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You should be able to evaluate the equations and plot them. Alternately, find the roots of the numerator and denominator and use the Bode straight line approximation graphs.
if i understand what u want is how to diffreniate between diff. types ,for that by simple qualitative analysis is putting the s=0 for low frequency and s=inf for high freq.
for example:
1-LPF: s=0 gives a constant while s=infinity gives zero which is how a LPF acts.
2-HPF: s=0 gives zero while s=inf. gives constant (i.e. HPF)
3-BPF: s=0 gives zero also s=inf gives zero which means band pass.
4-BSF: s=0 gives constant and s=inf gives constant which means band stop.
All analog continious time filters have a transfert function that can be written as N(s)/D(s)
where N(s) the numerator is a polynome of degree n
D(s) the denominator is a polynome of degree p
s the laplace variable
and real filter have p > or = n
in reality a fiter is defined by a differential equation betweet input and output ( due to kirschoff equations)
You need some maths to transpose this differential equation into a transfer function with laplace transform
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