Thread: Pole and Zero of Butterworth Filter in SAC

Started: 2014-06-09 01:14:57
Last activity: 2014-06-10 17:10:07
Topics: SAC Help
Hamidatul Husna Matondang
2014-06-09 01:14:57




Dear Sir

My research is filtering in  seismic signal. If I apply butterworth filter to my signal in SAC, I only get the result
of the filter. I want to know how much the value of pole and zero of Highpass Butterworth Filter in SAC.
Could you tell me, please.

Thank You Very Much.

Regards
Ami
  • George Helffrich
    2014-06-08 20:56:55
    Dear Amik Amik -

    This is a strange request because a filter is not exactly the same as an instrument response, and representing one in the same way conveys little additional value to processing a signal. However, you can think of your need as similar to inverting a frequency-amplitude-phase table for an equivalent pole-zero representation. See the article in Seismological Research Letters, vol. 85, p 197ff (2014) by Anderson and Lees for some suitable approaches.

    On 8 Jun 2014, at 11:14, amik Amik wrote:




    Dear Sir

    My research is filtering in seismic signal. If I apply butterworth filter to my signal in SAC, I only get the result
    of the filter. I want to know how much the value of pole and zero of Highpass Butterworth Filter in SAC.
    Could you tell me, please.

    Thank You Very Much.

    Regards
    Ami


    _______________________________________________
    sac-help mailing list
    sac-help<at>iris.washington.edu
    http://www.iris.washington.edu/mailman/listinfo/sac-help



    George Helffrich
    george.helffrich<at>bris.ac.uk


    • Hamidatul Husna Matondang
      2014-06-10 15:54:23
      Thank You Very Much Sir,


       I've been read research paper that you recommended it
      "Anderson Jake F. and Lees, J.M., (2013) Instrument Corrections by Time-Domain Deconvolution,
      Seismological Research Letters. Vol. 85(1): pp. 197-201". From this paper, I found the statement :
             Another common method is that of the TRANSFER
             command in the widely used software package SAC(University
             of California, 2012). This command uses a zero-phase highpass
             or band-pass filter (through the freqlimits option) to
             ensure the stability of the result. This filter is acausal and,
             therefore, problematic as well.
      I have some questions from statement above :
      1. Is acausal filter valid only for TRANSFER command - freqlimits or almost the entire of
         filter command like highpass, bandpass, or lowpass?
      2. Do you know how many the values of poles of Filter in SAC? I mean If I apply the Butterworth
         to my signal in SAC with "hp butter np 2 c 2" How many the value of poles in 2nd order/pole
         Butterworth in SAC (Seismic Code Analysis)?
        
      Thank You very much

      Best Regards,
      Ami


      Pada Minggu, 8 Juni 2014 19:56, George Helffrich <George.Helffrich<at>bristol.ac.uk> menulis:



      Dear Amik Amik -

      This is a strange request because a filter is not exactly the same as an instrument response, and representing one in the same way conveys little additional value to processing a signal.  However, you can think of your need as similar to inverting a frequency-amplitude-phase table for an equivalent pole-zero representation.  See the article in Seismological Research Letters, vol. 85, p 197ff (2014) by Anderson and Lees for some suitable approaches.

      On 8 Jun 2014, at 11:14, amik Amik wrote:






      Dear Sir

      My research is filtering in  seismic signal. If I apply butterworth filter to my signal in SAC, I only get the result
      of the filter. I want to know how much the value of pole and zero of Highpass Butterworth Filter in SAC.
      Could you tell me, please.

      Thank You Very Much.

      Regards
      Ami


      _______________________________________________
      sac-help mailing list
      sac-help<at>iris.washington.edu
      http://www.iris.washington.edu/mailman/listinfo/sac-help




                George Helffrich
                george.helffrich<at>bris.ac.uk
      • Milton Plasencia
        2014-06-10 14:51:02
        Hi Amik,

        My two cents to the topic,

        See below, please

        HTH,

        Milton
        * * * * * * * * * * * * * * * * * * * * * * *
        Milton P. PLASENCIA LINARES

        Centro di Ricerche Sismologiche (CRS)
        OGS - Istituto Nazionale di Oceanografia e di Geofisica Sperimentale

        Borgo Grotta Gigante 42/C
        (34010) Sgonico - Trieste - Italia
        Tel: +39 040 2140 141 (Udine)
        Tel: +39 040 2140 256 (Trieste)
        Cel.: +39 331 6481 935

        E-mail: mplasencia<at>inogs.it

        ASAIN (Antarctic Seismographic Argentinean Italian Network)
        *********************************


        On Jun 10, 2014, at 2:54 AM, amik Amik <amik.mamat<at>yahoo.co.id> wrote:

        Thank You Very Much Sir,


        I've been read research paper that you recommended it
        "Anderson Jake F. and Lees, J.M., (2013) Instrument Corrections by Time-Domain Deconvolution,
        Seismological Research Letters. Vol. 85(1): pp. 197-201". From this paper, I found the statement :
        Another common method is that of the TRANSFER
        command in the widely used software package SAC(University
        of California, 2012). This command uses a zero-phase highpass
        or band-pass filter (through the freqlimits option) to
        ensure the stability of the result. This filter is acausal and,
        therefore, problematic as well.
        I have some questions from statement above :
        1. Is acausal filter valid only for TRANSFER command - freqlimits or almost the entire of
        filter command like highpass, bandpass, or lowpass?

        The command transfer performs deconvolution (using spectral division) to remove instrument response
        and convolution to apply other instrument response; instead freqlimits use low pass and high pass filters
        (IIR filters, zero phase and "acausal") to stabilize the result.
        See the help transfer in SAC.



