Lab 5: Signal and Noise

The basic idea for this lab is to create an artificial "signal" and then see what we can do experimentally to make it easier or harder to detect. The fake signal will be an oscillating brightness of an LED. This can be accomplished by using the PWM output and changing the brightness value like so: \begin{equation} f(t) = A+B\sin(\omega t) \end{equation} where $A$ is the baseline brightness, and the oscillating term is added to it. $B$ will indicate the strength of the added signal and the frequency is determined by the argument of the $\sin()$ function.

The following simple sketch will create an oscillating ($f = 1 \; \textrm{Hz}$) brightness on the LED. Try it out before going any further. (Don't forget to include a 220 $\Omega$ resister in series with your LED! Otherwise, the arduino will supply too much current and it will overheat and destroy the LED)

  const int ledPin = 9;       // pin that the LED is attached to
  const int TWOPI = 2*3.1415926;

  int brightness;

  void setup() {
    pinMode(ledPin, OUTPUT);
  }

  void loop() {
    brightness = 100+50*sin(1.0*TWOPI*millis()/1000);
    analogWrite(ledPin,brightness);
    delay(5);
  }

Next, set up a voltage divider circuit with the PhotoResistor so that you can measure the brightness of the LED.

You should be able to reproduce this effect, shown in the animation. The LED is changing brightness periodically. Play with the parameters of the $\sin()$ function to make sure you understand what's going on there.

And you should be able to obtain a plot like this of the 'faked' signal.

Make sure you can do all this before moving forward. (This is just the introduction - the actual experiment hasn't started.)

If you look closely at your data (try adding the line: ax.set_xlim([1,3]) right after your plot command to restrict the range of the horizontal axis), you should a not very pretty sin function. The amplitude is certainly oscillating, but there is a lot of 'noise'. This noise is an artifact arising from the fact that in addition to our added oscillations at frequency $f$, there is also a blinking occurring at a much faster frequency due to the PWM that controls the brightness. Remember, the LED is only changing it's apparent brightness to our eyes because the duty cycle is being changed.

You can review this concept here: https://www.arduino.cc/en/Tutorial/Foundations/PWM if it's still unclear.

If we didn't include any averaging, then our small signal measurement would look like this. It's impossible to see the 1 Hertz oscillations now, since they are dominated by the PWM fluctuations that are occurring at much faster times scales.