Homework Eleven

Present an Octave (or Matlab) example using the DFT

Nick Christman

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For my example of DFT, I have chosen to demonstrate digital filtering.

The process of digital filtering in Matlab is quite simple. To demonstrate this I must first obtain an original signal and I have chosen to use Audacity to create a short, four second clip of an electronic-genre music file. The artist is known as Air and the song I have chosen is "Electronic Performers." After this, I had to create a noisy signal and to accomplish this I simply super-imposed a sum of sine and cosine waves over the original signal (i.e. I literally added noise to my original signal). This is the Matlab code I used to accomplish these tasks:

close all;
clear all;

% Constants to scale noise
a = 50;         % noise amplitude a
b = 50;         % noise amplitude b
c = 50;         % noise amplitude c
n = 10000000;   % frequency scaling factor

tune = 'audio1.wav';         % location/name of .WAV file

[audio fs] = wavread(tune);  % turn .WAV file into binary format and get the sampling frequency

[N C] = size(audio);         % Get the number of rows and columns of the audio matrix

t = 0:(N-1);
noise = a*sin(fs*t/n) + b*sin(fs*t/n) + c*sin(fs*t/n);  % create some noise!
noise = [noise' zeros(N,1)];                            % reformat the noise to match the dimensions of the audio matrix
noisy = audio + noise;                                  % create the noisy signal by adding the noise to the audio matrix

% we now have an original signal called "audio" and a noisy signal called "noisy".