• For homework 2 we wrote function csfv=fit_calsrc(t,v) to fit the data in 050517_calsrc1_edit.mat to function sinusoid.m. We had to have a good guess as to the correct frequency to get it to work.
  • Modify the function to make fit_calsrc2 which extracts an estimate of the correct frequency by doing an fft on each waveform.
  • Confirm it works by running it on the data in file syn_calsrc.mat where the frequencies do vary and the sinusoids are soaked in noise.
  • Write a wrapper script which loads the syn data, does the fit and generates plots which demonstrate that it has worked correctly.

  Start with the 4 files on cpteach in the directory ~pryke/astr401/exam/qu1. (Be sure to use the slightly modified 050517_calsrc1_edit2.mat version of the input data.)

• Write a function vals=hrndm(x,y,n) which returns n random values sampled from the input pdf specified by x and y. i.e. such that we can do:

  x=0:0.01:2;
  y=0.5*exp(0.7*x)+gauss([3,1,0.05],x);
  vals=hrndm(x,y,10000);
  hfill(vals,100,0,2);
  

  and see a noisy histogram of a gaussian peak sitting on an exponential background. [Hint: You need only the functions cumsum, rand and interp1 and can do it cleanly with 3 lines of code and no loops.]

• Write a script which fits the histogram generated above first to a 2 parameter exponential baseline, and then to the full exp+gauss model. The fit must use the correct Possion likelihood of each bin contents given the trial model - i.e. you must use matmin and logl. Have the script plot the histogram with fit line overplotted in red. [Hint: if you didn't manage to make a working hrndm load the vals from file ~pryke/astr401/exam/qu3/vals.mat]

• Load in the file ~pryke/astr401/exam/qu4/corrmap000001.mat which contains structure map with fields ad and T. These are "axis data" and sim CMB temperature anistropy map. Write a script which uses the function conv2 to smear this pattern with a Gaussian "beam" with FWHM 0.5deg and displays the result. Make sure that the convolution operation does not change the normalization of the image. [Hint: use an option to conv2 to make the smoothed image the same size as the initial one.]

• Using the maps T and E in the structure above write a script which generates the T, E auto power spectra and also the TE cross power spectrum and plots them. Don't try and get the normalization of the spectra right but do convert them to conventional l(l+1)C_l/2*pi form. [Hint: see class6 and 7 notes for how to gen power spectra.]

Remember to keep the code simple and clean!