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speech signal process tools

PKMC_FILT(1-ESPS)                           ENTROPIC RESEARCH LAB



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     pkmc_filt - design an equiripple FIR filter using the Parks-McClellan algorithm

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     ppppkkkkmmmmcccc____ffffiiiilllltttt ----PPPP _p_a_r_a_m__f_i_l_e [ ----xxxx _d_e_b_u_g__l_e_v_e_l ] _f_i_l_e._f_i_l_t_e_r

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     The program _p_k_m_c__f_i_l_t designs a linear-phase  finite-impulse
     response  (FIR)  filter that meets the specification defined
     in the parameter file _p_a_r_a_m__f_i_l_e.  The  filter  coefficients
     are saved in the output file _f_i_l_e._f_i_l_t_e_r.  If _f_i_l_e._f_i_l_t_e_r is
     replaced by "-", the standard output is written.

     The design method is based on the Parks-McClellan algorithm.
     The   resulting   filter   minimizes   the  maximum-weighted
     approximation-error.  One of the four standard FIR types  is
     produced.    For   a  filter  with  multiple  stopbands  and
     passbands, the Type 1 (symmetric and odd length) or  Type  2
     (symmetric  and even length) filter is designed.  For a dif-
     ferentiator or a Hilbert  Transformer,  either  the  Type  3
     (anti-symmetric  and  odd  length)  or  the  Type  4  (anti-
     symmmetric and even length) is designed.

     Frequency responses of Types 2 and 3 filters are equal to  0
     at PI, which is undesirable for a highpass filter.  For mul-
     tiple stopbands/passbands filters, type 1 and  2  are  used.
     For differentiator and Hilbert transformer, type 3 and 4 are
     used.

     A generic Parks-McClellan  algorithm  is  implemented  here,
     without  numerical  optimization.   Numerical problem occurs
     for   filter   with   more    than    100    taps,    narrow
     passbands/stopbands,   large   transition  bands,  and  non-
     symmetrical transition bands.  In some cases, the  algorithm
     does  not detect the problem.  Typically the filter gain for
     such cases are large, exceeding 1.0. Always check the result
     by _f_i_l_t_s_p_e_c (_1-_E_S_P_S) and _p_l_o_t_s_p_e_c (_1-_E_S_P_S).

     Also see the shell script _x_f_i_r__f_i_l_t(_1-_E_S_P_S) that is a  cover
     script for this and other FIR filter design programs.

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     The following option is supported:

     ----xxxx _d_e_b_u_g__l_e_v_e_l [0]
          If _d_e_b_u_g__l_e_v_e_l is positive, _p_k_m_c__f_i_l_t prints  debugging
          messages  and  other  information on the standard error
          output.  The messages proliferate  as  the  _d_e_b_u_g__l_e_v_e_l
          increases.   If _d_e_b_u_g__l_e_v_e_l is 0 (the default), no mes-
          sages are printed.





        Copyright Entropic Research Laboratory, Inc. 1G1        1






PKMC_FILT(1-ESPS)                           ENTROPIC RESEARCH LAB



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     The following parameters are read from the _p_a_r_a_m__f_i_l_e:

     _f_i_l_t__t_y_p_e - _s_t_r_i_n_g
          The type of filter desired.  Use _M_U_L_T_I_B_A_N_D for lowpass,
          highpass,  bandpass,  bandstop,  and arbitrary multiple
          stop/passbands FIRs.  Use  _D_I_F_F_E_R_E_N_T_I_A_T_O_R  for  a  dif-
          ferentiator and _H_I_L_B_E_R_T for Hilbert transform filter.

     _f_i_l_t__l_e_n_g_t_h - _i_n_t
          Number of taps for the filter.

     _n_g_r_i_d - _i_n_t
          This is an optional parameter. It specifies the  number
          of  grid  points used for interpolation from 0 to PI/2.
          The default value is 2 * _f_i_l_t__l_e_n_g_t_h.

     _s_a_m_p__f_r_e_q - _f_l_o_a_t
          The sampling frequency.  This number is used  for  res-
          caling the values of bandedge parameters.

     _n_b_a_n_d_s - _i_n_t
          Number of bands from 0 to  _s_a_m_p__f_r_e_q/_2.   For  example,
          for  a  _M_U_L_T_I_B_A_N_D  filter  type, a lowpass filter has 2
          bands -- a passband from 0 to some frequency _f_1  and  a
          stopband  from  some frequency _f_2 to _s_a_m_p__f_r_e_q/_2, where
          _f_1<_f_2.  For a differentiator, _n_b_a_n_d_s is  1  if  a  full
          band differentiator is desired, 2 otherwise. For a Hil-
          bert transform filter, _n_b_a_n_d_s is always 1, and its band
          extend from 0 to _s_a_m_p__f_r_e_q/_2.

     The following set  of  the  parameters  have  the  forms  of
     _b_a_n_d[_i]__e_d_g_e_1,  _b_a_n_d[_i]__e_d_g_e_2,  _b_a_n_d[_i]__d_e_s, and _b_a_n_d[_i]__w_t,
     where _i denotes the band number.  For  example,  _b_a_n_d_2__e_d_g_e_1
     is  a  parameter  for the left edge of the second band.  The
     number of sets of these parameters must be equal to  _n_b_a_n_d_s.
     Band  1  is the left-most band, band _n_b_a_n_d is the right-most
     band.

