Let's suppose I have a speech signal with frequency content >300 Hz. I then add noise to this signal, that happens to be somewhere below 300 Hz. I then high-pass filter the signal (300+ Hz) and I have increased the mutual information and seemingly violated the data processing inequality. Can anyone explain why this can occur? I assume it's because the data processing inequality does not apply since the input signal is not stationary and it's probably not really a Markov chain...but I'm not sure. Thanks!