<PAGE>   1
                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION

                             WASHINGTON, D.C. 20549

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

                                    FORM 6-K

                        REPORT OF FOREIGN PRIVATE ISSUER
                       PURSUANT TO RULE 13a-16 OR 15d-16

                                     UNDER

                      THE SECURITIES EXCHANGE ACT OF 1934

                           FOR THE MONTH OF JUNE 1999

                        SPECTRUM SIGNAL PROCESSING INC.
                              (REGISTRANT'S NAME)

                    100 PRODUCTION COURT, 8525 BAXTER PLACE
                              BURNABY, BC V5A 4V7
                    (Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports
under cover Form 20-F or Form 40-F.

                           Form 20-F        Form 40-F  X
                                     ---              ---

Indicate by check mark whether the registrant by furnishing the information
contained in this Form is also thereby furnishing the information to the
Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

                                  Yes      No  X
                                      ---     ---

If "Yes" is marked, indicate below the file number assigned to the registrant
in connection with Rule 12g3-2(b): 82-       .
                                      -------



<PAGE>   2
                         SPECTRUM SIGNAL PROCESSING INC.
                           CONSOLIDATED BALANCE SHEETS
                (EXPRESSED IN THOUSANDS OF UNITED STATES DOLLARS)
          (PREPARED IN ACCORDANCE WITH UNITED STATES GENERALLY ACCEPTED
                        ACCOUNTING PRINCIPLES, UNAUDITED)


<TABLE>
<CAPTION>


                                                            March 31,        December 31,
ASSETS                                                        1999              1998
--------------------------------------------------------------------------------------------
                                                                              (Restated)

<S>                                                         <C>               <C>
Current assets
    Cash and cash equivalents                                $  2,732          $  1,693
    Accounts receivable                                         3,678             5,404
    Inventories                                                 5,140             4,935
    Prepaid expenses                                              197               203
--------------------------------------------------------------------------------------------
                                                               11,747            12,235


Property and equipment                                          2,233             2,287
Other assets*                                                   4,597             4,925
--------------------------------------------------------------------------------------------

                                                             $ 18,577          $ 19,447
============================================================================================

LIABILITIES AND SHAREHOLDERS' EQUITY
--------------------------------------------------------------------------------------------


Current liabilities
     Bank indebtedness                                       $  2,965          $  2,202
     Accounts payable                                           2,572             3,680
     Accrued liabilities                                        1,050             1,303
     Current portion of long-term debt                             57                80
--------------------------------------------------------------------------------------------
                                                                6,644             7,265

Long-term debt                                                     73                75
Deferred income taxes                                             434               346

Shareholders' equity
Share capital
    Authorized: 50,000,000 common shares, no par value
    Issued:  10,268,954 (1998 - 10,268,954)                    16,309            16,309
    Outstanding:  10,035,654 (1998 - 10,035,654)
Warrants                                                          140               140
Additional paid-in capital                                         76                76
Treasury stock, at cost, 233,300 shares (1998 - 233,300)       (1,232)           (1,232)
Retained earnings (deficit)                                    (1,827)           (1,671)
Accumulated other comprehensive income
    Cumulative translation adjustments                         (2,040)           (1,861)
--------------------------------------------------------------------------------------------
                                                               11,426            11,761
--------------------------------------------------------------------------------------------


                                                             $ 18,577          $ 19,447
============================================================================================
</TABLE>

* Currently subject to review by the SEC

<PAGE>   3

                         SPECTRUM SIGNAL PROCESSING INC.
      CONSOLIDATED STATEMENTS OF OPERATIONS AND RETAINED EARNINGS (DEFICIT)
  (EXPRESSED IN THOUSANDS OF UNITED STATES DOLLARS, EXCEPT NUMBERS OF SHARES)
          (PREPARED IN ACCORDANCE WITH UNITED STATES GENERALLY ACCEPTED
                        ACCOUNTING PRINCIPLES, UNAUDITED)


<TABLE>
<CAPTION>
                                                                 3 months ended March 31,
                                                                  1999             1998
--------------------------------------------------------------------------------------------
                                                                                 (Restated)

