
<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                 SCHEDULE 14D-1
              TENDER OFFER STATEMENT PURSUANT TO SECTION 14(D)(1)
                     OF THE SECURITIES EXCHANGE ACT OF 1934

                        AMATI COMMUNICATIONS CORPORATION
                           (Name of Subject Company)

                          DSL ACQUISITION CORPORATION
                                    (Bidder)

                     COMMON STOCK, PAR VALUE $.20 PER SHARE
                         (Title of Class of Securities)

                                  023115 10 8
                     (CUSIP Number of Class of Securities)

                                CHARLES D. TOBIN
                         TEXAS INSTRUMENTS INCORPORATED
                               7839 CHURCHILL WAY
                           P.O. BOX 650311, M/S 3995
                              DALLAS, TEXAS 75265
                                  972-917-3810
                 (Name, Address and Telephone Number of Person
     Authorized to Receive Notices and Communications on Behalf of Bidders)

                                    COPY TO:
                              R. SCOTT COHEN, ESQ.
                           WEIL, GOTSHAL & MANGES LLP
                         100 CRESCENT COURT, SUITE 1300
                            DALLAS, TEXAS 75201-6950
                                  214-746-7738

                           CALCULATION OF FILING FEE
                      TRANSACTION VALUATION* $499,701,060
                        AMOUNT OF FILING FEE $99,940.21
<PAGE>   2
*        Estimated for purposes of calculating the amount of the filing fee
         only.  The amount assumes the purchase of (i) 19,768,978 shares of
         common stock, par value $.20 per share (the "Shares"), of Amati
         Communications Corporation (the "Company") at a price per Share of
         $20.00 in cash (the "Offer Price"), (ii) the cancellation of and
         settlement with respect to (a) 4,885,599 options granted under the
         Company's stock option plans and (b) 330,476 warrants.  Such number of
         Shares, options and warrants represents all of the Shares, options and
         warrants outstanding as of October 31, 1997 (except for 300,000
         warrants to be cancelled and terminated without payment of any
         consideration).

[ ]      Check box if any part of the fee is offset as provided by Rule
         0-11(a)(2) and identify the filing with which the offsetting fee was
         previously paid.  Identify the previous filing by registration
         statement number, or the form or schedule and the date of its filing.
         Amount previously paid: none Form or registration no.: n/a Filing
         party: n/a Date filed: n/a





                                       2
<PAGE>   3
                                  TENDER OFFER

         This Tender Offer Statement on Schedule 14D-1 relates to the offer by
DSL Acquisition Corporation, a Delaware corporation (the "Purchaser") and a
direct wholly owned subsidiary of Texas Instruments Incorporated, a Delaware
corporation ("Parent"), to purchase all outstanding shares of common stock, par
value $.20 per share (the "Shares"), of Amati Communications Corporation, a
Delaware corporation, at $20.00 per Share, net to the seller in cash, without
interest, on the terms and subject to the conditions set forth in the Offer to
Purchase dated November 25, 1997 (the "Offer to Purchase") and in the related
Letter of Transmittal, copies of which are attached hereto as Exhibits (a)(1)
and (a)(2), respectively (which, together with any amendments or supplements,
collectively constitute the "Offer").  The item numbers and responses thereto
below are in accordance with the requirements of Schedule 14D-1.

ITEM 1.  SECURITY AND SUBJECT COMPANY

         (a)     The name of the subject company is Amati Communications
Corporation, a Delaware corporation (the "Company").  The address of the
Company's principal executive offices is 2043 Samaritan Drive, San Jose,
California 95124.

         (b)     The information set forth in the Introduction of the Offer to
Purchase is incorporated herein by reference.

         (c)     The information set forth in Section 6 -- "Price Range of
Shares; Dividends on the Shares" of the Offer to Purchase is incorporated
herein by reference.

ITEM 2.  IDENTITY AND BACKGROUND

         (a)-(d), (g)  This Statement is filed by the Purchaser and Parent.
The information set forth in the Introduction, in Section 9 -- "Certain
Information Concerning the Purchaser and Parent" and in Schedule I of the Offer
to Purchase is incorporated herein by reference.

