<PAGE>   1
                                                                    EXHIBIT 10.5

                             ENDOSONICS CORPORATION

                           INVESTOR'S RIGHTS AGREEMENT



            THIS INVESTOR'S RIGHTS AGREEMENT (the "Agreement") is entered into
as of September 21, 1998, by and among ENDOSONICS CORPORATION, a Delaware
corporation (the "Company") and FUKUDA DENSHI CO., LTD., a Japanese corporation
(the "Investor").

                                    RECITALS

            A. The Company proposes to sell and issue up to 965,730 shares of
its Common Stock pursuant to the Common Stock Purchase Agreement between the
Company and the Investor of even date herewith (the "Purchase Agreement"); and

            B. As a condition of entering into the Purchase Agreement, the
Investor has requested that the Company extend to it registration rights, as set
forth below.

            NOW, THEREFORE, in consideration of the mutual promises,
representations, warranties, covenants and conditions set forth in this
Agreement and in the Purchase Agreement, the parties mutually agree as follows:

SECTION 1.  GENERAL

            1.1 DEFINITIONS. As used in this Agreement the following terms shall
have the following respective meanings:

            "EXCHANGE ACT" means the Securities Exchange Act of 1934, as
amended.

            "FORM S-3" means such form under the Securities Act as in effect on
the date hereof or any successor registration form under the Securities Act
subsequently adopted by the SEC which permits inclusion or incorporation of
substantial information by reference to other documents filed by the Company
with the SEC.

            "HOLDER" means any person owning of record Registrable Securities
that have not been sold to the public or any assignee of record of such
Registrable Securities in accordance with Section 2.8 hereof.

            "REGISTER," "REGISTERED," and "REGISTRATION" refer to a registration
effected by preparing and filing a registration statement in compliance with the
Securities Act, and the declaration or ordering of effectiveness of such
registration statement or document.


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            "REGISTRABLE SECURITIES" means (a) Common Stock of the Company
purchased by the Investor pursuant to that certain Common Stock Purchase
Agreement dated as of September __, 1998, between the Company and the Investor.
Notwithstanding the foregoing, Registrable Securities shall not include any
securities sold by a person to the public pursuant to a registration statement
or Rule 144 or sold in a private transaction in which the transferor's rights
under Section 2 of this Agreement are not assigned.

            "REGISTRATION EXPENSES" shall mean all expenses incurred by the
Company in complying with Sections 2.1 and 2.2 hereof, including, without
limitation, all registration and filing fees, printing expenses, fees and
disbursements of counsel for the Company, blue sky fees and expenses and the
expense of any special audits incident to or required by any such registration
(but excluding the compensation of regular employees of the Company which shall
be paid in any event by the Company).

            "SEC" OR "COMMISSION" means the Securities and Exchange Commission.

            "SECURITIES ACT" shall mean the Securities Act of 1933, as amended.

            "SELLING EXPENSES" shall mean all underwriting discounts and selling
commissions applicable to the sale.

SECTION 2.  REGISTRATION

            2.1 PIGGYBACK REGISTRATIONS. If (but without any obligation to do
so) the Company proposes to register (including for this purpose a registration
effected by the Company for the Company or for stockholders other than the
Investor) any of its stock under the Securities Act in connection with the
public offering of such securities solely for cash (other than a registration
relating solely to the sale of securities to participants in a Company stock
plan or a transaction covered by Rule 145 under the Securities Act or a
registration in which the only stock being registered is Common Stock issuable
upon conversion of debt securities which are also being registered), the Company
shall, at such time, promptly give the Investor written notice of such
registration. Upon the written request of the Investor given within thirty (30)
days after receipt of such notice by the Company, the Company shall, subject to
the provisions of Section 2.1(a), cause to be registered under the Securities
Act all of the Registrable Securities that the Investor has requested to be
registered.

