filter.rgeme.old

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a much longer
description of the 
file contents; the comment is terminated by a control-d on the last line.
Many ESPS filter design programs have this mechanism for
adding comments to describe the designed filter.
The response for this 
filter is shown on a linear scale in Figure 2-6 and a decibel scale
in Figure 2-7.
.bp
.GP fig2-4.gps 3.5 6 0 0
.GE
.sp 1
.ce
.b "Figure 2-4: Desired function input to wmse_filt."
.GP fig2-5.gps 3.5 6 0 0
.GE
.sp 1
.ce
.b "Figure 2-5: Weighting function input to wmse_filt."
.bp
.GP fig2-6.gps 3.5 6 0 0
.GE
.sp 1
.ce
.b "Figure 2-6: Designed with wmse_filt in the points mode."
.GP fig2-7.gps 3.5 6 0 0
.GE
.sp 1
.ce
.b "Figure 2-7: Designed with wmse_filt in the points mode."
.bp
.sh 2 "zero_pole"
.pp
The program 
.i "zero_pole (5\-\s-1ESPS\s+1)"
allows the user to
design a filter by arbitrary placement of poles and zeroes in the
complex plane.  The user simply specifies the pole and zero locations
in one or two ASCII files, 
and the program computes the coefficients
and deposits them in a FILT (5\-\s-1ESPS\s+1) file.
.pp
The 
.i zero_pole 
program will be demonstrated by converting an
analog Butterworth filter to its discrete equivalent by using the bilinear
transformation.
.[
dsp tretter
.]
The analog filter is a sixth-order low-pass filter
with a 3-dB 
corner frequency at one eighth the sampling rate.  
After the transformation,
in the Z-domain
this filter has six zeroes at -1, and poles at the following locations:
.nf
.sp 1
        p0 = 0.597716978 + 0.577350268 i        p5 = p0 conjugate.
        p1 = 0.471404518 + 0.333333333 i        p4 = p1 conjugate.
        p2 = 0.420143458 + 0.108741129 i        p3 = p2 conjugate.
.sp 1
The filter is then designed with the following command:
.sp 1
.ul
    zero_pole -c "Sixth order Butterworth." -g 1  butter6.filt  butter6  butter6
.sp 1
.fi
.pp
The \fI-g\fR option is used above to insure that the filter coefficients are 
normalized to have unity gain at 0 Hz.  The ASCII file 
.i butter6
is shown below.  
Note that if zero and pole locations are both to be read out of
the same file, 
it must be given twice on the command line.  Also, for any pole
or zero off of the real axis, the complex conjugate is automatically included
and therefore should not be listed in the input ASCII file.
.sp 1
Contents of
.i  butter6:
.sp 1
.nf
6
-1.0  0.0
-1.0  0.0
-1.0  0.0
-1.0  0.0
-1.0  0.0
-1.0  0.0
3
0.597716978  0.577350268
0.471404518  0.333333333
0.420143458  0.108741129
.fi
.sp
.pp
The frequency response of this filter is shown in Figure 2-8.
.bp
.GP fig2-8.gps 3 6 0 0
.GE
.sp 1
.ce
.b "Figure 2-8: Filter designed with zero_pole."
.sp 1
.sh 2 "impulse_resp"
.sp 1
.pp
The program 
.i "impulse_resp (5\-\s-1ESPS\s+1)"
is used to calculate the impulse response of a filter.  A specified number of
points on the impulse response are calculated and written either to an
output FILT (5\-\s-1ESPS\s+1) file, to be used as an FIR filter, or to an SD (sampled data)
file for plotting in the time domain.  As an example, the Butterworth 
filter designed in the last section will be converted to an FIR filter
using 
.i impulse_resp.
