
<PAGE>   1
                                                                 EXHIBIT (a)(7)


         This announcement is neither an offer to purchase nor a solicitation
of an offer to sell Shares. The Offer is made solely by the Offer to Purchase
dated November 25, 1997 and the related Letter of Transmittal, and any
amendments and supplements thereto, and is not being made to, nor will tenders
be accepted from or on behalf of, holders of Shares in any jurisdiction in
which the making of the Offer or acceptance thereof would not be in compliance
with the laws of such jurisdiction. In those jurisdictions where securities,
blue sky or other laws require the Offer to be made by a licensed broker or
dealer, the Offer shall be deemed to be made on behalf of the Purchaser by
Morgan Stanley & Co.  Incorporated or one or more registered brokers or dealers
licensed under the laws of such jurisdictions.

                      Notice of Offer to Purchase for Cash
                     All Outstanding Shares of Common Stock
                                       of
                        AMATI COMMUNICATIONS CORPORATION
                                       at
                              $20.00 NET PER SHARE
                                       by
                          DSL ACQUISITION CORPORATION
                      a direct wholly owned subsidiary of
                         TEXAS INSTRUMENTS INCORPORATED

         DSL Acquisition Corporation (the "Purchaser"), a Delaware corporation
and a direct wholly owned subsidiary of Texas Instruments Incorporated, a
Delaware corporation ("Parent"), is offering to purchase all outstanding shares
of common stock, par value $.20 per share (the "Shares"), of Amati
Communications Corporation, a Delaware corporation (the "Company"), at $20.00
per Share, net to the seller in cash, without interest, upon 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 (which,
together with any amendments or supplements, collectively constitute the
"Offer").  Following the consummation of the Offer, the Purchaser intends to
effect the "Merger" described below.

                  THE OFFER AND WITHDRAWAL RIGHTS WILL EXPIRE
                     AT 12:00 MIDNIGHT, NEW YORK CITY TIME,
          ON TUESDAY, DECEMBER 23, 1997, UNLESS THE OFFER IS EXTENDED.
<PAGE>   2
         THE OFFER IS CONDITIONED UPON, AMONG OTHER THINGS, THERE BEING VALIDLY
TENDERED AND NOT WITHDRAWN PRIOR TO THE EXPIRATION OF THE OFFER, THAT NUMBER OF
SHARES WHICH, TOGETHER WITH ANY SHARES BENEFICIALLY OWNED BY PARENT OR THE
PURCHASER, REPRESENT AT LEAST A MAJORITY OF THE SHARES OUTSTANDING ON A FULLY
DILUTED BASIS. THE OFFER IS ALSO SUBJECT TO OTHER TERMS AND CONDITIONS SET
FORTH IN THE OFFER TO PURCHASE, INCLUDING, WITHOUT LIMITATION, THE EXPIRATION
OR TERMINATION OF ALL WAITING PERIODS UNDER THE HART-SCOTT-RODINO ANTITRUST
IMPROVEMENTS ACT OF 1976, AS AMENDED.

         The Offer is being made pursuant to an Agreement and Plan of Merger,
dated as of November 19, 1997 (the "Merger Agreement"), by and among the
Company, Parent and the Purchaser. The Merger Agreement provides, among other
things, that following the consummation of the Offer and the satisfaction or
waiver of the other conditions set forth in the Merger Agreement, the Purchaser
will be merged with and into the Company (the "Merger"). Following the Merger,
the Company will continue as the surviving corporation and will be a direct
wholly owned subsidiary of Parent. At the effective time of the Merger, each
outstanding Share (other than Shares owned by Parent, the Purchaser or any
other wholly owned subsidiary of Parent and Shares held by stockholders who
have demanded and perfected dissenter's rights under Delaware law) will be
converted automatically into the right to receive the per Share price paid in
the Offer in cash, without interest.

         THE BOARD OF DIRECTORS OF THE COMPANY HAS UNANIMOUSLY APPROVED THE
MERGER AGREEMENT, THE OFFER AND THE MERGER, HAS DETERMINED THAT THE OFFER AND
THE MERGER ARE FAIR TO AND IN THE BEST INTERESTS OF THE STOCKHOLDERS OF THE
COMPANY AND UNANIMOUSLY RECOMMENDS THAT STOCKHOLDERS ACCEPT THE OFFER AND
TENDER THEIR SHARES PURSUANT TO THE OFFER.

         For purposes of the Offer, the Purchaser will be deemed to have
accepted for payment, and thereby purchased, tendered Shares if, as and when
the Purchaser gives oral or written notice to the Depositary of its acceptance
of the tenders of such Shares. Payment for Shares accepted for payment pursuant
to the Offer will be made by deposit of the purchase price with ChaseMellon
Shareholder Services, L.L.C. (the "Depositary"), which will act as agent for
tendering stockholders for the purpose of receiving payment from the Purchaser
and transmitting payment to tendering stockholders.  In all cases, payment for
Shares purchased pursuant to the Offer will be made only after timely receipt
by the Depositary of (i) certificates evidencing such Shares (or timely
confirmation of a book-entry transfer of such Shares into the Depositary's
account at one of the Book-Entry Transfer Facilities (as defined in the Offer
to Purchase)), (ii) a Letter of Transmittal (or facsimile thereof), properly
completed and duly executed, with any required signature guarantees (or in the
case of a





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<PAGE>   3
book-entry transfer, an Agent's Message (as defined in the Offer to Purchase)
in lieu of a Letter of Transmittal) and (iii) any other documents required by
the Letter of Transmittal.

