Optfir is a Fortran program performing classical FIR filter design using the Parks-McClellan algorithm. There is nothing unusual about this program, so almost any DSP book will give an adequate explanation of the algorithm as well as the meaning of its arguments. Briefly, the program permits the design of bandpass filters, differentiators, hilbert transformers, and half-band filters. Bandpass filters include lowpass, highpass, bandstop, and multiband, where each band can have a different gain (the "desired value"). A desired value of 0 specifies a stopband. The weight associated with each band determines the ratio of ripple in each band; a higher weight means less ripple.
The following example should serve to illustrate use of the program. Invoke the program through
pigi by calling up "equiripple FIR" in the "Filter" menu. Alternatively, you can start the program directly from any terminal window by typing the command optfir. The questions posed by the program are indicated below. The text in Courier-Bold are your response.
Enter name of input command file (press <Enter> for manual entry, Sorry, no tilde-expansion. Give path relative to your home or start-up directory):
<Return>You can put your responses in a file to avoid having to type them each time you execute the program. Here, I assume you are typing them interactively.
Enter filter type (1=Bandpass, 2=Differentiator, 3=Hilbert transformer, 4=Half-band):
1Lowpass, Highpass and Bandpass filters are all called Bandpass.
Enter filter length (enter 0 for estimate):
32The number of taps. If you enter 0, the program figures out how many you need for your specification.
Enter sampling rate of filter:
1Use 1Hz.
Enter number of filter bands:
2There will be a passband and a stopband.
Enter lower band edge for band 1:
0For a lowpass filter, this should be 0 for d.c.
Enter upper band edge for band 1:
0.1
Enter desired value for band 1:
1Specify unity gain in the passband.
Enter weight factor for band 1:
1Using 1 here and 1 in the stopband will give ripples of the same size in both bands. You could experiment with allowing more ripple in the passband by making this number smaller.
Enter lower band edge for band 2:
0.15Lower edge of the stopband.
Enter upper band edge for band 2:
0.5Since this is the Nyquist frequency, it specifies the top of the stopband.
Enter desired value for band 2:
0Zero here defines this to be the stopband.
Enter weight factor for band 2:
1See comment above on weight.
Do you want x/sin(x) predistortion? (y/n):
nNote that the program will design a filter that predistorts to compensate for the effect of the zero-order hold in a D/A converter.
Enter name of coefficient output file (Sorry, no tilde-expansion. Give path relative to your home directory):
filter_tapsThe name of the file in which to store the impulse response of the design. The resulting file can be used in an FIR star or a WaveForm star using the syntax
< filename to read it. Note that the file will be stored in your home directory.
Executing ...
Finite Impulse Response (FIR)
Linear Phase Digital Filter Design
Remez Exchange Algorithm
Bandpass Filter
Filter length = 32
Impulse Response Coefficients:
h( 1) = 0.2199929E-02 = h( 32)
h( 2) = -0.1615105E-01 = h( 31)
h( 3) = -0.1167266E-01 = h( 30)
h( 4) = -0.5506404E-02 = h( 29)
h( 5) = 0.6444952E-02 = h( 28)
h( 6) = 0.1864344E-01 = h( 27)
h( 7) = 0.2227415E-01 = h( 26)
h( 8) = 0.1105212E-01 = h( 25)
h( 9) = -0.1328082E-01 = h( 24)
h( 10) = -0.3894535E-01 = h( 23)
h( 11) = -0.4806972E-01 = h( 22)
h( 12) = -0.2521652E-01 = h( 21)
h( 13) = 0.3334328E-01 = h( 20)
h( 14) = 0.1151020E+00 = h( 19)
h( 15) = 0.1945332E+00 = h( 18)
h( 16) = 0.2434263E+00 = h( 17)
Lower band edge: 0.0000000 0.1500000
Upper band edge: 0.1000000 0.5000000
Desired value: 1.0000000 0.0000000
Weight factor: 1.0000000 1.0000000
Deviation: 0.0236464 0.0236464
Deviation in dB: 0.4108557 -32.5247154
Extremal frequencies:
0.0000000 0.0312500 0.0625000 0.0878906 0.1000000In the above, we have designed a lowpass filter with 32 taps with the edge of the passband at 0.1 Hz and the edge of the stopband at 0.15.
0.1500000 0.1617188 0.1871094 0.2183594 0.2496094
0.2828125 0.3160156 0.3492188 0.3824219 0.4156250
0.4507813 0.4839844