                        (a) UNDERWRITING. In connection with any offering
involving an underwriting of shares of the Company's capital stock, the Company
shall not be required under this Section 2 to include any securities of the
Investor or any other stockholders of the Company that have a contractual right
to include their securities in such underwritten offering unless the Investor or
such other stockholders accept the terms of the underwriting as agreed upon
between the Company and the underwriters selected by it (or by other persons
entitled to select the underwriters), and then only in such quantity as the
underwriters determine in good faith will not jeopardize the success of the
offering by the Company; provided, however, that the number of


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shares that may be included in the underwriting shall be allocated, first, to
the Company; and second, to the Investor and to any stockholders of the Company
that have a contractual right to include their shares in such underwritten
offering on a pro rata basis based upon the total number of shares that the
Investor and such other stockholders request be included in the offering, and
provided further, that no such reduction shall reduce the amount of securities
of the Investor and any other stockholders below twenty-five percent (25%) of
the total amount of securities in such registration. If the total amount of
Registrable Securities requested by the Investor to be included in such offering
exceeds the amount of securities sold other than by the Company that the
underwriters determine in their sole discretion is compatible with the success
of the offering, then the Company shall be required to include in the offering
only that number of such securities, including Registrable Securities, which the
underwriters determine in their sole discretion will not jeopardize the success
of the offering (the securities so included to be apportioned pro rata among any
selling stockholders according to the total amount of securities entitled to be
included therein owned by each selling stockholder or in such other proportions
as shall mutually be agreed to by such selling stockholders).

                        (b) RIGHT TO TERMINATE REGISTRATION. The Company shall
have the right to terminate or withdraw any registration initiated by it under
this Section 2.1 prior to the effectiveness of such registration whether or not
the Investor has elected to include securities in such registration.

            2.2 FORM S-3 REGISTRATION. In case the Company shall receive from
the Investor a written request or requests that the Company effect a
registration on Form S-3 (or any successor to Form S-3) or any similar
short-form registration statement and any related qualification or compliance
with respect to all or a part of the Registrable Securities owned by the
Investor, the Company will:

                        (a) as soon as practicable, effect such registration and
all such qualifications and compliances as may be so requested and as would
permit or facilitate the sale and distribution of all or such portion of the
Investor's Registrable Securities as are specified in such request; provided,
however, that the Company shall not be obligated to effect any such
registration, qualification or compliance pursuant to this Section 2.2:

                                    (i)  prior to the first anniversary of the 
date of this Agreement, or

                                    (ii) if Form S-3 (or any successor or
similar form) is not available for such offering by the Investor, or

                                    (iii) if the Investor proposes to sell
Registrable Securities and such other securities (if any) at an aggregate
price to the public of less than one million dollars ($1,000,000), or

                                    (iv) if the Company shall furnish to the
Investor a certificate signed by the President or Chairman of the Board
of Directors of the Company stating that in the good faith judgment of the Board
of Directors of the Company, it would be seriously detrimental to the Company
and its shareholders for such Form S-3 registration to be effected at such time,
in 


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which event the Company shall have the right to defer the filing of the Form S-3
registration statement for a period of not more than forty five (45) days after
receipt of the request of the Investor under this Section 2.2; provided, that
such right to delay a request shall be exercised by the Company not more than
twice in any twelve (12) month period, or

                                    (v)  if the  Company  has,  within the 
twelve (12) month period preceding the date of such request, already effected
two (2) registrations on Form S-3 for the Investor pursuant to this Section 2.2,
or

                                    (vi) if the Company has already  effected 
four (4) registrations on Form S-3 for the Investor pursuant to this Section
2.2, or

                                    (vii) in any particular jurisdiction in
which the Company would be required to qualify to do business or to
execute a general consent to service of process in effecting such registration,
qualification or compliance.

                        (b) Subject to the foregoing, the Company shall file a
Form S-3 registration statement covering the Registrable Securities
and other securities so requested to be registered as soon as practicable after
receipt of the request or requests of the Investor.

            2.3 EXPENSES OF REGISTRATION. All Registration Expenses incurred in
connection with any registration, qualification or compliance pursuant to
Sections 2.1 and 2.2 shall be borne by the Company. All Selling Expenses
incurred in connection with any registrations hereunder, shall be borne by the
Investor. The Company shall not, however, be required to pay for expenses of any
registration proceeding begun pursuant to Section 2.1 or 2.2, the request of
which has been subsequently withdrawn by the Investor unless the withdrawal is
based upon material adverse information concerning the Company of which the
Investor was not aware at the time of such request.

