1. 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

2. 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

3. 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

4. 1 c N 
Pass
Band
Stop H
Low-pass:

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

6. amplification
attenuation
window size = 30

7. input
output

8. amplification
attenuation
window size = 30

9. window size = 20

10. window size = 10

12. window size = 20