<PAGE>   1
                                                                     Exhibit 3.2
                                                          FEDERAL IDENTIFICATION
                                                                   NO. 042814792
                                                                   -------------


/s/ JSD                  THE COMMONWEALTH OF MASSACHUSETTS
----------                      WILLIAM FRANCIS GALVIN
Examiner
                             Secretary of the Commonwealth
                 One Ashburton Place, Boston, Massachusetts 02108-1512

                                 ARTICLES OF AMENDMENT
                        (GENERAL LAWS, CHAPTER 156B, SECTION 72)

/s/ YE, RES, MB
---------------
Name
Approved

             We, Eric R. Giler                                      , *President
                 ---------------------------------------------------
             and David W. Duehren                                       , *Clerk
                 -------------------------------------------------------
             of  Brooktrout Technology, Inc.                                   ,
                 --------------------------------------------------------------
                               (Exact name of corporation)

             located at: 410 First Avenue, Needham, Massachusetts 02494        ,
                         ------------------------------------------------------
                    (Street address of corporation in Massachusetts)

             certify that these Articles of Amendment affecting articles
             numbered:

             One
             ------------------------------------------------------------------
               (Number those articles 1, 2, 3, 4, 5, and/or 6 being amended)

             of the Articles of Organization were duly adopted at a meeting held
             on May 13, 1999, by vote of:
                ------  ----

             9,832,447 shares of common stock, $.01 par value of 10,907,012
             ---------           ----------------------------    ----------
                                (type, class & series, if any)

             shares outstanding,

                       shares of                              of
             ---------           ----------------------------    ----------
                                (type, class & series, if any)

             shares outstanding, and

                       shares of                              of
             ---------           ----------------------------    ----------
                                (type, class & series, if any)

             shares outstanding.

   C   [ ]   (1) ** being at least a majority of each type, class or series
   P   [ ]          outstanding and entitled to vote thereon:
   M   [ ]
 R.A.  [ ]
                    Voted: That the name of the Corporation be changed from
                           Brooktrout Technology, Inc. to Brooktrout, Inc.

             * Delete the inapplicable words.  ** Delete the inapplicable
             clause.
             (1) For amendments adopted pursuant to Chapter 156B, Section 70.
             (2) For amendments adopted pursuant to Chapter 156B, Section 71.
             Note: If the space provided under any article or item on this form
             is insufficient, additions shall be set forth on one side only of
             separate 8 1/2 x 11 sheets of paper with a left margin of at least
    4        1 inch. Additions to more than one article may be made on a single
----------   sheet so long as each article requiring each addition is clearly
P.C.         indicated.
<PAGE>   2
To change the number of shares and the par value (if any) of any type, class or
series of stock which the corporation is authorized to issue, fill in the
following:


The total presently authorized is:

<TABLE>
<S>                    <C>                    <C>                     <C>                                <C>
--------------------------------------------------------------------------------------------------------------------
        WITHOUT PAR VALUE STOCKS                                       WITH PAR VALUE STOCKS
--------------------------------------------------------------------------------------------------------------------
TYPE                    NUMBER OF SHARES       TYPE                    NUMBER OF SHARES                    PAR VALUE
--------------------------------------------------------------------------------------------------------------------
Common:                                       Common:
--------------------------------------------------------------------------------------------------------------------
Preferred:                                    Preferred:
--------------------------------------------------------------------------------------------------------------------

--------------------------------------------------------------------------------------------------------------------

</TABLE>

Change the total authorized to:

<TABLE>
<S>                    <C>                    <C>                     <C>                                <C>
--------------------------------------------------------------------------------------------------------------------
        WITHOUT PAR VALUE STOCKS                                       WITH PAR VALUE STOCKS
--------------------------------------------------------------------------------------------------------------------
TYPE                    NUMBER OF SHARES       TYPE                    NUMBER OF SHARES                    PAR VALUE
--------------------------------------------------------------------------------------------------------------------
Common:                                       Common:
--------------------------------------------------------------------------------------------------------------------
Preferred:                                    Preferred:
--------------------------------------------------------------------------------------------------------------------

--------------------------------------------------------------------------------------------------------------------
</TABLE>
<PAGE>   3
The foregoing amendment(s) will become effective when these Articles of
Amendment are filed in accordance with General Laws, Chapter 156B, Section 6
unless these articles specify, in accordance with the vote adopting the
amendment, a later effective date not more than thirty days after such filing,
in which event the amendment will become effective on such later date.

Later effective date:
                      ---------------------------------------------------------.


SIGNED UNDER THE PENALTIES OF PERJURY, this 13th day of May, 1999.


                                /s/ Eric R. Giler, *President /
                                -------------------------------------
                                    Eric R. Giler


                                /s/ David W. Duehren, *Clerk /
                                -------------------------------------
                                    David W. Duehren


*Delete the inapplicable words.