            2.4 OBLIGATIONS OF THE COMPANY. Whenever required to effect the
registration of any Registrable Securities, the Company shall, as expeditiously
as reasonably possible:

                        (a) Prepare and file with the SEC a registration
statement with respect to such Registrable Securities and use all reasonable
efforts to cause such registration statement to become effective and remain
effective for a period of sixty (60) days. The Company shall not be required to
file, cause to become effective or maintain the effectiveness of any
registration statement that contemplates a distribution of securities on a
delayed or continuous basis pursuant to Rule 415 under the Securities Act.

                        (b) Prepare and file with the SEC such amendments and
supplements to such registration statement and the prospectus used in connection
with such registration statement as may be necessary to comply with the
provisions of the Securities Act with respect to the disposition of all
securities covered by such registration statement for the period set forth in
paragraph (a) above.


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                        (c) Furnish to the Investor such number of copies of a
prospectus, including a preliminary prospectus, in conformity with the
requirements of the Securities Act, and such other documents as they may
reasonably request in order to facilitate the disposition of Registrable
Securities owned by them.

                        (d) Use its reasonable best efforts to register and
qualify the securities covered by such registration statement under
such other securities or Blue Sky laws of such jurisdictions as shall be
reasonably requested by the Investor; provided that the Company shall not be
required in connection therewith or as a condition thereto to qualify to do
business or to file a general consent to service of process in any such states
or jurisdictions.

                        (e) In the event of any underwritten public offering,
enter into and perform its obligations under an underwriting agreement, in usual
and customary form, with the managing underwriter(s) of such offering. The
Investor participating in such underwriting shall also enter into and perform
its obligations under such an agreement.

                        (f) Notify the Investor at any time when a prospectus
relating thereto is required to be delivered under the Securities Act of the
happening of any event as a result of which the prospectus included in such
registration statement, as then in effect, includes an untrue statement of a
material fact or omits to state a material fact required to be stated therein or
necessary to make the statements therein not misleading in the light of the
circumstances then existing.

                        (g) Use its best efforts to furnish, on the date that
such Registrable Securities are delivered to the underwriters for sale, if such
securities are being sold through underwriters, (i) an opinion, dated as of such
date, of the counsel representing the Company for the purposes of such
registration, in form and substance as is customarily given to underwriters in
an underwritten public offering, addressed to the underwriters, if any, and (ii)
a letter dated as of such date, from the independent certified public
accountants of the Company, in form and substance as is customarily given by
independent certified public accountants to underwriters in an underwritten
public offering addressed to the underwriters.

            2.5 TERMINATION OF REGISTRATION RIGHTS. All registration rights
granted under this Section 2 shall terminate and be of no further force and
effect if all Registrable Securities held by and issuable to the Investor (and
its affiliates, partners, former partners, members and former members) may be
sold under Rule 144 during any ninety (90) day period.

            2.6 DELAY OF REGISTRATION; FURNISHING INFORMATION.

                        (a) The Investor shall not have any right to obtain or
seek an injunction restraining or otherwise delaying any such registration as
the result of any controversy that might arise with respect to the
interpretation or implementation of this Section 2.

                        (b) It shall be a condition precedent to the obligations
of the Company to take any action pursuant to Section 2.1 or 2.2 that the
Investor shall furnish to the Company such information regarding itself, the
Registrable Securities held by it and the intended method of 


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disposition of such securities as shall be required to effect the registration
of its Registrable Securities.

