ESS210B
Prof. Jin-Yi Yu
Calculate the Red Noise Spectrum for Test
qThe red noise power spectrum can be calculated using the following formula:
qP(h, r, M) is the power spectrum at
frequency h
h = 0, 1, 2, 3, …., M
h = 0, 1, 2, 3, …., M
r = autocorrelation coefficient at
one time lag
qWe would normally obtain the parameter r from the original time series as the average of the
one-lag autocorrelation and the square root of the two-lag
autocorrelation.
qWe then make the total power (variance) of this red noise spectrum equal to the total power (variance)
of the power spectrum we want to test.
´
Power of the
Tested Spectrum
Power of the Red
Noise