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                                                                    Exhibit 31.2

                                  CERTIFICATION

I, J. Neal Armstrong, certify that:

    1. I have reviewed this Quarterly Report on Form 10-Q of Aspect Medical
       Systems, Inc.;

    2. Based on my knowledge, this report does not contain any untrue statement
       of a material fact or omit to state a material fact necessary to make the
       statements made, in light of the circumstances under which such
       statements were made, not misleading with respect to the period covered
       by this report;

    3. Based on my knowledge, the financial statements, and other financial
       information included in this report, fairly present in all material
       respects the financial condition, results of operations and cash flows of
       the registrant as of, and for, the periods presented in this report;

    4. The registrant's other certifying officer and I are responsible for
       establishing and maintaining disclosure controls and procedures (as
       defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) for the registrant
       and have:

          a)   Designed such disclosure controls and procedures,  or caused such
               disclosure  controls  and  procedures  to be  designed  under our
               supervision,  to ensure that material information relating to the
               registrant,  including  its  consolidated  subsidiaries,  is made
               known to us by others within those entities,  particularly during
               the period in which this quarterly report is being prepared;

          b)   [Paragraph omitted in accordance with SEC transition instructions
               contained in SEC Release 34-47986]

          c)   Evaluated  the  effectiveness  of  the  registrant's   disclosure
               controls  and   procedures  and  presented  in  this  report  our
               conclusions  about the  effectiveness of the disclosure  controls
               and  procedures,  as of the  end of the  period  covered  by this
               report based on such evaluation; and

          d)   Disclosed in this report any change in the registrant's internal
               control over financial reporting that occurred during the
               registrant's most recent fiscal quarter that has materially
               affected, or is reasonably likely to materially affect, the
               registrant's internal control over financial reporting; and

    5. The registrant's other certifying officer and I have disclosed, based on
       our most recent evaluation of internal control over financial reporting,
       to the registrant's auditors and the audit committee of the registrant's
       board of directors (or persons performing the equivalent functions):

          a)   All significant deficiencies and material weaknesses in the
               design or operation of internal control over financial reporting
               which are reasonably likely to adversely affect the registrant's
               ability to record, process, summarize and report financial
               information; and

          b)   Any fraud, whether or not material, that involves management or
               other employees who have a significant role in the registrant's
               internal control over financial reporting


Dated:  August 11, 2004
                                                        /s/ J. Neal Armstrong
                                                        ------------------------
                                                        J. Neal Armstrong
                                                        Chief Financial Officer