         (e)-(f)  During the last five years, neither the Purchaser nor Parent
nor, to their knowledge, any of the persons listed in Schedule I (Directors and
Executive Officers) to the Offer to Purchase, (i) has been convicted in a
criminal proceeding (excluding traffic violations or similar misdemeanors) or
(ii) has been a party to a civil proceeding of a judicial or administrative
body of competent jurisdiction and as a result of such proceeding was or is
subject to a judgment, decree or final order enjoining future violations of, or
prohibiting activities subject to, federal or state securities laws or finding
any violation of such laws.

ITEM 3.  PAST CONTACTS, TRANSACTIONS OR NEGOTIATIONS WITH THE SUBJECT COMPANY

         (a)     Not applicable.

         (b)     The information set forth in Section 11 -- "Background of the
Offer; Contacts with the Company" and in Section 12 -- "Purpose of the Offer and
the Merger; Plans for the Company; Merger Agreement; Loan Agreement; Retention
Agreements; Consulting Agreement; Confidentiality Agreement; Other Matters" of
the Offer to Purchase is incorporated herein by reference.

ITEM 4.  SOURCE AND AMOUNT OF FUNDS OR OTHER CONSIDERATION

         (a)     The information set forth in Section 10 -- "Source and Amount
of Funds" of the Offer to Purchase is incorporated herein by reference.





                                       3
<PAGE>   4
         (b)  Not applicable.

         (c)  Not applicable.

ITEM 5.  PURPOSE OF THE TENDER OFFER AND PLANS OR PROPOSALS OF THE BIDDERS

         (a)-(g)  The information set forth in the Introduction, in Section 7
-- "Effect of the Offer on the Market for the Shares; NASDAQ Trading; Exchange
Act Registration; Margin Securities" and in Section 12 -- "Purpose of the Offer
and the Merger; Plans for the Company; Merger Agreement; Loan Agreement;
Retention Agreements; Consulting Agreement; Confidentiality Agreement; Other 
Matters" of the Offer to Purchase is incorporated herein by reference.

ITEM 6.  INTEREST IN SECURITIES OF THE SUBJECT COMPANY

         (a)-(b)  Not Applicable.

ITEM 7.  CONTRACTS, ARRANGEMENTS, UNDERSTANDINGS OR RELATIONSHIPS WITH RESPECT
TO THE SUBJECT COMPANY'S SECURITIES

         The information set forth in the Introduction, in Section 11 --
"Background of the Offer; Contacts with the Company" and in Section 12 --
"Purpose of the Offer and the Merger; Plans for the Company; Merger Agreement;
Loan Agreement; Retention Agreements; Consulting Agreement; Confidentiality 
Agreement; Other Matters" of the Offer to Purchase is incorporated herein 
by reference.

ITEM 8.  PERSONS RETAINED, EMPLOYED OR TO BE COMPENSATED

         The information set forth in the Introduction, in Section 16 -- "Fees
and Expenses" and in Section 17 -- "Miscellaneous" of the Offer to Purchase is
incorporated herein by reference.

ITEM 9.  FINANCIAL STATEMENTS OF CERTAIN BIDDERS

         Not applicable.

ITEM 10. ADDITIONAL INFORMATION

         (a)     The information set forth in the Introduction, in Section 11
-- "Background of the Offer; Contacts with the Company" and in Section 12 --
"Purpose of the Offer and the Merger; Plans for the Company; Merger Agreement;
Loan Agreement; Retention Agreements; Consulting Agreement; Confidentiality 
Agreement; Other Matters" of the Offer to Purchase is incorporated herein 
by reference.

         (b)-(c) The information set forth in Section 12 -- "Purpose of the
Offer and the Merger; Plans for the Company; Merger Agreement; Loan Agreement;
Retention Agreements; Consulting Agreement; Confidentiality Agreement; Other 
Matters," in Section 15 -- "Certain Legal Matters" and in Section 17 -- 
"Miscellaneous" of the Offer to Purchase is incorporated herein by reference.

         (d) The information set forth in Section 7 -- "Effect of the Offer on
the Market for the Shares; NASDAQ Trading; Exchange Act Registration; Margin
Securities" of the Offer to Purchase is incorporated herein by reference.





                                       4
<PAGE>   5
         (e) Not applicable.