<S>                                                           <C>               <C>
Sales                                                         $  5,638          $  5,276
Cost of sales                                                    2,165             1,950
--------------------------------------------------------------------------------------------

Gross profit                                                     3,473             3,326

Expenses
    Administrative                                                 926               774
    Sales and marketing                                          1,456             1,716
    Amortization                                                   359               171
    Acquired in-process research and development charge *            -             2,640
    Research and development                                       832               841
--------------------------------------------------------------------------------------------
                                                                 3,573             6,142
--------------------------------------------------------------------------------------------

Earnings (loss) from operations                                   (100)           (2,816)

Other
    Interest income (expense) and bank charges                     (45)              (14)
    Other income (expense)                                          56                (8)
--------------------------------------------------------------------------------------------

Earnings (loss) before income taxes                                (89)           (2,838)

Income tax expense (recovery)                                       67              (554)
--------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------
Net earnings (loss) for the period                                (156)           (2,284)
--------------------------------------------------------------------------------------------

Retained earnings (deficit), beginning of period                (1,671)            1,237

--------------------------------------------------------------------------------------------
Retained earnings (deficit), end of period                    $ (1,827)         $ (1,047)
============================================================================================

Earnings (loss) per share
    Basic                                                     $  (0.02)         $  (0.24)
    Diluted                                                   $  (0.02)         $  (0.24)

Weighted average shares (in thousands)
    Basic                                                       10,036             9,356
    Diluted                                                     10,036             9,356
</TABLE>

* Currently subject to review by the SEC

<PAGE>   4

                         SPECTRUM SIGNAL PROCESSING INC.
                      CONSOLIDATED STATEMENTS OF CASH FLOWS
                (EXPRESSED IN THOUSANDS OF UNITED STATES DOLLARS)
          (PREPARED IN ACCORDANCE WITH UNITED STATES GENERALLY ACCEPTED
                        ACCOUNTING PRINCIPLES, UNAUDITED)


<TABLE>
<CAPTION>
                                                                         3 months ended March 31,
                                                                            1999            1998
-------------------------------------------------------------------------------------------------------
                                                                                          (Restated)
<S>                                                                      <C>             <C>
 CASH FLOWS FROM OPERATING ACTIVITIES
     Net earnings (loss) from operations                                 $  (156)        $ (2,284)

     Adjustments to reconcile net earnings (loss) to net cash
       provided by operating activities
         Amortization                                                         518             225
         Acquired in-process research and development                           -           2,640
         Deferred income taxes                                                 67            (554)
         Changes in operating assets and liabilities
           Accounts receivable                                              1,745             936
           Inventories                                                        (43)           (653)
           Prepaid expenses                                                     9            (134)
           Accounts payable                                                (1,760)          2,003
           Accrued liabilities                                                  5            (589)
           Deferred revenue                                                     -             (18)
-------------------------------------------------------------------------------------------------------
 Net cash provided by operating activities                                    385           1,572
-------------------------------------------------------------------------------------------------------

 CASH FLOWS FROM INVESTING ACTIVITIES
     Purchase of property and equipment                                       (85)           (229)
     Software and related development costs                                     -            (294)
     Acquisition of net assets of Alex Computer, net of cash received           -          (2,204)
-------------------------------------------------------------------------------------------------------
 Net cash used in investing activities                                        (85)         (2,727)
-------------------------------------------------------------------------------------------------------

 CASH FLOWS FROM FINANCING ACTIVITIES
     Increase in bank indebtedness                                            763               -
     Issue of shares from share options                                         -              29
     Repayment of long-term debt                                              (23)              -
-------------------------------------------------------------------------------------------------------
 Net cash provided by financing activities                                    740              29
-------------------------------------------------------------------------------------------------------

 Effect of foreign currency exchange rates on cash and cash equivalents        (1)           (198)
-------------------------------------------------------------------------------------------------------

 Net increase (decrease) in cash and cash equivalents during the period     1,039          (1,324)
 Cash and cash equivalents, beginning of period                             1,693           1,383
-------------------------------------------------------------------------------------------------------
 Cash and cash equivalents, end of period                                $  2,732          $   59
=======================================================================================================
</TABLE>