the results in each Scope block. `Filter` outputs a variable number of signal values each time it executes. `Average` outputs a variable number of signal values each time it executes. The block returns approximately half the number of the unique values. 