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DIGITAL FILTERS

DIGITAL FILTERS. Box Car filter. Running Mean. Moving Average. M = 48. M = 49. M = 50. Impulse Response. Normalized SINC function windowed by the Lanczos window. M is the filter length (# of filter coefficients)  N is the sampling frequency = 2π/ Δ t

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DIGITAL FILTERS

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  1. DIGITAL FILTERS

  2. Box Car filter Running Mean Moving Average

  3. M = 48 M = 49 M = 50 Impulse Response

  4. Normalized SINC function windowed by the Lanczos window M is the filter length (# of filter coefficients) Nis the sampling frequency = 2π/Δt cis the cut-off frequency = 2π/Tc

  5. repeat wrap

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

  7. Impulse Response Frequency Response (Fourier Transform of Impulse Response) Frequency Response or Admittance Function

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

  9. High-pass: H 1 Pass Band Stop Band  0 c N

  10. Band-pass: H 1 Stop Band Stop Band Pass Band c2  0 c1 N

  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. Gibbs’ Phenomenon H( ) Frequency Response or Admittance Function (Running Mean)  / N

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

  14. Butterworth Filter q = 4 q = 10 q = 1 http://cnx.org/content/m10127/latest/

  15. Exercises http://www.falstad.com/dfilter/

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