     The response at the band edges is  automatically  determined
     by  the  algorithm,  the  error on the band edge is the same
     equi-ripple error of the  band.   The  generic  header  item
     _r_i_p_p_l_e__d_b  in the output file contains the equi-ripple error
     in dB that represents the smallest approximation error  that
     meets the specification.

     _b_a_n_d[_i]__e_d_g_e_1 - _f_l_o_a_t
          The  left  edge  of  _ith  band.   It  must  be  0   for
          _b_a_n_d_1__e_d_g_e_1.

     _b_a_n_d[_i]__e_d_g_e_2 - _f_l_o_a_t
          The right edge of _ith band.  It must be _s_a_m_p__f_r_e_q/_2 for



        Copyright Entropic Research Laboratory, Inc. 2G2        2






PKMC_FILT(1-ESPS)                           ENTROPIC RESEARCH LAB



          the  last  band.  _b_a_n_d[_i]__e_d_g_e_2 and _b_a_n_d[_i+_1]__e_d_g_e_1 can
          not be  the  same  number.   In  fact  _b_a_n_d[_i]__e_d_g_e_2  >
          _b_a_n_d[_i+_1]__e_d_g_e_1.

     _b_a_n_d[_i]__d_e_s - _f_l_o_a_t
          For _M_U_L_T_I_B_A_N_D filter type, it is the  desired  constant
          value  for  the  _ith  band.   For _D_I_F_F_E_R_E_N_T_I_A_T_O_R filter
          type, it is the slope of the frequency response on  the
          passband.   The  slope  is  measured  by  the amplitude
          response over normalized frequency axis.  For  _H_I_L_B_E_R_T,
          it should be set to 1.

     _b_a_n_d[_i]__w_t - _f_l_o_a_t
          For _M_U_L_T_I_B_A_N_D filter type, it is the constant weighting
          factor  for  the  approximation error in _ith band.  The
          weights in bands are  relative  to  one  another.   For
          example,  in  a  two  band  filter,  _b_a_n_d_1__w_t of 10 and
          _b_a_n_d_2__w_t of 20 are the same as _b_a_n_d_1__w_t of 1 and 2  for
          the  other  band.   For _D_I_F_F_E_R_E_N_T_I_A_T_O_R filter type, the
          weighting function _1/_f is appplied to the the  passband
          region  of  the  differentiator. For _H_I_L_B_E_R_T, it should
          always be set to 1.

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     No ESPS common parameter processing is used.

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     A new FEAFILT header is created for the  output  file.   The
     program  fills  in  appropriate values in the common part of
     the header as well as the  following  generic  header  items
     associated with the FEAFILT type.

     The _s_a_m_p__f_r_e_q generic header  item  contains  value  of  the
     _s_a_m_p__r_e_q parameter.

     The _b_a_n_d__e_d_g_e_s generic header item of size  _2*_n_b_a_n_d_s  is  an
     array containing the left and rights band edges of bands.

     The _d_e_s_i_r_e_d__v_a_l_u_e generic header item of size _n_b_a_n_d_s  is  an
     array containing the _b_a_n_d[_i]__d_e_s parameters

     The _d_e_s_i_r_e_d__w_e_i_g_h_t generic header item of size _n_b_a_n_d_s is  an
     array containing the _b_a_n_d[_i]__w_t parameters

     The _r_i_p_p_l_e__d_b generic header item of size _n_b_a_n_d_s is an array
     containing the error in dB for each band.

     In addition, the generic header  item  _d_e_l_a_y__s_a_m_p_l_e_s   (type
     DOUBLE)  is  added   to the header. _D_e_l_a_y__s_a_m_p_l_e_s  is  equal
     to (filter length  -  1)/2. This represents  the  delay   to
     the  center  of  the peak of the impulse response.




        Copyright Entropic Research Laboratory, Inc. 3G3        3






PKMC_FILT(1-ESPS)                           ENTROPIC RESEARCH LAB



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     The following parameter file designs a bandpass filter  with
     stop  band  from 0 to 500 Hz, passband from 1000 to 2000 Hz,
     and stopband from 2500 to 4000 Hz.

          int filt_length = 32;
          float band1_edge1 = 0.000000;
          float band1_edge2 = 500.000000;
          float band1_des = 0.000000;
          float band1_wt = 1.000000;
          float band2_edge1 = 1000.000000;
          float band2_edge2 = 2000.000000;
          float band2_des = 1.000000;
          float band2_wt = 1.000000;
          float band3_edge1 = 2500.000000;
          float band3_edge2 = 4000.000000;
          float band3_des = 0.000000;
          float band3_wt = 1.000000;
          string filt_type = "MULTIBAND";
          float samp_freq = 8000.000000;
          int nbands = 3;

     The unspecified regions from 500 to 1000 Hz and 2000 to 2500
     Hz  are  unspecified and are taken as transition bands which
     will have arbitray repsonse.

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     None known.

RRRREEEEFFFFEEEERRRREEEENNNNCCCCEEEESSSS
     Oppenheim & Schafer, _D_i_s_c_r_e_t_e-_T_i_m_e _S_i_g_n_a_l _P_r_o_c_e_s_s_i_n_g,  Pren-
     tice Hall, 1989

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     xfir_filt(1- ESPS),  cb_filt(1 - ESPS),  win_filt(1 - ESPS),
     notch_filt(1 - ESPS),  FEA_FILT(5 - ESPS),  atofilt(1-ESPS),
     wmse_filt(1-ESPS), iir_filt(1-ESPS), sfconvert(1-ESPS)

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     Derek Lin










        Copyright Entropic Research Laboratory, Inc. 4G4        4