            2.7 INDEMNIFICATION. In the event any Registrable Securities are
included in a registration statement under Sections 2.1 or 2.2:

                        (a) To the extent permitted by law, the Company will
indemnify and hold harmless the Investor, the partners, officers and directors
of the Investor, any underwriter (as defined in the Securities Act) for such
Investor and each person, if any, who controls such Investor or underwriter
within the meaning of the Securities Act or the Exchange Act, against any
losses, claims, damages, or liabilities (joint or several) to which they may
become subject under the Securities Act, the Exchange Act or other federal or
state law, insofar as such losses, claims, damages or liabilities (or actions in
respect thereof) arise out of or are based upon any of the following statements,
omissions or violations (collectively a "Violation") by the Company: (i) any
untrue statement or alleged untrue statement of a material fact contained in
such registration statement, including any preliminary prospectus or final
prospectus contained therein or any amendments or supplements thereto, (ii) the
omission or alleged omission to state therein a material fact required to be
stated therein, or necessary to make the statements therein not misleading, or
(iii) any violation or alleged violation by the Company of the Securities Act,
the Exchange Act, any state securities law or any rule or regulation promulgated
under the Securities Act, the Exchange Act or any state securities law in
connection with the offering covered by such registration statement; and the
Company will pay as incurred to the Investor, partner, officer, director,
underwriter or controlling person for any legal or other expenses reasonably
incurred by them in connection with investigating or defending any such loss,
claim, damage, liability or action; provided however, that the indemnity
agreement contained in this Section 2.7(a) shall not apply to amounts paid in
settlement of any such loss, claim, damage, liability or action if such
settlement is effected without the consent of the Company, which consent shall
not be unreasonably withheld, nor shall the Company be liable in any such case
for any such loss, claim, damage, liability or action to the extent that it
arises out of or is based upon a Violation which occurs in reliance upon and in
conformity with written information furnished expressly for use in connection
with such registration by the Investor or such partner, officer, director,
underwriter or controlling person of the Investor.

                        (b) To the extent permitted by law, the Investor will,
if Registrable Securities held by the Investor are included in the securities as
to which such registration qualifications or compliance is being effected,
indemnify and hold harmless the Company, each of its directors, its officers and
each person, if any, who controls the Company within the meaning of the
Securities Act and any underwriter selling securities under such registration
statement or any of such other Investor's partners, directors or officers or any
person who controls such Investor, against any losses, claims, damages or
liabilities (joint or several) to which the Company or any such director,
officer, controlling person, underwriter or other such Investor, or partner,
director, officer or controlling person of such other person may become subject
under the Securities Act, the Exchange Act or other federal or state law,
insofar as such losses, claims, damages or liabilities (or actions in respect
thereto) arise out of or are based upon any Violation, in each case to the
extent (and only to the extent) that such Violation occurs in reliance upon and
in 


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conformity with written information furnished by the Investor under an
instrument duly executed by the Investor and stated to be specifically for use
in connection with such registration; and the Investor will pay as incurred any
legal or other expenses reasonably incurred by the Company or any such director,
officer, controlling person, underwriter or other person, or partner, officer,
director or controlling person of such other person in connection with
investigating or defending any such loss, claim, damage, liability or action if
it is judicially determined that there was such a Violation; provided, however,
that the indemnity agreement contained in this Section 2.7(b) shall not apply to
amounts paid in settlement of any such loss, claim, damage, liability or action
if such settlement is effected without the consent of the Investor, which
consent shall not be unreasonably withheld; provided further, that in no event
shall any indemnity under this Section 2.7 exceed the net proceeds from the
offering received by the Investor.

                        (c) Promptly after receipt by an indemnified party under
this Section 2.7 of notice of the commencement of any action (including any
governmental action), such indemnified party will, if a claim in respect thereof
is to be made against any indemnifying party under this Section 2.7, deliver to
the indemnifying party a written notice of the commencement thereof and the
indemnifying party shall have the right to participate in, and, to the extent
the indemnifying party so desires, jointly with any other indemnifying party
similarly noticed, to assume the defense thereof with counsel mutually
satisfactory to the parties; provided, however, that an indemnified party shall
have the right to retain its own counsel, with the fees and expenses to be paid
by the indemnifying party, if representation of such indemnified party by the
counsel retained by the indemnifying party would be inappropriate due to actual
or potential differing interests between such indemnified party and any other
party represented by such counsel in such proceeding. The failure to deliver
written notice to the indemnifying party within a reasonable time of the
commencement of any such action, if materially prejudicial to its ability to
defend such action, shall relieve such indemnifying party of any liability to
the indemnified party under this Section 2.7, but the omission so to deliver
written notice to the indemnifying party will not relieve it of any liability
that it may have to any indemnified party otherwise than under this Section 2.7.

