Parks-McClellan FIR Filter Design

(Java 1.1 Version)

Note
The Java 1.1 applet on this page should work on the HotJava 1.1 browser, Internet Explorer 4.0 or Netscape Navigator 4.0 with the Java 1.1 upgrade patch applied. The applet does not work on older browsers such as Navigator 2.0 or 3.0

Introduction

The applet implements the Parks-McClellan equiripple FIR filter design algorithm (sometimes referred to as the Remez exchange algorithm). This design method allows an FIR filter to be designed to a frequency response specification consisting of an arbitrary number of passbands and stopbands, in each of which a specified amount of ripple can be tolerated.

For the sake of simplicity, the applet restricts the filter type to one of the following:

Note that this applet differs from the filter design applets elsewhere on this site in that all frequencies are normalised, ie expressed as a fraction of the sampling frequency. The upper frequency limit, corresponding to the folding or "Nyquist" frequency, is therefore 0·5; entering any frequency value above 0·5 will cause an error. The use of normalised frequencies has the advantage that the applet is not tied to a particular sampling frequency.

Outline instructions

The various filter settings are reasonably self-explanatory.

Filter type
Select the appropriate radio button to specify a LP, HP, BP or BS filter.
Passband
Enter the normalised passband frequencies in the text boxes. For a LP filter, the lower passband frequency is automatically set to 0; for a HP filter the upper passband frequency is set to 0·5.
Transition bandwidth
Enter the required width of the transition band as a normalised frequency (in the range 0 - 0·5). In the case of a BP or BS filter, the transition bandwidth applies equally to both transition bands.
Passband ripple
Enter the tolerable passband ripple in dB. This specifies how much variation is allowed in the filter gain in the passband above and below the ideal value of 1.
A ripple value of r dB corresponds to a variation in passband gain between 1 + delta and 1 - delta, where delta = 1 - 10 - r / 20
Stopband attenuation
Enter the minimum tolerable attenuation (maximum tolerable gain) in the stopband in dB.
An attenuation of A dB corresponds to a filter gain of 10 - A / 20 in the stopband.
Order
Type in the required filter order, and press <Enter>. Alternatively, click the Estimate button to estimate the order based on the design settings.
Note that the order estimation (using the Kaiser formula) may underestimate the order needed to meet the design specification; an increased value can be typed in the text box if necessary.

Once the filter settings have been chosen, click the Design button to design the filter.

Click the Plot response button to display the gain frequency response of the resulting filter. The frequency scale covers the range 0 - 0·5 of normalised frequencies. The gain is on a log (dB) scale, with 0 dB at the top; the selected Minimum plot gain defines the gain value (in dB) at the bottom of the plot. Changing this setting allows you to view the frequency response at different levels of detail.

As mentioned above, the estimated order may be too low, and may need to be increased to meet the design specifications. Note also that there can be a significant difference in the response obtained with even and odd orders. Adjust the filter order until you are satisfied with the design.

Click the Coefficients button to list the filter coefficients. These can be copied and pasted to a text editor if desired.

Acknowledgement

This Java applet is derived from a C program "Parks-McClellan algorithm for FIR filter design" Copyright (C) 1995 Jake Janovetz (janovetz@coewl.cen.uiuc.edu), modified under the terms of the GNU General Public License published by the Free Software Foundation.

Download source code (zip Archive)

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