This task involves putting the various parts of the signal processing algorithm together. This task will help you see the entire signal processing algorithm at work, and will demonstrate that the filters you designed in Tasks 1 and 2 actually do what they were designed to do.

Essentially, this milestone combines Task 1 and Task 2 together.

• Add a square wave at one of the player frequencies to the optical noise provided in Task 2. Remember that these signals should all be sampled at 100 ksamples/s.
• Decimate the signal (a two-step process):
  • Filter the 100 ksamples/s signal using your low pass FIR filter
  • Down-sample the signal to 10 ksamples/s
• Filter the resulting 10 ksamples/s signal using the 10 IIR bandpass filters
• Calculate and display the signal energy of each of the 10 resulting filtered signals

For your convenience, the measured signal from the fluorescent lights can be found here: light.zip

The ten player frequencies (in Hz) are: 1471, 1724, 2000, 2273, 2632, 2941, 3333, 3571, 3846, 4167

1. For the anti-aliasing filter, use your low-pass filter designed in Task 2
   1. Filter is Finite Impulse Response (FIR)
   2. Filter is described by 81 'b' coefficients
   3. Of the 'a' coefficients of an FIR filter, only a_0 is non-zero, and has a value of 1
   4. For this task, you should just read in your 'b' coefficients from the file you saved them in when you designed the filter in Task 2

1. Use your bank of band-pass filters designed in Task 1
   1. Filters are Infinite Impulse Response (IIR)
   2. Each filter is described by 11 'b' coefficients and 11 'a' coefficients
   3. The center-of-passband frequencies for the filters are the ten player frequencies
   4. For this task, you should read in your 'b' and 'a' coefficients from the file(s) you saved them in when you designed the filter in Task 1

Show the following plots for a shot by player 1.

1. Time-domain plot of square wave for player 1
   1. f = 1471Hz
   2. Amplitude of 0.1V (square wave with voltage of either 0 or 0.1V)
   3. Zoom in on a section of the x-axis 4ms wide when you are showing this for pass-off
   4. y-axis of -1V to 1V
   5. Sampling frequency of Fs = 100kHz
2. Time-domain plot of optical noise (from lights.mat)
   1. Same axis as square wave
3. Time-domain plot showing sum of optical noise and square wave
   1. Same axis as square wave
4. Frequency-domain plot of sum of optical noise and square wave (on an axis going from 0 to 50 kHz)
5. Frequency-domain plot of decimated signal (on an axis going from 0 to 5 kHz)
   1. Low pass filter signal and then down-sampled to Fs = 10kHz
   2. Then use fft to view in frequency domain
6. Frequency-domain signal filtered by bandpass filter centered at f = 1471Hz
7. Frequency-domain signal filtered by bandpass filter centered at another player frequency
8. The signal energy for the signal through all 10 bandpass filters
   1. Signal length of 200ms

Here is the MATLAB code for creating the signal.

%Load in optical noise
load light 

%we only want 200ms of data or 200e-3*100e3 = 20000 sample
t=linspace(0,.2,20000)';
y=y(1:20000);

%create the square wave signal
freq=1471;
y1=0.1*(0.5+0.5*square(2*pi*freq*t));

%Add square wave to the noise
y2=y+y1;

After creating the signal you will be using the MATLAB code that you developed as part of Task 1 and Task 2.