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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 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: May 12, 2004
                                                       /s/ J. Neal Armstrong
                                                       -------------------------
                                                       J. Neal Armstrong
                                                       Chief Financial Officer