.pp
To obtain another FILT (5\-\s-1ESPS\s+1) file from butter6.filt:
.sp 1
.ul
    impulse_resp -n 100  butter6.filt  butter6_fir.filt
.sp 1
.pp
The response for this filter is shown in Figure 2-9.  If the user wishes to
plot the impulse response in the time domain, the following command should
be used to obtain an SD file:
.sp 1
.ul
    impulse_resp  -s  -n 100  butter6.filt  butter6_fir.sd
.sp 1
This file is plotted in Figure 2-10 using 
.i "plotsd (5\-\s-1ESPS\s+1)".
.bp
.GP fig2-9.gps 3.5 6 0 0
.GE
.sp 1
.ce
.b "Figure 2-9: Designed with impulse_resp."
.GP fig2-10.gps 3.5 6 0 0
.GE
.sp 1
.ce
.b "Figure 2-10: SD file created by impulse_resp."
.bp
.sh 2 "atofilt"
.sp 1
.pp
The program
.i "atofilt (5\-\s-1ESPS\s+1)"
is used to convert a set of known filter coefficients into a FILT (5\-\s-1ESPS\s+1) file.  The
coefficients may be placed in one or two ASCII files, or may be typed
in directly from the standard input.  The user is strongly advised to
use the comment facility of this program to record
information about the coefficients in the file header.
.pp
An example command line would be:
.sp 1
.ul
    atofilt  filter1.filt  filter1.num  filter1.den
.sp 1
Since the \fI-c\fR 
option is not used above, the user will be prompted for his
comments.
.sh 2 "iir_filt"
.sp 1
.pp
The program
.i "iir_filt (5\-\s-1ESPS\s+1)"
designs digital IIR filters by first designing 
Butterworth or Chebyshev analog filters and then converting
them to digital
filters by using the bilinear transformation.
\fIIir_filt \fR supports the design of 
low pass (LP), high pass (HP), band pass (BP), and band stop (BS)
filters.
The user must specify the sampling frequency, the filter type (\fIe.g.\fR
Butterworth), filter response type (\fIe.g.\fR low pass), and the order 
of the filter.
These design parameters may be specified in a 
parameter file, but the easiest way to design IIR filters is
by invoking \fIiir_filt\fR with the \fIeparam (1\-\s-1ESPS\s+1)\fR
command. By doing this,
the user is prompted for all the design parameters.
.pp
The design of a sixth-order low-pass Butterworth filter 
with a 3-dB cutoff frequency equal to 1000 Hz.
(identical to the one shown in Figure 2-8) is shown below
to illustrate the procedure. As before,
the initial command line is shown below with the subsequent
computer prompts following in bold face and the user's responses in regular
type.
.sp 1
.ul
    eparam iir_filt Bworth6.filt
.sp 1
.pp
.ft B
Desired filter order. [3]:
.ft
6
.pp
.ft B
Desired sampling frequency. [8000.0]:
.ft
.pp
.ft B
Desired pass pand gain. [1.0]:
.ft
.pp
.ft B
Desired filter type: BUTTERWORTH or CHEBYSHEV1. [BUTTERWORTH]:
.ft
.pp
.ft B
Desired filter response: LP, HP, BP, or BS. [LP]:
.ft
.pp
.ft B
3 dB (BUTTERWORTH) or critical (CHEBYSHEV) freqs. [0] <250.0>:
.ft
1000
.pp
.ft B
3 dB (BUTTERWORTH) or critical (CHEBYSHEV) freqs. [1] <0.0>:
.ft
.sp 1
.pp
Only one 3-dB frequency is required for LP and HP filter
designs;
the reply to the prompt for a second 3-dB frequency is 
ignored by \fIiir_filt\fR.
Also notice,
several of the defaults (\fIe.g.\fR filter response \- LP)
were appropriate for the desired filter,
so simply hitting return is enough to specify those parameters.
The filter response is shown below in Figure 2-11.
.bp
.GP fig2-11.gps 3 6 0 0
.GE
.sp 1
.ce
.b "Figure 2-11: Butterworth filter designed with iir_filt."
