Linear Prediction

For background and further explanations, please refer to the lecture notes on

The linear constant-coefficient difference equation form of causal FIR and IIR filters
The z transform
More on the z transform and the LPC spectrum
Notes on LPC analysis

You should not need to master all of those first -- the goal of this exercise is to set the stage for a deeper dive.

The scripts linked below are based on (part of) the second of those lecture notes -- perhaps having the material in script form will make the exercise easier!

Part I: Analysis

Download the audio file SX133.wav and the Octave script nHomework3a.m.

Run the script, as we did in class, and make sure you understand what it's doing, and how it's doing it.

Now use that script as a basis for the creating your own script(s) to do the following things:

1. On the same audio sample, run 10th-order, 12th-order, 16th-order, and 18th-order LPC analyses. Plot the LPC spectra (with the fft spectra), and list the pole frequencies and bandwidths. Which order would you choose as a basis for "formant analysis"? Why?
2. Pick some other audio sample -- record your own if you want -- and do the same analysis on a suitable piece of it. Note that we tried to select exactly three pitch periods. Try some other selection(s) to see if this makes any difference.

Part II: Reconstruction

Download the script nHomework3b.m and run it. 

Now design your own inverse-filtering experiment(s), and use that script as a basis for the exploration.