There's one definition I heard by a deceased televangelist Gene Scott which I remember. He said, "faith is an action based on belief sustained by confidence". Of course that definition can be used to demonstrate faith in any object including an undesirable object while emphasizing a personal act in or of ourselves. We in or of ourselves as an object of faith are powerless to save and such definition wrongly credits ourselves for salvation by our own works. Therefore, I think a better definition "faith is the instrument which we lay hold of the alien righteousness of Jesus Christ".
As to where from faith originates:
2 Thessalonians 3:1-2 Finally, brothers, pray for us, that the word of the Lord may speed ahead and be honored, as happened among you, and that we may be delivered from wicked and evil men. For not all have faith.
Philippians 1:29 For it has been granted to you that for the sake of Christ you should not only believe in him but also suffer for his sake,
2 Peter 1:1 Simeon Peter, a servant and apostle of Jesus Christ, To those who have obtained a faith of equal standing with ours by the righteousness of our God and Savior Jesus Christ:
Hebrews 12:2 looking to Jesus, the founder and perfecter of our faith, who for the joy that was set before him endured the cross, despising the shame, and is seated at the right hand of the throne of God.
Ephesians 2:8-9 For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, not a result of works, so that no one may boast.
Lastly, another definition that came to mind is from Hebrews 11:1 where many people turn to in order to wrongly define faith by rejecting context.
Now faith, etc. Whoever made this the beginning of the eleventh chapter, has unwisely disjointed the context; for the object of the Apostle was to prove what he had already said that there is need of patience. (200) He had quoted the testimony of Habakkuk, who says that the just lives by faith; he now shows what remained to be proved — that faith can be no more separated from patience than from itself. The order then of what he says is this, — “We shall not reach the goal of salvation except we have patience, for the Prophet declares that the just lives by faith; but faith directs us to things afar off which we do not as yet enjoy; it then necessarily includes patience.” Therefore the minor proposition in the argument is this, Faith is the substance of things hoped for, etc. It is hence also evident, that greatly mistaken are they who think that an exact definition of faith is given here; for the Apostle does not speak here of the whole of what faith is, but selects that part of it which was suitable to his purpose, even that it has patience ever connected with it. (201) Let us now consider the words.
He calls faith the hypostasis, the substance of things hoped for. We indeed know that what we hope for is not what we have as it were in hand, but what is as yet hid from us, or at least the enjoyment of which is delayed to another time. The Apostle now teaches us the same thing with what we find in Rom_8:24; where it is said that what is hoped for is not seen, and hence the inference is drawn, that it is to be waited for in patience. So the Apostle here reminds us, that faith regards not present things, but such as are waited for. Nor is this kind of contradiction without its force and beauty: Faith, he says, is the hypostasis, the prop, or the foundation on which we plant our foot, — the prop of what? Of things absent, which are so far from being really possessed by us, that they are far beyond the reach of our understanding.
The same view is to be taken of the second clause, when he calls faith the evidence or demonstration of things not seen; for demonstration makes things to appear or to be seen; and it is commonly applied to what is subject to our senses. (202)
Then these two things, though apparently inconsistent, do yet perfectly harmonize when we speak of faith; for the Spirit of God shows to us hidden things, the knowledge of which cannot reach our senses: Promised to us is eternal life, but it is promised to the dead; we are assured of a happy resurrection, but we are as yet involved in corruption; we are pronounced just, as yet sin dwells in us; we hear that we are happy, but we are as yet in the midst of many miseries; an abundance of all good things is promised to us, but still we often hunger and thirst; God proclaims that he will come quickly, but he seems deaf when we cry to him. What would become of us were we not supported by hope, and did not our minds emerge out of the midst of darkness above the world through the light of God’s word and of his Spirit? Faith, then, is rightly said to be the subsistence or substance of things which are as yet the objects of hope and the evidence of things not seen. Augustine sometimes renders evidence “conviction,” which I do not disapprove, for it faithfully expresses the Apostle’s meaning: but I prefer “demonstration,” as it is more literal.