         The term "Expiration Date" shall mean 12:00 Midnight, New York City
time, on Tuesday, December 23, 1997, unless and until Purchaser, in accordance
with the terms of the Offer and the Merger Agreement, shall have extended the
period of time during which the Offer is open, in which event the term
"Expiration Date" shall mean the latest time and date at which the Offer, as so
extended by Purchaser, shall expire.

         The Purchaser expressly reserves the right, in its sole discretion, at
any time or from time to time, subject to the terms of the Merger Agreement and
regardless of whether or not any of the events set forth in Section 14 of the
Offer to Purchase shall have occurred or shall have been determined by the
Purchaser to have occurred, (i) to extend the period of time during which the
Offer is open and thereby delay acceptance for payment of, and the payment for,
any Shares, by giving oral or written notice of such extension to the
Depositary and (ii) to amend the Offer in any respect by giving oral or written
notice of such amendment to the Depositary. The rights reserved by the
Purchaser in this paragraph are in addition to the Purchaser's rights to
terminate the Offer pursuant to Section 14 of the Offer to Purchase. Any
extension, amendment or termination will be followed as promptly as practicable
by public announcement thereof, the announcement in the case of an extension to
be issued no later than 9:00 a.m., New York City time, on the next business day
after the previously scheduled Expiration Date. Without limiting the obligation
of the Purchaser under such rules or the manner in which the Purchaser may
choose to make any public announcement, the Purchaser currently intends to make
announcements by issuing a press release to the Dow Jones News Service.

         Tenders of Shares made pursuant to the Offer are irrevocable, except
as other wise provided below. Shares tendered pursuant to the Offer may be
withdrawn at any time prior to the Expiration Date and, unless theretofore
accepted for payment by the Purchaser, may also be withdrawn at any time after
January 23, 1998. For a withdrawal to be effective, a written, telegraphic or
facsimile transmission notice of withdrawal must be timely received by the
Depositary at one of its addresses set forth in the Offer to Purchase. Any such
notice of withdrawal must specify the name of the person who tendered the
Shares to be withdrawn, the number of Shares to be withdrawn and the name of
the registered holder, if different from that of the person who tendered such
Shares. If certificates evidencing Shares have been delivered or otherwise
identified to the Depositary, then prior to the release of such certificates,
the tendering stockholder must also submit the serial numbers shown on the
particular certificates evidencing the Shares to be withdrawn, and the
signature on the notice of withdrawal must be guaranteed by an Eligible
Institution (as defined in Section 3 of the





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<PAGE>   4
Offer to Purchase), except in the case of Shares tendered for the account of an
Eligible Institution. If Shares have been tendered pursuant to the procedure
for book-entry transfer set forth in Section 3 of the Offer to Purchase, the
notice of withdrawal must specify the name and number of the account at the
applicable Book-Entry Transfer Facility to be credited with the withdrawn
Shares. All questions as to form and validity (including time of receipt) of
notice of withdrawal will be determined by the Purchaser, in its sole
discretion, whose determination shall be final and binding on all parties. No
withdrawal of Shares shall be deemed to have been properly made until all
defects and irregularities have been cured or waived. None of the Purchaser,
Parent, the Dealer Manager, the Depositary, the Information Agent or any other
person will be under any duty to give notification of any defects or
irregularities in any notice of withdrawal or incur any liability for failing
to give such notification.

         The information required to be disclosed by Rule 14d-6(e)(1)(vii) of
the General Rules and Regulations under the Securities Exchange Act of 1934, as
amended, is contained in the Offer to Purchase and is incorporated herein by
reference.

         The Company has provided the Purchaser with the Company's stockholder
list and security position listings for the purpose of disseminating the Offer
to holders of Shares. The Offer to Purchase and the related Letter of
Transmittal will be mailed to record holders of Shares and will be furnished to
brokers, banks and similar persons whose names, or the names of whose nominees,
appear on the stockholder list or, if applicable, who are listed as
participants in a clearing agency's security position listing for subsequent
transmittal to beneficial owners of Shares.

         THE OFFER TO PURCHASE AND THE RELATED LETTER OF TRANSMITTAL CONTAIN
IMPORTANT INFORMATION WHICH SHOULD BE READ CAREFULLY BEFORE ANY DECISION IS
MADE WITH RESPECT TO THE OFFER.

         Questions and requests for assistance or for copies of the Offer to
Purchase, the related Letter of Transmittal, the Notice of Guaranteed Delivery
and other Offer materials may be directed to the Information Agent or the
Dealer Manager at their respective telephone number and addresses set forth
below. Holders of Shares may also contact brokers, dealers, commercial banks,
trust companies or other nominees for assistance concerning the Offer. Copies
of the Offer materials will be furnished at the Purchaser's expense. No fees or
commissions will be payable to brokers, dealers or other persons other than the
Dealer Manager and the Information Agent for soliciting tenders of Shares
pursuant to the Offer.





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<PAGE>   5
                    The Information Agent for the Offer is:

                        [Georgeson & Company Inc. logo]

                               Wall Street Plaza
                            New York, New York 10005
                Bankers and Brokers Call Collect: (212) 440-9800
                   All Others Call Toll-Free: (800) 223-2064


                      The Dealer Manager for the Offer is:

                       [Morgan Stanley Dean Witter logo]

                       Morgan Stanley & Co. Incorporated
                                 1585 Broadway
                            New York, New York 10036
                                 (212) 761-6863





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