Signal Processing with Deep Neural Networks

Deep Nets is an effective tool that can be used to solve complex signal processing estimation and detection problems. Consider a discrete purely in-deterministic process like a sine-wave on noise. It is a fact that it can be perfectly predicted from its past samples, in fact, it can be completely described by a second order difference equation. Let's train a LSTM network to predict a sine wave. Below is a graph depicting the prediction of a sine-wave. The first ~300 samples are used for training while the rest is the prediction of the net. Note, the net yielded close to perfect prediction.

Next, let's see what happens when we add noise, and train the net to filter it out:

zooming in on the transient:

Now, consider a more complex signal such as ECG. Below we can see how the net provide an excellent prediction of the ECG, giving the ability to detect anomalies which are high deviations from the prediction. The green line is the predicted curve.

Zooming in on the anomalous part:

Again, the green line is the prediction of the neural-net, while the blue line is what happened in real life.

These experiments were done using Python+Keras+Theano.