                        (d) If the indemnification provided for in this Section
2.7 is held by a court of competent jurisdiction to be unavailable to an
indemnified party with respect to any losses, claims, damages or liabilities
referred to herein, the indemnifying party, in lieu of indemnifying such
indemnified party thereunder, shall to the extent permitted by applicable law
contribute to the amount paid or payable by such indemnified party as a result
of such loss, claim, damage or liability in such proportion as is appropriate to
reflect the relative fault of the indemnifying party on the one hand and of the
indemnified party on the other in connection with the Violation(s) that resulted
in such loss, claim, damage or liability, as well as any other relevant
equitable considerations. The relative fault of the indemnifying party and of
the indemnified party shall be determined by a court of law by reference to,
among other things, whether the untrue or alleged untrue statement of a material
fact or the omission to state a material fact relates to information supplied by
the indemnifying party or by the indemnified party and the parties' relative
intent, knowledge, access to information and opportunity to correct or prevent
such statement or omission; provided, that in no event shall any contribution by
the Investor hereunder exceed the proceeds from the offering received by the
Investor.


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                        (e) The obligations of the Company and the Investor
under this Section 2.7 shall survive completion of any offering of Registrable
Securities in a registration statement and the termination of this agreement. No
indemnifying party, in the defense of any such claim or litigation, shall,
except with the consent of each indemnified party, consent to entry of any
judgment or enter into any settlement which does not include as an unconditional
term thereof the giving by the claimant or plaintiff to such indemnified party
of a release from all liability in respect to such claim or litigation.

            2.8 ASSIGNMENT OF REGISTRATION RIGHTS. The rights to cause the
Company to register Registrable Securities pursuant to this Section 2 may be
assigned by the Investor to a transferee or assignee of Registrable Securities
which (a) is a wholly owned subsidiary or parent of the Investor and (b)
acquires at least One Hundred Twenty-Five Thousand (125,000) shares of
Registrable Securities (as adjusted for stock splits and combinations);
provided, however, (i) the transferor shall, within ten (10) days after such
transfer, furnish to the Company written notice of the name and address of such
transferee or assignee and the securities with respect to which such
registration rights are being assigned and (ii) such transferee shall agree to
be subject to all restrictions set forth in this Agreement and the Purchase
Agreement.

            2.9 AMENDMENT OF REGISTRATION RIGHTS. Any provision of this Section
2 may be amended and the observance thereof may be waived (either generally or
in a particular instance and either retroactively or prospectively), only with
the written consent of the Company and the holders of at least sixty-six and
two-thirds percent (66-2/3%) of the Registrable Securities then outstanding. Any
amendment or waiver effected in accordance with this Section 2.9 shall be
binding upon each holder or Registrable Securities and the Company. By
acceptance of any benefits under this Section 2, holders of Registrable
Securities hereby agree to be bound by the provisions hereunder.

            2.10 RESTRICTIONS ON AND PROCEDURE FOR SALES. The Investor shall
comply with following procedures:

                        (a) If the Investor shall propose to sell any
Registrable Securities pursuant to a registration statement filed by the Company
pursuant to Section 2.2, the Investor shall notify the Company of its intent to
do so at least three (3) full business days prior to such sale (the "Notice of
Sale"). The Notice of Sale shall be deemed to constitute a representation that
any information previously supplied by such Investor is accurate as of the date
of such Notice of Sale.

                        (b) The Notice of Sale in substantially the form
attached as Exhibit A shall be delivered to the Company in writing. However, the
Investor may give the Notice of Sale orally by telephoning Richard Fischer or
the then current Chief Financial Officer of the Company at (916) 638-8008. An
oral Notice of Sale shall be deemed to have been received only at such time as
the selling Investor speaks directly with Mr. Fischer (or such then current
Chief Financial Officer). In addition, an oral Notice of Sale shall only be
deemed effective if it is followed by a written Notice of Sale received by the
Company by personal delivery or facsimile within twenty-four (24) hours after
giving the oral Notice of Sale.


