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                          SECURITIES AND EXCHANGE COMMISSION
                                WASHINGTON, D.C. 20549

                                     SCHEDULE 13G

               INFORMATION STATEMENT PURSUANT TO RULES 13d-1 AND 13d-2
                    UNDER THE SECURITIES AND EXCHANGE ACT OF 1934
                               (Amendment No.       )*


                                Alpha Industries, Inc.
- --------------------------------------------------------------------------------
                                   (Name of Issuer)


                                     Common Stock
- --------------------------------------------------------------------------------
                            (Title of Class of Securities)


                                      020753109
- --------------------------------------------------------------------------------
                                    (CUSIP Number)



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

*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).


                           (Continued on following page(s))
                                  Page 1 of 8 Pages


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CUSIP No. 020753109                   13G               Page  2  of  8  Pages   
- ----------------------                               ---------------------------

- --------------------------------------------------------------------------------
1    NAME OF REPORTING PERSON
     S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

               The TCW Group, Inc.
- --------------------------------------------------------------------------------
2    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a)  / /
                                                                        (b)  /X/
- --------------------------------------------------------------------------------
3    SEC USE ONLY

- --------------------------------------------------------------------------------
4    CITIZENSHIP OR PLACE OF ORGANIZATION

           Nevada corporation
- --------------------------------------------------------------------------------
            NUMBER OF              5    SOLE VOTING POWER
            SHARES                                                     556,500
         BENEFICIALLY              ---------------------------------------------
           OWNED BY                6    SHARED VOTING POWER
             EACH                                                          -0-
            REPORTING              ---------------------------------------------
            PERSON                 7    SOLE DISPOSITIVE POWER
             WITH                                                      556,500
                                   ---------------------------------------------
                                   8    SHARED DISPOSITIVE POWER
                                                                           -0-
- --------------------------------------------------------------------------------
9    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
                                                                       556,500
- --------------------------------------------------------------------------------
10   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES
     CERTAIN SHARES*
                                                                           / /
- --------------------------------------------------------------------------------
11   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)
      5.6%(see response to Item 4)
- --------------------------------------------------------------------------------
12   TYPE OF REPORTING PERSON*
                                        HC/CO
- --------------------------------------------------------------------------------



                    *SEE INSTRUCTIONS BEFORE FILLING OUT!


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CUSIP No. 020753109                 13G                 Page  3  of  8  Pages   
- ----------------------                               ---------------------------

- --------------------------------------------------------------------------------
1    NAME OF REPORTING PERSON
     S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

               Robert Day
- --------------------------------------------------------------------------------
2    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                        (a)  / /
                                                                        (b)  /X/
- --------------------------------------------------------------------------------
3    SEC USE ONLY

- --------------------------------------------------------------------------------
4    CITIZENSHIP OR PLACE OF ORGANIZATION

          United States Citizen
- --------------------------------------------------------------------------------
            NUMBER OF              5    SOLE VOTING POWER
            SHARES                                                     556,500
         BENEFICIALLY              ---------------------------------------------
           OWNED BY                6    SHARED VOTING POWER
             EACH                                                          -0-
            REPORTING              ---------------------------------------------
            PERSON                 7    SOLE DISPOSITIVE POWER
             WITH                                                      556,500
                                   ---------------------------------------------
                                   8    SHARED DISPOSITIVE POWER
                                                                           -0-
- --------------------------------------------------------------------------------
9    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
                                                                       556,500
- --------------------------------------------------------------------------------
10   CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES
     CERTAIN SHARES*
                                                                           / /
- --------------------------------------------------------------------------------
11   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)
      5.6%(see response to Item 4)
- --------------------------------------------------------------------------------
12   TYPE OF REPORTING PERSON*7
                                        HC/IN
- --------------------------------------------------------------------------------



                    *SEE INSTRUCTIONS BEFORE FILLING OUT!


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                                                            Page 4 of 8 Pages   

Item 1(a).  Name of Issuer:

            Alpha Industries, Inc.

