Notes are in scanned pdf



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%matplotlib inline
from IPython.display import Image

RR Lyrae light curve (dashed) with overlaid 1/2/8 mode Fourier approximation.

Aliasing effect when undersampling

Effect of non-uniform time sampling

Discrete Fourier transform of signal with low/high noise

FT of noisy signal has more small peaks in PSD(f) but the larger peak for the true signal frequency is the same height as for the lower noise signal.

LIGO noise spectrum breakdown

low frequencies dominated by seismic noise, higher by quantum noise:

LIGO wavelet analysis

Wavelet denoising for CMB

comparison to low-pass Wiener filter



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