Recommendation for studying filters
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.