Fourier Transforms on Simulated Pulsar Data Gamma-ray Large Area Space Telescope

Basic Pulsar Create series of evens distributed over s (5.7 days) Period of pulsar P 0 = 0.1 s Number of events ~ 500 (= bright Geminga like pulsar) Calculate the number of turns from the pulsar for the photon n turns n = F 0 * t n phase n = turns n – int (turns n )

Fourier Transform Calculate the Fourier Transform power = sqrt ((  sin (2  phase n )) 2 + (  cos (2  phase n )) 2 ) /n

Fourier Transform on Differences Calculate the number between two photons (i,j, i<j ) turns n = F 0 * (t j – t i ) where (t j – t i ) < max_diff phase n = turns n – int (turns n ) power = sqrt ((  sin (2  phase n )) 2 + (  cos (2  phase n )) 2 ) /n max_diff = 5000s

Re and Im part of the FT Power Re Im Phase offset 0 * 2 

Re and Im part of the FT Power Re Im Phase offset 0.3 * 2 

Re and Im part of the FT Power Re Im Phase offset 0 * 2 

Dependence on max_diff The influence of max_diff on the Signal to noise ratio

Mesurement of the noise level The dependanve of max_diff on the noise level

Dependence on max_diff The dependance of the signal with in the power spectrum on max_diff Pulse width ~ 1/max_diff

Adding a Gaussian distribution Phase diagram Normal FT FT on differences Sigma = P/5 Sigma = P/20Sigma = P/100

Adding a pulse

Adding a period derivative max_diff = s

Adding a period derivative The dependence of the signal with in the power spectrum on max_diff

Changing Max_diff with a Pd

S/N vs. max_diff The dependence of Signal/Noise on max_diff P1 = 3e-12 F1 = 3E-10 1/s*s max_diff = 1/ sqr(F1) max_diff = s