how to design a cosine modulated filter bank without using built-in function?

help me to design a 4 channel cosine modulated analysis filter bank without using built-in function.

[Adam]

The only occasions I know where the otherwise silly constraint of not using built-in functions is applied is for homework questions where it is expected for you to find the answer, not us.

So what have you tried so far?

If you have to do this without even using the cos function then that does seem quite a challenge.