        2. Do you know how many the values of poles of Filter in SAC? I mean If I apply the Butterworth
        to my signal in SAC with "hp butter np 2 c 2" How many the value of poles in 2nd order/pole
        Butterworth in SAC (Seismic Code Analysis)?
        It is most complicated answer, but i think the most important here is:
        When you use the filters is necessary to know that more poles we get, the sharper the cut-off,
        but it can generate problems (acausal) to the filtered signal, so use the number of poles with attention.
        Max poles number in SAC is 10. i always use 2 (4 maximum).

        Other important aspect in SAC filtering to avoid the acausal effect of IIR filters is the npasses option,
        use 2. the default in SAC lowpass command is 1.

        I think that to obtain the values of poles you must use other software, eg. DSP package of MatLab.

        Thank You very much

        Best Regards,
        Ami


        Pada Minggu, 8 Juni 2014 19:56, George Helffrich <George.Helffrich<at>bristol.ac.uk> menulis:


        Dear Amik Amik -

        This is a strange request because a filter is not exactly the same as an instrument response, and representing one in the same way conveys little additional value to processing a signal. However, you can think of your need as similar to inverting a frequency-amplitude-phase table for an equivalent pole-zero representation. See the article in Seismological Research Letters, vol. 85, p 197ff (2014) by Anderson and Lees for some suitable approaches.

        On 8 Jun 2014, at 11:14, amik Amik wrote:




        Dear Sir

        My research is filtering in seismic signal. If I apply butterworth filter to my signal in SAC, I only get the result
        of the filter. I want to know how much the value of pole and zero of Highpass Butterworth Filter in SAC.
        Could you tell me, please.

        Thank You Very Much.

        Regards
        Ami


        _______________________________________________
        sac-help mailing list
        sac-help<at>iris.washington.edu
        http://www.iris.washington.edu/mailman/listinfo/sac-help



        George Helffrich
        george.helffrich<at>bris.ac.uk



        _______________________________________________
        sac-help mailing list
        sac-help<at>iris.washington.edu
        http://www.iris.washington.edu/mailman/listinfo/sac-help


      • George Helffrich
        2014-06-10 15:35:33
        Dear Amik Amik -

        1. The filtering done in the TRANSFER function is not guaranteed causal. The other SAC filters are causal if they are one pass.

        2. The number of filter poles is given by the NPOLES parameter in any of the filter commands (2 <= N <= 10). If you want to know their values, refer to any books/papers on filter design -- the pole positions on the unit circle are standard.

        On 10 Jun 2014, at 01:54, amik Amik wrote:

        Thank You Very Much Sir,


        I've been read research paper that you recommended it
        "Anderson Jake F. and Lees, J.M., (2013) Instrument Corrections by Time-Domain Deconvolution,
        Seismological Research Letters. Vol. 85(1): pp. 197-201". From this paper, I found the statement :
        Another common method is that of the TRANSFER
        command in the widely used software package SAC(University
        of California, 2012). This command uses a zero-phase highpass
        or band-pass filter (through the freqlimits option) to
        ensure the stability of the result. This filter is acausal and,
        therefore, problematic as well.
        I have some questions from statement above :
        1. Is acausal filter valid only for TRANSFER command - freqlimits or almost the entire of
        filter command like highpass, bandpass, or lowpass?
        2. Do you know how many the values of poles of Filter in SAC? I mean If I apply the Butterworth
        to my signal in SAC with "hp butter np 2 c 2" How many the value of poles in 2nd order/pole
        Butterworth in SAC (Seismic Code Analysis)?

        Thank You very much

        Best Regards,
        Ami


        Pada Minggu, 8 Juni 2014 19:56, George Helffrich <George.Helffrich<at>bristol.ac.uk> menulis:


        Dear Amik Amik -

        This is a strange request because a filter is not exactly the same as an instrument response, and representing one in the same way conveys little additional value to processing a signal. However, you can think of your need as similar to inverting a frequency-amplitude-phase table for an equivalent pole-zero representation. See the article in Seismological Research Letters, vol. 85, p 197ff (2014) by Anderson and Lees for some suitable approaches.

        On 8 Jun 2014, at 11:14, amik Amik wrote:




        Dear Sir

        My research is filtering in seismic signal. If I apply butterworth filter to my signal in SAC, I only get the result
        of the filter. I want to know how much the value of pole and zero of Highpass Butterworth Filter in SAC.
        Could you tell me, please.

        Thank You Very Much.

        Regards
        Ami


        _______________________________________________
        sac-help mailing list
        sac-help<at>iris.washington.edu
        http://www.iris.washington.edu/mailman/listinfo/sac-help



        George Helffrich
        george.helffrich<at>bris.ac.uk






        George Helffrich
        george.helffrich<at>bris.ac.uk


        • Arthur Snoke
          2014-06-10 17:10:07
          If the intent is to use a Butterworth filter, it is best to use the SAC commands LP, BP, or HP. As George writes, one can make the filters causal or acausal.

          The SAC versions of Butterworth filters is not a simple pole-zero filter, which is what one does with analog filtering. As it says in the BANDPASS help file: " These analog prototype filters are mapped to digital filters via the bilinear transformation, a transformation which preserves the stability of the analog prototypes." This trasform maps the Nyquist into infinity, so the lowpass filter drops of more rapidly than a pole-zero analog filter would do.

          http://www.iris.edu/files/sac-manual/commands/bandpass.html

          There is no reason to use TRANSFER unless one wants to do a truly pole-zero version of the filter.
04:25:53 v.e73c6799