AGREEMENT

Exhibit 10.1

AGREEMENT

This Agreement (this “Agreement”) is made and entered into as of April 4, 2012, by and among DSP Group, Inc. (the “Company”) and the entities and natural persons listed on Exhibit A hereto and their respective Affiliates (collectively, “Starboard”) (each of the Company and Starboard, a “Party” to this Agreement, and collectively, the “Parties”).

RECITALS

WHEREAS, the Company and Starboard have engaged in various discussions and communications concerning the Company’s business, financial performance and strategic plans;

WHEREAS, Starboard is deemed to beneficially own shares of Common Stock of the Company (the “Common Stock”) totaling, in the aggregate, 2,222,079 shares, or approximately 9.8%, of the Common Stock issued and outstanding on the date hereof; and

WHEREAS the Company and the members of Starboard have determined to come to an agreement with respect to the election of members of the Company’s board of directors (the “Board”) at the 2012 annual meeting of stockholders of the Company (the “2012 Annual Meeting”), certain matters related to the 2012 Annual Meeting and certain other matters, as provided in this Agreement.

NOW, THEREFORE, in consideration of the foregoing premises and the mutual covenants and agreements contained herein, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the Parties hereto, intending to be legally bound hereby, agree as follows:

1. Board Matters; Board Appointments; 2012 Annual Meeting; Committees.

(a) Prior to the mailing of its definitive proxy statement for the 2012 Annual Meeting, the Company agrees that the Board shall take all necessary actions to (i) increase the size of the Board from eight (8) to nine (9) members, effective as of the 2012 Annual Meeting, (ii) nominate Kenneth H. Traub and Tom Lacey (together, the “Starboard Nominees”) for election to the Board as Class III directors at the 2012 Annual Meeting and (iii) cause Dr. Reuven Regev, a Class III director, to stand for re-election at the 2012 Annual Meeting for a term to expire at the 2013 annual meeting of stockholders.

(b) Prior to the execution of this Agreement, the Nomination and Corporate Governance Committee of the Board (the “Nomination Committee”) shall have reviewed and reasonably approved, in accordance with the Company’s Corporate Governance Guidelines and the charter of the Nomination Committee, the qualifications of the Starboard Nominees to serve as independent members of the Board and recommended to the Board that the Board nominate for election at the 2012 Annual Meeting the Starboard Nominees, in accordance with Section 1(a).

(c) Starboard hereby agrees not to (i) nominate any person for election at the 2012 Annual Meeting, (ii) submit any proposal for consideration at, or bring any other business

before, the 2012 Annual Meeting, directly or indirectly, or (iii) initiate, encourage or participate in any “withhold” or similar campaign with respect to the 2012 Annual Meeting, directly or indirectly. Starboard shall not publicly or privately encourage or support any other stockholder to take any of the actions described in this Section 1(c).

(d) The Company agrees that it will recommend, support and solicit proxies for the election of the Starboard Nominees to be elected at the 2012 Annual Meeting in the same manner as for the Company’s other nominees standing for election to the Board at the 2012 Annual Meeting.

(e) The Company agrees to use its reasonable best efforts to hold the 2012 Annual Meeting no later than May 31, 2012.

(f) At the first meeting of the Board following the execution of this Agreement, but in any event no later than April 13, 2012, the Starboard Nominees shall be appointed as observers to the Board (the “Board Observers”) until the 2012 Annual Meeting. Each of the Board Observers will (1) receive copies of all notices and written information furnished to the full Board at substantially the same time they are so furnished, and (2) be permitted to be present at all meetings of the full Board (whether by phone or in person). Notwithstanding the foregoing, (i) the Company shall be entitled to withhold any information and exclude the Board Observers from any meeting, or any portion thereof, as is reasonably determined by the Company to be necessary to protect the Company’s attorney-client privilege, or as otherwise may be appropriate until the 2012 Starboard Nominees are elected to the Board, and (ii) the Board Observers shall execute a confidentiality agreement in form and substance reasonably acceptable to the Company with respect to the information and discussions to which the Board Observers will have access. The rights of the Board Observers shall terminate upon the date of the 2012 Annual Meeting.

