1. DIGITAL FILTERS
h = time invariant weights (IMPULSE RESPONSE FUNCTION)
2M + 1 = # of weights
N = # of data points

2. Impulse Response :
Box Car filter
Running Mean
Moving Average

3. M = 48
M = 49
M = 50

4. Normalized SINC function windowed by the Lanczos window
Impulse Response:
Normalized SINC function windowed by the Lanczos window
M is the filter length (# of weights or filter coefficients)
N is the sampling frequency = 2π/Δt
c is the cut-off frequency = 2π/Tc

5. repeat
wrap

6. High-pass filtered : Original – Low-Pass

7. Frequency Response or Transfer Function or Admittance Function
Fourier Transform of yn
Convolution in time domain corresponds to multiplication in frequency domain
Frequency Response or Transfer Function or Admittance Function

8. 1 c N 
Pass
Band
Stop H
Low-pass:

9. High-pass: 1 c N 
Pass
Band
Stop H

10. 1
c1 N 
Pass
Band
Stop H
Band-pass:
Stop
Band
c2

11. Band-pass filtered
1) High-pass to cut-off the upper bound period (e.g. 18 hrs)
2) Low-pass to cut-off the lower bound period (e.g. 4 hrs)

12. Frequency Response or Transfer Function
Gibbs’ Phenomenon
Frequency Response or Transfer Function
(for Running Mean)
H( )
M > M > M
 / N

13. 
(  )
Lynch (1997, Month. Wea. Rev., 125, 655)

14. Butterworth Filter http://cnx.org/content/m10127/latest/ q = 4 q = 10

15. Exercises