Linear Filter :: Linear Filters (Neural Network Toolbox)

Neural Network Toolbox

Linear Filter

We can combine a tapped delay line with an linear network to create the linear filter shown below.

The output of the filter is given by

The network shown above is referred to in the digital signal-processing field as a finite impulse response (FIR) filter [WiSt85]. Let us take a look at the code that we use to generate and simulate such a specific network.

Suppose that we want a linear layer that outputs the sequence T given the sequence P and two initial input delay states Pi.

P = {1 2 1 3 3 2};
Pi = {1 3};
T = {5 6 4 20 7 8};

You can use newlind to design a network with delays to give the appropriate outputs for the inputs. The delay initial outputs are supplied as a third argument as shown below.

```
net = newlind(P,T,Pi);
```

Now we obtain the output of the designed network with

```
Y = sim(net,P,Pi)
```

to give

Y = [2.73]    [10.54]    [5.01]    [14.95]    [10.78]    [5.98]

As you can see, the network outputs are not exactly equal to the targets, but they are reasonably close, and in any case, the mean square error is minimized.

Linear Networks with Delays LMS Algorithm (learnwh)