(g) The Company agrees that prior to the 2013 annual meeting of stockholders of the Company (the “2013 Annual Meeting”), if either or both of the Starboard Nominees is unable to serve as a director, resigns as a director or is removed as a director, and at such time Starboard beneficially owns in the aggregate at least the lesser of 3.0% of the Company’s then outstanding Common Stock and 681,954 shares of Common Stock (subject to adjustment for stock splits, reclassifications, combinations and similar adjustments), Starboard shall have the ability to recommend a substitute person(s), who will be independent of Starboard and who will also qualify as “independent” pursuant to the listing standards of NASDAQ Stock Market, to fill the resulting vacancy or vacancies, subject to the approval of the Nomination Committee after consideration in good faith and exercising its fiduciary duties, which approval shall not be unreasonably withheld (any such replacement nominee(s) appointed in accordance with the provisions of this Section 1(g) shall be referred to individually as the “Replacement Director”). In the event the Nomination Committee does not accept a substitute person recommended by Starboard, Starboard will have the right to recommend additional substitute person(s), subject to the terms of this Section 1(g), for consideration by the Nomination Committee. Upon the acceptance of a replacement director nominee by the Nomination Committee, the Board will appoint such replacement director to the Board no later than five (5) business days after the Nomination Committee’s recommendation of such replacement director.

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(h) The parties hereto acknowledge that the only matters that may be presented by the Company for consideration at the 2012 Annual Meeting are (i) the election of directors, (ii) the approval of the Company’s 2012 Equity Incentive Plan, (iii) the amendment and restatement of the Company’s 1993 Employee Stock Purchase Plan to increase the number of Company shares reserved thereunder by 500,000, (iv) the ratification of the Company’s independent registered public accounting firm, and (v) the approval, on a non-binding basis, the compensation arrangements of the Company’s named executive officers.

(i) At the 2012 Annual Meeting, Starboard agrees to appear in person or by proxy at the 2012 Annual Meeting and vote all shares of Common Stock of the Company beneficially owned by Starboard at the meeting in favor of the proposals listed in clauses (i) through (v) of Section 1(h) above, unless, as relates solely to the proposals listed in clauses (ii) through (v), Institutional Shareholder Services Inc. (“ISS”) recommends otherwise, in which case Starboard shall be permitted to vote all shares of Common Stock of the Company beneficially owned by Starboard in accordance with the ISS recommendation if, after discussing the proposals with the Company in good faith, Starboard subsequently decides to follow the ISS recommendation rather than the Board’s recommendation.

(j) Starboard agrees that it will cause its Affiliates and Associates to comply with the terms of this Agreement. As used in this Agreement, the terms “Affiliate” and “Associate” shall have the respective meanings set forth in Rule 12b-2 promulgated by the Securities and Exchange Commission under the Securities Exchange Act of 1934, as amended, or the rules or regulations promulgated thereunder (the “Exchange Act”) and shall include all persons or entities that at any time during the term of this Agreement become Affiliates or Associates of any person or entity referred to in this Agreement.

(k) The Company agrees that by the end of the third quarter of 2012 the Company shall use its reasonable best efforts to report its financial results, including revenue and profitability, across at least two (2) of the Company’s business segments, including Home and Enterprise.

2. Standstill Provisions.

(a) Starboard agrees that, from the date of this Agreement until the earlier of (i) the date that is (ten) 10 business days prior to the deadline for the submission of stockholder nominations for the 2013 Annual Meeting pursuant to the Company’s bylaws or (ii) the date that is one-hundred (100) days prior to the first anniversary of the 2012 Annual Meeting (the “Standstill Period”), neither it nor any of its Affiliates or Associates under its control or direction will, and it will cause each of its Affiliates and Associates under its control not to, directly or indirectly, in any manner:

(i) solicit, or encourage or in any way engage in any solicitation of, any proxies or consents or become a “participant” in a “solicitation” as such terms are defined in Regulation 14A under the Exchange Act of proxies or consents (including, without limitation, any solicitation of consents that improperly seeks to call a special meeting of stockholders), in each case, with respect to securities of the Company;

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(ii) advise, encourage, support or influence any person with respect to the voting or disposition of any securities of the Company at any annual or special meeting of stockholders, except in accordance with Section 1, or seek to do so;

(iii) form, join or in any way participate in any “group” (within the meaning of Section 13(d)(3) of the Exchange Act) with respect to the Common Stock (other than a “group” that includes all or some of the persons identified on Exhibit A, but does not include any other entities or persons not identified on Exhibit A as of the date hereof); provided, however, that nothing herein shall limit the ability of an Affiliate of Starboard to join the “group” following the execution of this Agreement, so long as any such Affiliate agrees to be bound by the terms and conditions of this Agreement;

