Recommendation for studying filters I have a project to do about what happens to a periodic function when we pass it through a low-pass, high-pass and band-pass filter. 
I have no expressions for the filters or the function, I just have to analyse graphics. 
I already concluded that the low-pass filter passes the zones of the graphic that have a low variation, and that the high pass filter passes the zones of the graphic that have a high variation. In the case of the band-pass filter the resulting wave consists on various sinusoids (it just passes certain intervals of variations). 
Ok, I now have the general idea, but I was looking for a text that provided me  more rigorous explanation in terms of the frequencies, and their relation to the variation of a function.
Does anyone here knows a book, or a paper that covers this specific topic of signals filtering?
Thanks!
If you have some numerical  methods background,  Richard Hammings, Digital Filters, is a good place to start.  The book is from 1977 but the math hasn’t changed.  The book has also been released by Dover so it has a very low price, unlike Oppenheim and Schaefer’s book and also unlike Oppenheim and Schaefer, is compact.
The math level isn’t advanced. 

Hamming is one of the founders of Information Theory.  He essentially invented parity codes. He was also the first president of SIAM.