Is IEEE Signal Processing Society Membership enough to add "Student Member, IEEE" on a Journal author list? Is being member of the IEEE Signal Processing Society enough to add "Student Member, IEEE" on a Journal author list?

Or the IEEE membership is different from the IEEE Signal Processing Society membership? I pay this annually. Never understood well the differences between them.

thanks
Consult IEEE Editorial Style Manual: As per April 10, 2020 (and certainly for many years before):


  IEEE Membership Grades 
  
  IEEE Membership Grades included in the byline and biography are Student Member, Graduate Student Member, Associate Member, Member, Senior Member, Fellow, Life Associate Member, Life Member, Life Senior Member, and Life Fellow. 
  
  Note: Affiliate Members are not considered members for the purposes of the byline and biography.


These refer to general IEEE Membership grades, not Membership in a particular IEEE Society.

Therefore, if you are an IEEE Student Member, you can (and should) add Student Member, IEEE to the 


Byline
Biography




Therefore, if you are an IEEE Member of any grade (excluding affiliate memberships), you can add this grade to any IEEE journal papers regardless of your membership in the society.



Quick notes regarding the memberships and differences between them:


For the purpose of the question, only the general IEEE Membership is important
In addition to general IEEE Membership, one can join IEEE Societies within IEEE. Many exist: IEEE Signal Processing Society, IEEE Antennas and Propagation Society, etc. Membership in these societies have their own benefits (access to journals in IEEE Xplore, discounts on conferences, access to certain educational materials, participation in committees, etc.), but is not required in order to add Membership Grade to the byline or biography
One can join an IEEE Society directly without having a general IEEE Membership: that will be Affiliate Membership. In this case, the member joins the society for a slightly higher Society Membership fee but does not pay an IEEE Membership Fee. If one is interested only in getting benefits from 1-2 societies and general IEEE benefits are not relevant, that might be a viable choice from the financial point.
Thus, if a researcher is an Affiliate Member of IEEE Signal Processing Society they should not add IEEE Grade next to their name.
It is very unlikely to be a Student Affiliate Member. I do not know about IEEE societies that have this option, as IEEE Student Membership is very discounted as well as some IEEE Society Membership fees for students.



Disclosure: I am a Vice-Chair of Membership and Benefits Committee of IEEE Antennas and Propagation Society.