Item 1(b).  Address of Issuer's Principal Executive Offices:

            20 Sylvan Road
            Woburn, Massachusetts 01801
            
Item 2(a).  Name of Persons Filing:
Item 2(b).  Address of Principal Business Office:
Item 2(c).  Citizenship:

            The TCW Group, Inc.
            865 South Figueroa Street
            Los Angeles, CA 90017
            (Nevada Corporation)

            Robert Day 
            200 Park Avenue, Suite 2200
            New York, New York 10166
            (United States Citizen)

Item 2(d).  Title of Class of Securities:

            Common Stock

Item 2(e).  CUSIP Number:

            020753109


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                                                            Page 5 of 8 Pages   


Item 3.     If this statement is filed pursuant to Rules 13d-1(b), or 13d-2(b),
            check whether the person filing is a:

      (a)   [ ]  Broker or Dealer registered under Section 15 of the Act:

                     Not applicable

      (b)   [ ]  Bank as defined in Section 3(a)(6) of the Act:

                     Not applicable

      (c)   [ ]  Insurance Company as defined in Section 3(a)(19) of the Act:
                 
                     Not applicable

      (d)   [ ]  Investment Company registered under Section 8 of the
                 Investment Company Act:

                     Not applicable

      (e)   [ ]  Investment Adviser registered under Section 203 of the
                 Investment Advisers Act of 1940:

                     Not applicable

      (f)   [ ]  Employee Benefit Plan, Pension Fund which is subject to the
                 provisions of the Employee Retirement Income Security Act of
                 1974 or Endowment Fund (SEE 13d-1(b)(1)(ii)(F)):

                     Not applicable

      (g)   [X]  Parent Holding Company, in accordance with Rule
                 13d-1(b)(ii)(G) (SEE Item 7):

                     The TCW Group, Inc.
                     Robert Day (individual who may be deemed to control The 
                         TCW Group, Inc. and other holders of the Common 
                         Stock of the issuer)

      (h)   [ ]  Group, in accordance with Rule 13d-1(b)(1)(ii)(H):

                     Not applicable.


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                                                            Page 6 of 8 Pages   


Item 4.   Ownership **

     THE TCW GROUP, INC.

          (a)    Amount beneficially owned: 556,500

          (b)    Percent of class: 5.6%

          (c)    Number of shares as to which such person has:

                 (i)   Sole power to vote or to direct the vote:           
                            556,500

                 (ii)  Shared power to vote or to direct the vote:  
                            none.

                 (iii) Sole power to dispose or direct the disposition of: 
                            556,500

                 (iv)  Shared power to dispose or to direct the disposition of: 
                            none.

     ROBERT DAY 

          (a)    Amount beneficially owned: 556,500

          (b)    Percent of class: 5.6%

          (c)    Number of shares as to which such person has:

                 (i)   Sole power to vote or to direct the vote:           
                            556,500

                 (ii)  Shared power to vote or to direct the vote: 
                            none.

                 (iii) Sole power to dispose or direct the disposition of: 
                            556,500

                 (iv)  Shared power to dispose or to direct the disposition of: 
                            none.

- --------------------
**   The filing of this Schedule 13G shall not be construed as an admission that
the reporting person or any of its affiliates is, for the purposes of Section
13(d) or 13(g) of the Securities Exchange Act of 1934, the beneficial owner of
any securities covered by this Schedule 13G.  In addition, the filing of this
Schedule 13G shall not be construed as an admission that the reporting person or
any of its affiliates is the beneficial owner of any securities covered by this
Schedule 13G for any other purposes than Section 13(d) of the Securities
Exchange Act of 1934.


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                                                            Page 7 of 8 Pages   

Item 5.   Ownership of Five Percent or Less of a Class.

                 Not applicable.

Item 6.   Ownership of More than Five Percent on Behalf of Another Person.

          Various persons other than as described in Item 4 have the right to
          receive or the power to direct the receipt of dividends from, or
          the proceeds from the sale of, the Common Stock of Alpha
          Industries, Inc.

Item 7.   Identification and Classification of the Subsidiary Which Acquired
          the Security Being Reported on by the Parent Holding Company.

          SEE Exhibit A.

Item 8.   Identification and Classification of Members of the Group.

          Not applicable. SEE Exhibits A and B.

