Coherence spectrum (coherency squared) < > = running mean or low-pass filter X is the Fourier Transform Cross-spectral power density Autospectrum of ‘x’ Autospectrum of ‘y’ Confidence level:  = 0.1, 0.05, 0.01

Frequency Response (of a linear system) Admittance or transfer function of a linear system: Cross-spectral power density gain or admittance amplitude input or stimulus or impulse cross-spectrum X is the Fourier transform auto-spectrum

Frequency Response or Transfer Function or Admittance Function REMINDER (from “Digital Filters”) Filtered Signal yn Fourier Transform of Filtered Signal Convolution in time domain corresponds to multiplication in frequency domain Frequency Response or Transfer Function or Admittance Function

1 c N  Pass Band Stop H Low-pass:

Example of admittance (two Salinity time series) Suwannee River Discharge Wilcox Gopher input output

amplification attenuation window size = 30

input output

amplification attenuation window size = 30

window size = 20

window size = 10

window size = 20