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I have this sentence:

We would like to prove the applicability of the algorithm to uniform filter bank.

I am not sure about the before uniform filter bank. To give the context for the sentence, I would like to say here that the algorithm is applicable to any uniform filter bank.

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3 Answers

Uniform filter bank is just a name; in this context, it requires a determiner, which pins down which holders of the name are involved. The determiner may be an article, a possessive or demonstrative adjective, or a quantifier. What determiner you employ depends on what exactly you mean. In this case, you have actually defined it in your question:

We would like to prove the applicability ... to any uniform filter bank.

You could also say

We would like to prove the applicability ... to all uniform filter banks.

In other circumstances you might have meant:

We would like to prove the applicability ... to many uniform filter banks.
We would like to prove the applicability ... to some uniform filter banks.
We would like to prove the applicability ... to these uniform filter banks.

And so forth... In some circumstances, another part of the sentence may act as a determiner through contrast. For instance, if you have already proved that the algorithm is applicable to non-uniform filter banks, you might then proceed:

We would now like to prove the applicability ... to uniform filter banks.

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The way it stands, the sentence makes me think that you are attempting to convince uniform filter banks that the algorithm is applicable to them. At the very least, it can be read that way. You could avoid that using on

We would like to prove the applicability ... on uniform filter banks.

Of course, a method can or cannot be applied to a problem not on it. Applying it on makes one think of make up.

So, to remove ambiguity and make it easier to read, I would go for:

We would like to prove that the algorithm can be applied to uniform filter banks.

In any case, while a perfectly good word which you can find in dictionaries, applicability still makes me cringe for some reason. I would tend to avoid it if at all possible.

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There's nothing wrong with OP's use of the preposition to here, as attested by...

enter image description here

But in the absence of a determiner (a, the, some, all, many, etc.) before it, uniform filter banks needs to be in the plural. By default, if no determiner is given, it effectively means all, any UFB's.

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