1. Write computer code to perform a Discrete Fourier Transform and use it to find the Fourier transform of the pressure data for Task 4 (the crank angle data and volume data are also given but you don't need it for this Task). The last piece of information that you may need is that the sampling rate of this data was 30 kHz (30 thousand samples per second!). Make two plots of the Power Spectrum versus frequency. First, plot the Power Spectrum versus frequency from 0 to 15 kHz. Then plot the Power Spectrum from 2 kHz to 15 kHz. Interpret your results. Can you explain why the graphs look the way they do. What happens to the pressure data and what frequency is excited? Why is that frequency excited?
2. Write computer code to perform Trapezoidal Rule Integration of the data for Task 5 to determine the work in J over each of the four strokes individually as well as the total work over the cycle. Note that the intake stroke corresponds to points 1 to 900, the compression stroke corresponds to points 901 to 1800, the expansion stroke corresponds to points 1801 to 2700, and finally the exhaust stroke corresponds to points 2701 to 3600. Do you think that this estimation of the work would benefit from the higher order/accuracy integration techniques we've discussed in class? Why or why not? (Note: remember from Thermodynamics that the Work is the integral of pressure over volume). (2nd Note: when I say 2701, that's point number or what I call the index location).