(iv) deposit any Common Stock in any voting trust or subject any Common Stock to any arrangement or agreement with respect to the voting of any Common Stock, other than any such voting trust, arrangement or agreement solely among the members of Starboard and otherwise in accordance with this Agreement;

(v) seek or encourage any person to submit nominations in furtherance of a “contested solicitation” for the election or removal of directors with respect to the Company; provided, however, that nothing herein will limit the ability of Starboard to recommend a Replacement Director(s) in accordance with Section 1(h);

(vi) (A) make any proposal for consideration by stockholders at any annual or special meeting of stockholders of the Company or (B) make any offer or proposal (with or without conditions, publicly or otherwise) with respect to a merger, acquisition, disposition, consolidation, recapitalization, restructuring, liquidation, dissolution, or other business combination or extraordinary transaction involving the Company or any subsidiary or Affiliate of the Company (each, a “Business Proposal”); provided, however, that nothing herein will limit the ability of (1) any member of Starboard, or its respective Affiliates and Associates to vote its shares of Common Stock on any matter submitted to a vote of the stockholders of the Company relating to a Business Proposal, and (2) Starboard to publicly announce its opposition, including the reasons therefor, to any Board-approved publicly announced Business Proposal; provided that other than the limited right to publicly announce its opposition and the reasons therefore, Starboard will not and will cause each of its Affiliates and Associates under its control not to, directly or indirectly, take any other action relating to the Board-approved publicly announced Business Proposal otherwise prohibited by this Section 2;

(vii) seek, alone or in concert with others, representation on the Board, except as specifically contemplated in Section 1;

(viii) otherwise act, alone or in concert with others, to seek to control or influence the management, Board of Directors or policies of the Company or any of its subsidiaries, affiliates or divisions;

(ix) enter into any discussions, negotiations, arrangements or understandings with any third party with respect to the matters set forth in this Section 2; or

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(x) take any action which could cause or require the Company or any Affiliate of the Company to make a public announcement regarding any of the foregoing, publicly seek or request permission to do any of the foregoing, publicly make any request to amend, waive or terminate any provision of this Section 2 (including, without limitation, this Section 2(a)(x), or make or seek permission to make any public announcement with respect to any of the foregoing.

(b) The Company agrees that it shall provide written notice to Starboard at least one-hundred (100) days prior to the date that the Company sets for holding its 2013 Annual Meeting.

3. Representations and Warranties of the Company.

The Company represents and warrants to Starboard that (a) the Company has the corporate power and authority to execute this Agreement and to bind it thereto, (b) this Agreement has been duly and validly authorized, executed and delivered by the Company, constitutes a valid and binding obligation and agreement of the Company, and is enforceable against the Company in accordance with its terms, except as enforcement thereof may be limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance or similar laws generally affecting the rights of creditors and subject to general equity principles and (c) the execution, delivery and performance of this Agreement by the Company does not and will not violate or conflict with (i) any law, rule, regulation, order, judgment or decree applicable to the Company, or (ii) result in any breach or violation of or constitute a default (or an event which with notice or lapse of time or both could constitute such a breach, violation or default) under or pursuant to, or result in the loss of a material benefit under, or give any right of termination, amendment, acceleration or cancellation of, any organizational document, agreement, contract, commitment, understanding or arrangement to which the Company is a party or by which it is bound.

4. Representations and Warranties of Starboard.

Starboard represents and warrants to the Company that (a) the authorized signatory of Starboard set forth on the signature page hereto has the power and authority to execute this Agreement and any other documents or agreements to be entered into in connection with this Agreement and to bind it thereto, (b) this Agreement has been duly authorized, executed and delivered by Starboard, and is a valid and binding obligation of Starboard, enforceable against Starboard in accordance with its terms, except as enforcement thereof may be limited by applicable bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance or similar laws generally affecting the rights of creditors and subject to general equity principles, (c) the execution of this Agreement, the consummation of any of the transactions contemplated hereby, and the fulfillment of the terms hereof, in each case in accordance with the terms hereof, will not conflict with, or result in a breach or violation of the organizational documents of Starboard as currently in effect, (d) the execution, delivery and performance of this Agreement by Starboard does not and will not violate or conflict with (i) any law, rule, regulation, order, judgment or decree applicable to Starboard, or (ii) result in any breach or violation of or constitute a default (or an event which with notice or lapse of time or both could constitute such a breach, violation or default) under or pursuant to, or result in the loss of a material benefit under, or give any right