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                        (c) Unless the Company has notified the Investor in
writing that the Company will not refuse the sale of Registrable Securities
identified in a Notice of Sale pursuant to this Section 2.10, at any time within
such three (3) business-day period, the Company may refuse to permit the
Investor to sell any Restricted Securities; provided, however, that in order to
exercise this right, the Company must deliver a certificate in writing from an
officer of the Company to the Investor to the effect that a delay in such sale
is necessary because a sale pursuant to the Registration Statement in its then
current form could constitute a violation of the federal securities laws. In no
event shall such delay exceed ten (10) trading days; provided, however, that if,
prior to the expiration of such ten (10) trading day period, the Company
delivers a certificate in writing from an officer of the Company to the Investor
to the effect that the Board of Directors of the Company has determined in
reasonable good faith that a further delay in such sale beyond such ten (10)
trading day period is necessary because a sale pursuant to such Registration
Statement in its then current form could constitute a violation of the federal
securities laws, the Company may refuse to permit the Investor to resell any
Shares for an additional period not to exceed ten (10) trading days. The Company
shall not exercise this right of delay for more than twenty (20) consecutive
trading days or for more than thirty (30) trading days in any six (6) month
period. In the event that the Company exercises its rights to refuse the sale of
Registrable Securities for any period under this Section 2.10(c), the Company
shall extend the period of effectiveness of the registration statement then in
effect for the same number of trading days as the Investor has been refused the
opportunity to sell Registrable Securities.

SECTION 3.  MISCELLANEOUS

             3.1 GOVERNING LAW. This Agreement shall be governed by and
construed under the laws of the State of California as applied to agreements
among California residents entered into and to be performed entirely within
California.

            3.2 SUCCESSORS AND ASSIGNS. Except as otherwise expressly provided
herein, the provisions hereof shall inure to the benefit of, and be binding
upon, the successors, assigns, heirs, executors, and administrators of the
parties hereto and shall inure to the benefit of and be enforceable by each
person who shall be a holder of Registrable Securities from time to time;
provided, however, that prior to the receipt by the Company of adequate written
notice of the transfer of any Registrable Securities specifying the full name
and address of the transferee, the Company may deem and treat the person listed
as the holder of such shares in its records as the absolute owner and holder of
such shares for all purposes, including the payment of dividends or any
redemption price.

            3.3 ENTIRE AGREEMENT. This Agreement, the Exhibits and Schedules
hereto, the Purchase Agreement and the other documents delivered pursuant
thereto constitute the full and entire understanding and agreement between the
parties with regard to the subjects hereof and no party shall be liable or bound
to any other in any manner by any representations, warranties, covenants and
agreements except as specifically set forth herein and therein.


<PAGE>   10

            3.4 SEVERABILITY. In case any provision of the Agreement shall be
invalid, illegal, or unenforceable, the validity, legality, and enforceability
of the remaining provisions shall not in any way be affected or impaired
thereby.

            3.5 AMENDMENT AND WAIVER.

                        (a) Except as otherwise expressly provided, this
Agreement may be amended or modified only upon the written consent of the
Company and the holders of at least two-thirds (66 2/3%) of the Registrable
Securities.

                        (b) Except as otherwise expressly provided, the
obligations of the Company and the rights of the holders of Registrable
Securities under this Agreement may be waived only with the written consent of
the holders of at least sixty-six and two-thirds percent (66 2/3%) of the
Registrable Securities.

                        (c) Notwithstanding the foregoing, this Agreement may be
amended with only the written consent of the Company to include additional
purchasers of Shares as "Investors" or parties hereto.

