Suggestions on how to use FIR model in sentence retrieval task
How can I use the above model where the input signal is a sentence.


makes no sense; your whole system is not linear (which is one of the requirements for your whole convolution approach); for example, if you you play back the words "fox" and "jumped" at the same time, you don't hear "lazy". 

Not linear means your system can't be represented by an impulse response. 

Your signal model is overly simplistic, too. You might map words to numbers as soon as you know the words, but that's only happening after speech recognition (and might be helpful in understanding logically what has been said), but not before.

So, your whole approach shows you haven't dealt with a lot of speech recognition before – which is OK, but it means that you can't just come up with some approach and assume it makes sense from the start.

I'd recommend reading a book on speech recognition. There's certainly a big wealth of literature out there.