1. Coherence spectrum (coherency squared)  = 0.1, 0.05, 0.01 X is the Fourier Transform Cross-spectral power density Confidence level: = running mean or low-pass filter

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

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

4. Low-pass: 0 1 cc NN  Pass Band Stop Band H

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

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