.sp 2
.sh 1 "FILTERING PROGRAMS"
.sp 1
.pp
This section describes the two programs that may be 
used to filter sampled data:
.i "filter (5\-\s-1ESPS\s+1)"
and
.i "fft_filter (5\-\s-1ESPS\s+1)".
\fIFft_filter (5\-\s-1ESPS\s+1)\fR
works with FIR filters only, but \fIfilter (5\-\s-1ESPS\s+1)\fR
works with both IIR and FIR fitlers.
.sp 1
.sh 2 "filter"
.sp 1
.pp
The program 
.i "filter (1-ESPS)"
is used to perform a digital filtering operation on sampled data.
The program implements FIR or IIR filters and may  read its
coefficients from a FILT (5\-\s-1ESPS\s+1) file, or from a parameter file.
.pp
The program may also implement upsampling or downsampling filters
to raise or lower the sampling rate 
of the data.  Upsample filtering, or interpolation,
means that
the appropriate number of zero samples are inserted between each data sample
and the resulting data is then filtered to smooth the
resulting
data sequence and interpolate the values between the original
data values. By doing this the sampling rate of the
signal is increased.  
Downsample filtering, or decimation, 
means that 
the signal is first band limited by a digital filtering operation
and then the data is decimated to the correct
sampling rate by removing samples from the data sequence.
This results in a signal at a lower sampling rate.
.pp
The following example converts a 48 kHz. sampled signal
into a 32 kHz. sampled signal by increasing the sampling
rate to 96 kHz. (2 X 48 kHz.), 
filtering the data with a 16 kHz. low pass
filter, and decimating the signal down to 32 kHz. (96 kHz. / 3)
by keeping
every third sample.
The 16 kHz. low pass filter coefficients are read from a FILT (5\-\s-1ESPS\s+1) file called 
.i interp.filt.
.sp 1n
.ul
    filter  -i 2/3  -Finterp.filt  speech48.sd  speech32.sd
.sp 1
It is assumed here that the FILT (5\-\s-1ESPS\s+1) file
.i interp.filt
contains only one filter record.  This means that it is unnecessary to
use the -f option, which specifies the set of coefficients in the FILT (5\-\s-1ESPS\s+1)
file to use.
.pp
In the above example, 
the starting point and the number of points to process
from the input sampled data file are read from the parameter file
below.
Setting 
.i nan
= 0 will cause all the data in
.i speech48.sd
to be processed.
.sp 1
Contents of
.i params:
.sp 1
.nf
# This file processes all of the data.
int start = 1 : "Starting point for analysis.";
int nan = 0 : "Number of points to process.";
.fi
.sp 1
.pp
The following command reads IIR filter coefficients from a parameter file
and filters the data.  This time the 
sampling rate of the output file matches that of the input file.
Note that the filter must be named on the command line to extract
the correct set of coefficients from the parameter file.
.sp 1
.ul
    filter  -P params.filt  -f low_pass  brian_speech.sd  fbrian_speech.sd
.sp 1
The parameter file 
.i params.filt
is shown below.  In this example the filtering
operation begins at the 10,000th point in the input file and processes
20,000 points.
.sp 1
Contents of
.i params.filt:
.sp 1
.nf
# Don't do the whole file.
int start = 10000 : "Starting point for analysis.";
int nan = 20000 : "Number of points to process.";

# Define the filter.  Third order Butterworth.
int low_pass_nsiz = 4 : "Number of numerator coefficients. ";
int low_pass_dsiz = 2 : "Number of denominator coefficients. ";
float low_pass_num = {0.166666, 0.5, 0.5, 0.166666} : "Numerator coefficients.";
float low_pass_den = {1.0, 0.33333} : "Denominator coefficients. ";
.fi
.sp 2
.sh 2 "fft_filter"
.pp
The program
.i "fft_filter (5\-\s-1ESPS\s+1)"
implements FIR filtering operations on sampled data by performing the
convolution in the frequency domain rather in the time domain as
.i filter
does.  This algorithm is computationally more efficient than that
used by 
.i filter
when the number of filter coefficients is large.  If 
$N sub 1$
is the number of data points to process and
$N sub 2$
is the size of the filter, the regular filtering algorithm requires
on the order of
${N sub 1}{N sub 2}$
multiplications.  
