Lab 1: Entropy estimation of real world signals

Task

The goal of the lab is to make simple random models for some different signals (audio and images) and estimate entropies for the models

The work should be done in groups of 1 or 2 students.

Examination of the lab is by written report.

Audio signals

The audio signals consist of two music signals and one speech signal. The music signals are mono, sampled with 44.1 kHz sampling frequency and quantized to 8 bits/sample (256 levels). The speech signal is mono, sampled with 8 kHz sampling frequency and quantized to 8 bits/sample (256 levels).

• hey04_8bit.wav
• nuit04_8bit.wav
• speech.wav

In Matlab, WAV files can be easily read using the function audioread. It will return a vector of samples, scaled so that they take values between -1 and 1. To get integers between -128 and 127 just multiply the signal by 128.

Entropy estimation

To get an idea of what theoretical performance can be expected, you should estimate some entropies. The entropies to be estimated are H(X_i), H(X_i,X_i+1) (pair entropy) and H(X_i+1 | X_i) (conditional entropy), assuming that the signal can be viewed as a stationary process X_i.

Still images

The images are greyscale images quantized to 8 bits/pixel, ie each pixel can take values between 0 (black) and 255 (white). There are three images to test:

• baboon.png
• boat.png
• woodgrain.png

You can read images in Matlab using the function imread. It will return a two dimensional matrix of the type uint8. In order to be able to properly manipulate data, it can be a good idea to convert to the data type double (eg x=double(x);).

Entropy estimation

To get an idea of what theoretical performance can be expected, you should estimate some entropies. The entropies to be estimated are H(X_i,j), H(X_i,j,X_i+1,j), H(X_i,j,X_i,j+1) (pair entropy vertically and horizontally), H(X_i+1,j | X_i,j) and H(X_i,j+1 | X_i,j) (conditional entropy vertically and horizontally).

Examination

Examination of the lab is by a short written report. Describe how you solved the problems and what your results are. Also include any program code you’ve written.

Send an electronic version of your report (in PDF format) to Harald. Give the name, person number and email adress of every group member.

Deadline

No hard deadline. I would prefer if you send in your reports before the exam period. If you are late, you might have to wait until the next exam period for your points to be reported into Ladok.

Questions?

If you have any questions about the lab, contact Harald.