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C.2 optfir - equiripple FIR filter design

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):
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):
Lowpass, Highpass and Bandpass filters are all called Bandpass.

Enter filter length (enter 0 for estimate):
The number of taps. If you enter 0, the program figures out how many you need for your specification.

Enter sampling rate of filter:
Use 1Hz.

Enter number of filter bands:
There will be a passband and a stopband.

Enter lower band edge for band 1:
For a lowpass filter, this should be 0 for d.c.

Enter upper band edge for band 1:
Upper edge of the passband.
Enter desired value for band 1:
Specify unity gain in the passband.

Enter weight factor for band 1:
Using 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:
Lower edge of the stopband.

Enter upper band edge for band 2:
Since this is the Nyquist frequency, it specifies the top of the stopband.

Enter desired value for band 2:
Zero here defines this to be the stopband.

Enter weight factor for band 2:
See comment above on weight.

Do you want x/sin(x) predistortion? (y/n):
Note 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):
The 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 0.1000000
0.1500000 0.1617188 0.1871094 0.2183594 0.2496094
0.2828125 0.3160156 0.3492188 0.3824219 0.4156250
0.4507813 0.4839844

In 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.

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