Item 9.   Notice of Dissolution of Group.

          Not applicable.

Item 10.  Certification.

     Because this statement is filed pursuant to Rule 13d-1(b), the following
     certification is included:


     By signing below I certify that, to the best of my knowledge and belief,
     the securities referred to above were acquired in the ordinary course of
     business and were not acquired for the purpose of and do not have the
     effect of changing or influencing the control of the issuer of such
     securities and were not acquired in connection with or as a participant
     in any transaction having such purpose or effect.


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                                                            Page 8 of 8 Pages   


                                      SIGNATURE


          After reasonable inquiry and to the best of my knowledge and
belief, I certify that the information set forth in this statement is true,
complete and correct.


Dated this 12th day of February, 1997.


                                The TCW Group, Inc.


                                By: /s/ Mohan V. Phansalkar
                                    -------------------------
                                    Mohan V. Phansalkar
                                    Authorized Signatory              
                            


                                Robert Day


                                By: /s/ Mohan V. Phansalkar
                                    -------------------------
                                    Mohan V. Phansalkar
                                    Under Power of Attorney dated January
                                    30, 1996, on File with Schedule 13G
                                    Amendment Number 1 for Matrix Service
                                    Co. dated January 30, 1996.





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                                      EXHIBIT A


                   RELEVANT SUBSIDIARIES OF PARENT HOLDING COMPANY

PART A: TCW ENTITIES

PARENT HOLDING COMPANY:

         The TCW Group, Inc.

         Robert Day (an individual who may be deemed to control The TCW Group,
         Inc.)


RELEVANT SUBSIDIARIES THAT ARE PERSONS DESCRIBED IN RULE 13d-1(b):

    (i)  Trust Company of the West, a California corporation and a bank as
    defined in Section 3(a)(6) of the Securities Exchange Act of 1934.

    (ii) TCW Asset Management Company, a California corporation and an
    Investment Adviser registered under Section 203 of the Investment Advisers
    Act of 1940.

Note:    No Common Stock of Alpha Industries, Inc. is held directly by The
         TCW Group, Inc.  Other than the indirect holdings of The TCW
         Group, Inc. no Common Stock of Alpha Industries, Inc. is held
         directly or indirectly by Robert Day, an individual who may be
         deemed to control The TCW Group, Inc.

PART B: NON TCW ENTITIES

PARENT HOLDING COMPANY:

              Robert Day (an individual who may be deemed to control the
              holders described below which are not subsidiaries of The TCW
              Group, Inc.)

RELEVANT SUBSIDIARIES THAT ARE PERSONS DESCRIBED IN
RULE 13d-1(b):

              Oakmont Corporation, a California corporation and an Investment
              Adviser registered under Section 203 of the Investment Advisers
              Act of 1940.

              Cypress
 International Partners Limited, a British Virgin Islands
              corporation and an Investment Adviser registered under Section
              203 of the Investment Advisers Act of 1940.


                                         A-1



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                                      EXHIBIT B

                                JOINT FILING AGREEMENT


         The undersigned acknowledge and agree that the foregoing statement on
Schedule 13G is filed on behalf of each of the undersigned and that all
subsequent amendments to this statement on Schedule 13G shall be filed on behalf
of each of the undersigned without the necessity of filing additional joint
acquisition statements.  The undersigned acknowledge that each shall be
responsible for the timely filing of such amendments, and for the completeness
and accuracy of the information concerning him or it contained therein, but
shall not be responsible for the completeness and accuracy of the information
concerning the other, except to the extent that he or it knows or has reason to
believe that such information is accurate.


Dated: February 12, 1997


                             The TCW Group, Inc.


                             By:  /s/ Mohan V. Phansalkar
                                  ------------------------------
                                  Mohan V. Phansalkar
                                  Authorized Signatory



                             Robert Day


                             By:  /s/ Mohan V. Phansalkar
                                  ------------------------------
                                  Mohan V. Phansalkar
                                  Under Power of Attorney dated January 30,
                                  1996, on File with Schedule 13G Amendment
                                  Number 1 for Matrix Service Co. dated January
                                  30, 1996.


                                         B-1