# lect32 - UCF Physics AST 5765/4762(Advanced Astronomical...

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UCF Physics: AST 5765/4762: (Advanced) Astronomical Data Analysis Fall 2009 Lecture Notes: 32. Discrete Fourier Transfrom 1 Check In: 10:30 — 10:40, 10 min Questions? HW10 due 9 November, HW11 due 16 November Correction: Basis Functions -¿ Orthonormal Basis Functions Who read Press? 2 Amplitude, Phase, Power Spectrum in Python: 10:40 — 11:30, 50 min 20fft.py Steps for FFT: Variables are ( t ) ( f ) Times and frequencies of the elements of t and f are implicit, even spacings Read data into array t (can be complex) f=np.fft.fft(t) t=np.fft.ifft(f) Power: P=np.abs(f) ** 2 Power Spectral Density: PSD=P/P[0] Chance that Poisson process (e.g., photons) produces PSD F by chance is p ( F ) = e - F A 3 σ detection thus requires PSD 6.5 Amplitude: a=np.abs(f) Phase: ph=np.arctan2(np.imag(f), np.real(f)) Frequencies: nu = np.arange(N/2)/(N * dt) Plot: plt.plot(nu, P[0:N/2-1]) Signals and noise 1

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3 FFT Algorithm: 11:30 — 11:40, 10 min
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lect32 - UCF Physics AST 5765/4762(Advanced Astronomical...

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