Finite v non-finite verb forms
A finite verb is a tensed verb. A non-finite verb is an untensed verb such as a participle or an infinitive.
A finite verb can also be defined as follows:
Finite verbs can function on their own as the core of an independent sentence, whereas nonfinite verbs cannot.
As James K stated, participles (including "past" and "present" participles) are non-tensed (despite their conventional names). (Some grammars call them the -ed and -ing participles instead.)
Most learners (and EFL/ESL teaching materials) see constructions such as the present perfect as "tenses". This might lead you to look upon both verb forms as finite, when actually only the auxiliary is. (But the clause as a whole is also finite.)
Most linguists would say that English has only two tenses (although Huddleston and Pullum would prefer to say two primary tenses) - the present and past. (There is no inflection for the future; "will" is a modal verb.) The auxiliary (often tensed) can be followed by a participle to form a progressive, perfect, or progressive perfect. (The auxiliary can also be untensed, as in "to have taken".)
Auxiliaries (even when finite) are followed by non-finite forms.
In "I do take" or "I will take", the verb "take" is non-finite (specifically a bare infinitive), and in "I have taken", "taken" is also non-finite.
Note: modals are counted as finite even though they don't have visible tense markings, so "will" is finite (in fact, the modals have no infinitives nor participles).
Finite v non-finite clauses
Having said that, although the participle is non-finite, it may be part of a finite clause:
Finiteness is a property not only of verbs, but also of clauses. The finiteness of a clause is determined by the finiteness of its head.
So, although "I have taken" combines a finite and non-finite verb form, the clause as a whole is finite.
You may also be interested in my answer on the English language & usage stack here.