            3.6 DELAYS OR OMISSIONS. It is agreed that no delay or omission to
exercise any right, power, or remedy accruing to the Investor, upon any breach,
default or noncompliance of the Company under this Agreement shall impair any
such right, power, or remedy, nor shall it be construed to be a waiver of any
such breach, default or noncompliance, or any acquiescence therein, or of any
similar breach, default or noncompliance thereafter occurring. It is further
agreed that any waiver, permit, consent, or approval of any kind or character on
the Investor's part of any breach, default or noncompliance under the Agreement
or any waiver on the Investor's part of any provisions or conditions of this
Agreement must be in writing and shall be effective only to the extent
specifically set forth in such writing. All remedies, either under this
Agreement, by law, or otherwise afforded the Investor, shall be cumulative and
not alternative.

            3.7 NOTICES. All notices required or permitted hereunder shall be in
writing and shall be deemed effectively given: (a) upon personal delivery to the
party to be notified, (b) when sent by confirmed telex or facsimile if sent
during normal business hours of the recipient; if not, then on the next business
day, (c) ten (10) days after having been sent by registered or certified
airmail, return receipt requested, postage prepaid, or (d) four (4) day after
deposit with an internationally recognized overnight courier, specifying next
day delivery, with written verification of receipt. All communications shall be
sent to the party to be notified at the address as set forth on the signature
pages hereof or Exhibit A hereto or at such other address as such party may
designate by ten (10) days advance written notice to the other parties hereto.

            3.8 ATTORNEYS' FEES. In the event that any dispute among the parties
to this Agreement should result in litigation, the prevailing party in such
dispute shall be entitled to recover from the losing party all fees, costs and
expenses of enforcing any right of such prevailing party under or with respect
to this Agreement, including without limitation, such reasonable fees and
expenses of attorneys and accountants, which shall include, without limitation,
all fees, costs and expenses of appeals.


<PAGE>   11

            3.9 TITLES AND SUBTITLES. The titles of the sections and subsections
of this Agreement are for convenience of reference only and are not to be
considered in construing this Agreement.

             3.10 COUNTERPARTS. This Agreement may be executed in any number of
counterparts, each of which shall be an original, but all of which together
shall constitute one instrument.



                      [THIS SPACE INTENTIONALLY LEFT BLANK]

            IN WITNESS WHEREOF, the parties hereto have executed this Investor's
Rights Agreement as of the date set forth in the first paragraph hereof.

COMPANY:                                       INVESTORS:

ENDOSONICS CORPORATION                         FUKUDA DENSHI CO., LTD.

By: /s/ Reinhard J. Warnking                   By: /s/ Kotaro Fukuda
   --------------------------------------         ------------------------------

Name:   Reinhard J. Warnking                   Name:   Kotaro Fukuda
     ------------------------------------           ----------------------------
Title:  President & CEO                        Title:  President
      -----------------------------------            ---------------------------

Address:  2870 Kilgore Road                    Address:  3-39-4 Hongo Bunkyo-Ku
          Rancho Cordova, California 95670               Tokyo 113
          U.S.A.                                         Japan


                  SIGNATURE PAGE TO INVESTOR'S RIGHTS AGREEMENT


<PAGE>   12


                                    EXHIBIT A

                             ENDOSONICS CORPORATION

                                 NOTICE OF SALE



            Pursuant to Section 2.10 of the Investors' Rights Agreement dated as
of ___ __, 1998 among EndoSonics Corporation (the "Company") and the
undersigned, the undersigned hereby gives notice to the Company of the
undersigned's intent to sell _______ shares of the Company's Common Stock
registered pursuant to the Registration Statement on Form S-3 (File No.
33-_____).



Dated:   ______________, 199__           By:
                                            ------------------------------------
                                                         (signature)


                                         Name:
                                               ---------------------------------
                                                            (print)


                                         Title:
                                               ---------------------------------
                                                        (if applicable)


[NOTE: THIS NOTICE OF SALE MUST BE COMPLETED AND DELIVERED (VIA PERSONAL
DELIVERY OR FACSIMILE) TO THE CHIEF FINANCIAL OFFICER OF THE COMPANY AT LEAST
THREE (3) BUSINESS DAYS PRIOR TO SALE OF THE SHARES OF THE COMPANY'S COMMON
STOCK REGISTERED PURSUANT TO THE REGISTRATION STATEMENT.]