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of termination, amendment, acceleration or cancellation of, any organizational document, agreement, contract, commitment, understanding or arrangement to which such member is a party or by which it is bound, and (e) as of the date of this Agreement, (i) Starboard is deemed to beneficially own in the aggregate 2,222,079 shares of Common Stock and (ii) Starboard does not currently have, and does not currently have any right to acquire, any interest in any other securities of the Company or any Other Equity Rights.

5. Press Release.

Promptly following the execution of this Agreement, the Company and Starboard shall jointly issue a mutually agreeable press release (the “Mutual Press Release”) announcing certain terms of this Agreement, in the form attached hereto as Exhibit B. Prior to the issuance of the Mutual Press Release, neither the Company nor Starboard shall issue any press release or public announcement regarding this Agreement without the prior written consent of the other Party. During the Standstill Period, neither the Company nor Starboard or the Starboard Nominees shall make any public announcement or statement that is inconsistent with or contrary to the statements made in the Mutual Press Release, except as required by law or the rules of any stock exchange or with the prior written consent of the other Party; provided, however, that nothing herein will limit Starboard’s limited ability to make public announcements of the type described in Section 2(a)(vi)(B) above.

6. Specific Performance.

Each of the members of Starboard, on the one hand, and the Company, on the other hand, acknowledges and agrees that irreparable injury to the other party hereto would occur in the event any of the provisions of this Agreement were not performed in accordance with their specific terms or were otherwise breached and that such injury would not be adequately compensable by the remedies available at law (including the payment of money damages). It is accordingly agreed that Starboard (or any of the entities and natural persons listed on Exhibit A), on the one hand, and the Company, on the other hand (the “Moving Party”), shall each be entitled to specific enforcement of, and injunctive relief to prevent any violation of, the terms hereof, and the other party hereto will not take action, directly or indirectly, in opposition to the Moving Party seeking such relief on the grounds that any other remedy or relief is available at law or in equity.

7. Expenses.

The Company shall reimburse Starboard for its reasonable, documented out-of-pocket fees and expenses (including legal expenses) incurred in connection with the matters related to the 2012 Annual Meeting, the filing of a Schedule 13D in connection with this Agreement and the negotiation and execution of this Agreement, provided that such reimbursement shall not exceed $40,000 in the aggregate.

8. Severability.

If any term, provision, covenant or restriction of this Agreement is held by a court of competent jurisdiction to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Agreement shall remain in full force and effect and

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shall in no way be affected, impaired or invalidated. It is hereby stipulated and declared to be the intention of the Parties that the Parties would have executed the remaining terms, provisions, covenants and restrictions without including any of such which may be hereafter declared invalid, void or unenforceable. In addition, the Parties agree to use their best efforts to agree upon and substitute a valid and enforceable term, provision, covenant or restriction for any of such that is held invalid, void or enforceable by a court of competent jurisdiction.

9. Notices.

Any notices, consents, determinations, waivers or other communications required or permitted to be given under the terms of this Agreement must be in writing and will be deemed to have been delivered: (i) upon receipt, when delivered personally; (ii) upon receipt, when sent by facsimile (provided confirmation of transmission is mechanically or electronically generated and kept on file by the sending party); or (iii) one business day after deposit with a nationally recognized overnight delivery service, in each case properly addressed to the party to receive the same. The addresses and facsimile numbers for such communications shall be:

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10. Applicable Law.