         (f) The information set forth in the Offer to Purchase and the Letter
of Transmittal, copies of which are attached hereto as Exhibits (a)(1) and
(a)(2), respectively, is incorporated herein by reference.

ITEM 11. MATERIAL TO BE FILED AS EXHIBITS

       99(a)(1)  Offer to Purchase, dated November 25, 1997.

       99(a)(2)  Letter of Transmittal.

       99(a)(3)  Notice of Guaranteed Delivery.

       99(a)(4)  Letter to Brokers, Dealers, Commercial Banks, Trust Companies
and Other Nominees.

       99(a)(5)  Letter to Clients for use by Brokers, Dealers, Commercial
Banks, Trust Companies and Other Nominees.

       99(a)(6)  Guidelines for Certification of Taxpayer Identification Number
on Substitute Form W-9.

       99(a)(7)  Form of Summary Advertisement, dated November 25, 1997.

       99(a)(8)  Text of Press Release, dated November 19, 1997.
            
       99(c)(1)  Agreement and Plan of Merger, dated as of November 19, 1997, by
and among the Company, Parent and the Purchaser.

       99(c)(2)  Loan and Security Agreement, dated November 19, 1997, by and
between Parent and the Company.

       99(c)(3)  Confidentiality Agreement, dated as of July 22, 1997, by and
between Parent and the Company.

       99(c)(4)  Retention Agreement, dated as of November 19, 1997, by and
between Parent and James E. Steenbergen.

       99(c)(5)  Retention Agreement, dated as of November 19, 1997, by and
between Parent and Ronald Carlini.

       99(c)(6)  Retention Agreement, dated as of November 19, 1997, by and
between Parent and Dr. John Cioffi.

       99(d)     None.

       99(e)     Not applicable.

       99(f)     None.





                                       5
<PAGE>   6
                                   SIGNATURES

         After due inquiry and to the best of their knowledge and belief, the
undersigned certify that the information set forth in this statement is true,
complete and correct.

                                       Dated: November 25, 1997
                                       
                                       DSL ACQUISITION CORPORATION
                                       
                                                                             
                                       By:  /s/ GEORGE BARBER             
                                          -----------------------------------
                                            George Barber, President
                                                                             
                                                                             
                                       TEXAS INSTRUMENTS INCORPORATED        
                                                                             
                                                                             
                                       By:  /s/ WILLIAM A. AYLESWORTH        
                                          -----------------------------------
                                            William A. Aylesworth, Senior 
                                            Vice President, Treasurer and
                                            Chief Financial Officer     
                                                                             



                                       6
<PAGE>   7
                                 EXHIBIT INDEX

EXHIBIT                                                           

99(a)(1)   Offer to Purchase, dated November 25, 1997. 
99(a)(2)   Letter of Transmittal. 
99(a)(3)   Notice of Guaranteed Delivery. 
99(a)(4)   Letter to Brokers, Dealers, Commercial Banks, Trust Companies and
           Other Nominees. 
99(a)(5)   Letter to Clients for use by Brokers, Dealers, Commercial Banks,
           Trust Companies and Other Nominees.
99(a)(6)   Guidelines for Certification of Taxpayer Identification Number on
           Substitute Form W-9. 
99(a)(7)   Form of Summary Advertisement, dated November 25, 1997. 
99(a)(8)   Text of Press Release, dated November 19, 1997. 
99(c)(1)   Agreement and Plan of Merger, dated as of November 19, 1997, by and
           among the Company, Parent, and the Purchaser. 
99(c)(2)   Loan and Security Agreement, dated November 19, 1997, by and between
           Parent and the Company.
99(c)(3)   Confidentiality Agreement, dated as of July 22, 1997, by and between
           Parent and the Company. 
99(c)(4)   Retention Agreement, dated as of November 19, 1997, by and between
           Parent and James E. Steenbergen.
99(c)(5)   Retention Agreement, dated as of November 19, 1997, by and between
           Parent and Ronald Carlini.
99(c)(6)   Retention Agreement, dated as of November 19, 1997, by and between
           Parent and Dr. John Cioffi.
99(d)      None.
99(e)      Not applicable.
99(f)      None.




                                       7
