DFiltFIR

Routine

DFiltFIR [options] [FiltFile]

Purpose

Design minimax linear phase FIR filters

Description

1: Equiripple Linear Phase Filter (multiple passbands and stopbands). The filter is specified in terms of the desired response in bands. The band specifications include desired value, relative weighting and limits on the allowed response values in the band. The resulting filter is a weighted minimax approximation (with constraints) to the given specifications. The filter coefficients have an even symmetry about the middle of the filter.

2: Equiripple Linear Phase Filter (multiple passbands and stopbands) with sin(x)/x compensation. The filter is specified in terms of the desired response in bands. The band specifications include desired value, relative weighting and limits on the allowed response values in the band. The resulting filter is a weighted minimax approximation (with constraints) to the given specifications. The filter coefficients have an even symmetry about the middle of the filter.

3: Equiripple Differentiator. The filter is specified in terms of the desired slope in bands. The band specifications include desired slope, relative weighting and limits on the allowed slopes in the band. The resulting filter is a weighted minimax approximation (with constraints) to the given specifications. The filter coefficients have an odd symmetry about the middle of the filter.

4: Equiripple Hilbert Transform Filter. The filter is specified in terms of the desired response in bands. The band specifications include desired value, relative weighting and limits on the allowed values in the band. The resulting filter is a weighted minimax approximation (with constraints) to the given specifications. The filter coefficients have an odd symmetry about the middle of the filter.

This program implements the filter design procedure outlined by McClellan, Parks and Rabiner. This procedure has been modified to include constraints as described by Grenez.

References:

F. Grenez, "Design of linear or minimum-phase FIR filters by constrained Chebyshev approximation", Signal Processing, vol. 5, pp. 325-332, July 1983.

The filter will have weighted deviations from the desired values which have equal peak values. The weighting is specified as a function of frequency. Higher (relative) weights mean smaller deviations. The summary printout gives the deviation attained and the corresponding value in dB. For passbands (non-zero desired value), the deviation in dB is reported as 0.5*dB((V+dev)/(V-dev)). This is the average of the dB value of the deviation above the desired value V and the dB value of the deviation below the desired value. For stopbands (zero desired value), the deviation in dB is dB(dev).

Parameters

-t FTYPE, --type=FTYPE

Filter type, default multiple passband/stopband

 "bpf" - multiple passband/stopband
 "receive" - multiple passband/stopband filter used as a
     reconstruction filter (sin(x)/x compensation)
 "differentiator" - differentiator
 "hilbert_transform" - Hilbert transform filter

-n NCOF, --number_coefficients=NCOF

Number of filter coefficients.

-s SFREQ, --srate=SFREQ

Sampling frequency. If the sampling frequency is not specified, a normalized frequency of one is used.

-w WTYPE, --weight=WTYPE

Weight specification type, default band weights

 "weight" - band weights
 "deviation" - band deviations (inverse of band weights)
 "dB-deviation" - band dB deviations.  The band deviation are
   determined by inverting the formulas for the dB deviations.

-g NGRID, --grid_density=NGRID

Grid density (number of grid points per extremum of the response). The default is chosen to give at least 1000 grid points or 16 points per extremum.

-e, --extremal_values

Print high precision coefficient values and extremal frequency information.

-h, --help

Print a list of options and exit.

-v, --version

Print the version number and exit.

The filter specifications are read from standard input. The specifications are discrete values given in order of increasing frequency within a frequency band. Within each band, piecewise monotonic cubic interpolation is used between the tabulated values. Bands are separated by transition lines. These are empty (or white-space) lines. Each specification line has 5 values (the last two are optional). The specifications are of the form,

  Freq Value Weight [Low_Value High_Value]
  Freq       - Frequency
  Value      - Desired filter response value (or desired slope for
               differentiators)
  Weight     - Relative weighting for the value (or slope)
  Low_Value  - Lower limit on the filter response (or slope for
               differentiators)
  High_Value - Upper limit on the filter response (or slope for
               differentiators)

1: A frequency equal to half of the sampling frequency (normalized frequency of 0.5) is entered,

2: An empty line appears after a transition, or

3: An end-of-file is encountered.

Notes:

- The specification lines must be in order of increasing frequency. - A maximum of 200 specification lines can be given. - The weight values can be relative weights, relative deviations (inverse weights), or a relative dB-deviations. The latter can be set to the desired passband ripple (dB) and the desired stopband response (dB). This sets the weights such that when the filter order is chosen correctly, both the passband and stopband specifications will be met. - The limit values are optional.

Example, 32 tap constrained bandpass filter: The stopbands are from 0 to 0.1 and 0.425 to 0.5, and the passband is from 0.2 to 0.35. The relative weights are 10 in the stopbands and 1 in the passband. The response is constrained to be positive (between 0 and 1) in the first stopband. The filter coefficients will be written to file filt.cof. A Unix shell script for this design would be as follows.

 DFiltFIR -t bpf -n 32 filt.cof << EoF
 0   0 10 0 1
 0.1 0 10 0 1
 <empty line>
 0.2  1 1
 0.35 1 1
 <empty line>
 0.425 0 10
 0.5   0 10
 EoF

Author / version