PHYCS 3730/6720 Lab Exercise

Reading and references:
Answer file Mylab15.txt.

Exercise 1. Numpy Discrete Fourier Transforms

A pure cosine signal
   f(t) = cos(w*t)
is sampled 128 times at the times t = j Dt for j = 0,1,...,127. The frequency is nu = 20/(128*Dt) = 0.15625/Dt. The angular frequency is w = 2 pi times that. So the discrete signal is
   fj = cos(40*Pi*j/N)
for N = 128. Compute its discrete Fourier transform and plot the power spectrum. Note that the power spectrum looks continuous, but that is only because pyplot connects the 128 plot points. Copy your Python commands (your interactive session) to the answer file. Then also put the answers to the questions below in your answer file:

Exercise 2. Damped oscillation

Use Python to construct the power spectrum for the signal f(t) = exp(-0.2*t/Dt)*cos(0.8*t/Dt) using the same discretization as above. That is, sample at t/Dt = j = 0,1,...,127. The line shape you get in power vs frequency is called a Lorentzian.

In your answer file give the Python commands you used. Then answer these questions: