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. Low pass filter
   1. FIR
   2. length 81
2. Bandpass filters
   1. IIR
   2. length 11
   3. Ten filters centered at player frequencies

Show the following plots for a shot by player 1.

1. Square wave for player 1
   1. f=1471Hz
   2. Amplitude of 0.1V (square wave with voltage of either 0 or 0.1V)
   3. x-axis of 4 ms near the middle of the spectrum
   4. y-axis of -1V to 1V
   5. Sampling frequency of Fs=100kHz
2. Optical noise (from lights.mat)
   1. Same axis as square wave
3. Sum of optical noise and square wave
   1. Same axis as square wave
4. Decimated signal
   1. Low pass filtered and then down-sampled to Fs=10kHz
   2. Same axis as square wave
5. Signal filtered by bandpass filter centered at f=1471Hz
6. The power 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.