Dear Janesh,


Re:

> Dear Franklin Bretschneider,
> 
> Thank you so much for your reply and explanation about the filter using the stats and signal package. 
> 
> I decided to opt the filter method in signal package. I have a simple question about the cut off frequency here. 
> 
> I have 30 minute collected tidal data and I want to use the 48 hour low pass filter to my data to remove the fluctuations and then get only the residuals. What should be the cutoff frequency in my case ? I have tried to figure out cut off frequency with the following rationale : . 
> 
> The parameters for butter filter are n, Wn and type. In the help, W	 is defined as critical frequencies of the filter. W must be a scalar for low-pass and high-pass filters, and W must be a two-element vector c(low, high) specifying the lower and upper bands. For digital filters, W must be between 0 and 1 where 1 is the Nyquist frequency.
> 
> A value of 1 corresponds to half the sampling frequency. In my case the sampling frequency is 2 hr^-1. Hence a value of 0.01 corresponds to a frequency cutoff of .01*1 = .01 hr^-1 or 100 hrs time. Using unitary method, if 100 hours cut off frequency is 0.01 then 48 hours cut off frequency is 0.01/100*48 = 0.0048 hr^-1 . Is that correct ?
> 
> Thank you so much
> 
> Janesh
> 


With digital filters (called "z-plane" in the signal package), the cut-off frequency must indeed be given as a fraction of the Nyquist freqency.

With your tidal data, taken at 2 samples per hour, the nyquist is 1 per hour. So, a cutoff interval of 48 h means a cutoff frequncy of 1/48 f(nyq) , or 0.020833. This must be fed into the butterworth function.

Note btw that at the cut-off frequency, the amplitude is still rather high (about 0.707), so the tidal signal (period about 12.5 h) will not be attenuated much.
I hope this helps. It's always best to check with a simple example, such as an f= 1/48 sine, which after your filter should be reduced to an amplitude of 0.707). Then check with a simulated tidal signal (say, a sine of about 12:25 h period). 
With such simple tests, I often find my own programming errors.
Best wishes,


Franklin
--


Franklin Bretschneider
--
Dept Biology
Kruyt Building W711
Padualaan 8
3584 CH Utrecht
The Netherlands






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