By contrast the algorithm used by
.i fft_filter
requires only about
$2{N sub 1} log {N sub 2} + {N sub 1}$
multiplications.
.[
dsp tretter
%P 298-303
.]
In experimental results on a Masscomp 5600 system, filtering 100,000
samples,
.i fft_filter
required only one eighth as much time as
.i filter
to implement a 401 point filter and 25 % less time to implement a 51 point 
filter.  In implementing an 11 point filter, however,
.i fft_filter
was only half as fast as
.i filter.
.pp
The command below illustrates the use of 
.i fft_filter.
Note that if the -F option is used to specify the filter coefficients
and the \fI-p\fR option is used to specify the range of data points, no
parameter file is necessary.  The command below causes all of the
data in the file to be processed.
.sp 1
.ul
    fft_filter -F low_pass.filt -p1:  input.sd  output.sd
.sp 2
.sh 1 "FILTER SPECTRAL RESPONSES"
.pp
The program 
.i "filtspec (5\-\s-1ESPS\s+1)"
is used to find the frequency response of a filter.  The program reads
coefficients from a FILT (5\-\s-1ESPS\s+1) file and produces an output FEA_SPEC (5\-\s-1ESPS\s+1) file.  The
program 
.i "plotspec (5\-\s-1ESPS\s+1)"
can then be used to plot the response on a terminal
or printer.
.pp
Here are the
commands used to produce the
plots shown in this document.
.nf
.sp 1
.b "Figure 2-1:"
.ul 3
filtspec  -s 8000  -n 8193  notch120.filt  notch120.spec
plotspec  -t "Notch centered at 120 Hz. with 20 Hz. bandwidth." -T imagen  notch120.spec
.sp 1
.b "Figure 2-2:"
.ul 3
filtspec  -s 8000  bandpass1.filt  bandpass1.spec
plotspec  -y -100:50  -t "201 point bandpass filter."  -t "Uniform error weighting, 
    no transition band."  -T imagen  bandpass1.spec
.sp 1
.b "Figure 2-3:"
.ul 3
filtspec  -s 8000  bandpass2.filt  bandpass2.spec
plotspec  -y -100:50  -t "201 point bandpass filter."  -t "100 Hz. transition bands."
    -T imagen  bandpass2.spec
.sp 1
.b "Figure 2-6:"
.ul 3
filtspec  -s 20000  -m l  fm_demod.filt  fm_demod.spec
plotspec  -t "401 point FM demodulation filter."  -t "Linear scale."  -T imagen  fm_demod.lspec
.sp 1
.b "Figure 2-7:"
.ul 3
filtspec  -y -100:50  -s 20000  fm_demod.filt  fm_demod.spec
plotspec  -t "401 point FM demodulation filter."  -t "Decibel Scale."  -T imagen  fm_demod.spec
.sp 1
.b "Figure 2-8:"
.ul 3
filtspec  -s 8000  butter6.filt  butter6.spec
plotspec  -y -100:50  -t "6th order Butterworth filter."  -T imagen  butter6.filt
.sp 1
.b "Figure 2-9:"
.ul 3
filtspec  -s 8000  butter6_fir.filt  butter6_fir.spec
plotspec  -y -100:50  -t "FIR version of 6th order Butterworth filter."  -T imagen  butter6_fir.spec
.sp 1
.b "Figure 2-10:"
.ul 2
plotsd -t"Impulse response of butter6.filt." -T imagen butter6_fir.sd
.sp 1
.b "Figure 2-11:"
.ul 3
filtspec Bworth6.filt Bworth6.spec
plotspec -y -100:50 -t "IIR version of 6th order Butterworth filter." -T imagen Bworth6.spec
.fi
.sp 1
.sh 1 "REFERENCES"
.[
$LIST$
.]