This Agreement shall be governed by and construed and enforced in accordance with the laws of the State of Delaware without reference to the conflict of laws principles thereof. Each of the Parties hereto irrevocably agrees that any legal action or proceeding with respect to this Agreement and the rights and obligations arising hereunder, or for recognition and enforcement of any judgment in respect of this Agreement and the rights and obligations arising hereunder brought by the other party hereto or its successors or assigns, shall be brought and determined exclusively in the Delaware Court of Chancery and any state appellate court therefrom within the State of Delaware (or, if the Delaware Court of Chancery declines to accept jurisdiction over a particular matter, any state or federal court within the State of Delaware). Each of the Parties hereto hereby irrevocably submits with regard to any such action or proceeding for itself and in respect of its property, generally and unconditionally, to the personal jurisdiction of the aforesaid courts and agrees that it will not bring any action relating to this Agreement in any court other than the aforesaid courts. Each of the Parties hereto hereby irrevocably waives, and agrees not to assert in any action or proceeding with respect to this Agreement, (i) any claim that it is not personally subject to the jurisdiction of the above-named courts for any reason, (ii) any claim that it or its property is exempt or immune from jurisdiction of any such court or from any legal process commenced in such courts (whether through service of notice, attachment prior to judgment, attachment in aid of execution of judgment, execution of judgment or otherwise) and (iii) to the fullest extent permitted by applicable legal requirements, any claim that (A) the suit, action or proceeding in such court is brought in an inconvenient forum, (B) the venue of such suit, action or proceeding is improper or (C) this Agreement, or the subject matter hereof, may not be enforced in or by such courts.

11. Counterparts. This Agreement may be executed in two or more counterparts, each of which shall be considered one and the same agreement and shall become effective when counterparts have been signed by each of the Parties and delivered to the other Party (including by means of electronic delivery or facsimile).

12. Entire Agreement; Amendment and Waiver; Successors and Assigns; Third Party Beneficiaries.

This Agreement contains the entire understanding of the Parties hereto with respect to its subject matter. There are no restrictions, agreements, promises, representations, warranties, covenants or undertakings between the Parties other than those expressly set forth herein. No modifications of this Agreement can be made except in writing signed by an authorized representative of each the Company and Starboard. No failure on the part of any party to

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exercise, and no delay in exercising, any right, power or remedy hereunder shall operate as a waiver thereof, nor shall any single or partial exercise of such right, power or remedy by such party preclude any other or further exercise thereof or the exercise of any other right, power or remedy. All remedies hereunder are cumulative and are not exclusive of any other remedies provided by law. The terms and conditions of this Agreement shall be binding upon, inure to the benefit of, and be enforceable by the Parties hereto and their respective successors, heirs, executors, legal representatives, and permitted assigns. No party shall assign this Agreement or any rights or obligations hereunder without, with respect to any member of Starboard, the prior written consent of the Company, and with respect to the Company, the prior written consent of Starboard. This Agreement is solely for the benefit of the Parties hereto and is not enforceable by any other persons.

13. Mutual Non-Disparagement.

Each of the Parties covenants and agrees that, during the Standstill Period, neither it nor any of its respective agents, subsidiaries, affiliates, successors, assigns, officers, key employees or directors and with respect to Starboard its Starboard Nominees and Replacement Directors, shall in any way disparage, call into disrepute, or otherwise defame or slander the other Parties or such other Parties’ subsidiaries, affiliates, successors, assigns, officers (including any current officer of a Party or a Parties’ subsidiaries who no longer serves in such capacity following the execution of this Agreement), directors (including any current director of a Party or a Parties’ subsidiaries who no longer serves in such capacity following the execution of this Agreement), employees, stockholders, agents, attorneys or representatives, or any of their products or services, in any manner that would damage the business or reputation of such other Parties, their products or services or their subsidiaries, affiliates, successors, assigns, officers (or former officers), directors (or former directors), employees, stockholders, agents, attorneys or representatives. For purposes of this Section, the Starboard Nominees shall not be deemed to be agents, affiliates, officers, key employees or directors of the Company or Starboard and no actions taken by any agent or other representative of a Party in any capacity other than as a representative of such Party shall be covered by this Agreement.

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IN WITNESS WHEREOF, this Agreement has been duly executed and delivered by the duly authorized signatories of the Parties as of the date hereof.

DSP GROUP, INC.

STARBOARD:

[Signature Page to Agreement]

EXHIBIT A

Starboard

STARBOARD VALUE AND OPPORTUNITY MASTER FUND LTD

STARBOARD VALUE AND OPPORTUNITY S LLC

STARBOARD VALUE LP

STARBOARD VALUE GP LLC

STARBOARD PRINCIPAL CO LP

STARBOARD PRINCIPAL CO GP LLC

JEFFREY C. SMITH

MARK MITCHELL

PETER A. FELD

EXHIBIT B

PRESS RELEASE