Some facts:
1. Filter transfer function H(f) (in frequency domain) and filter impulse response h(t) (in time domain) are Fourier transform pair, i.e. F{h(t)} = H(f)
2. If you have the serie of N different filters with corresponding transfer functions H1(f), H2(f), ..., Hn(f), then overall transfer function is H(f)=H1(f) x H2(f) x ... x Hn(f) (the sign "x" stands for multiplication)
3. If you have the serie of N different filters with corresponding impulse responses h1(t), h2(t), ..., hn(t), then overall transfer function is h(t)=h1(t) * h2(t) * ... * hn(t) (the sign "*" stands for convolution)
Q: What is easier to calculate: multiple product or multiple convolution?
A (IMHO): Multiple product
This is what you should do:
1. Find the Fourier transform of impulse response F{h(t)} = H(f)
2. Calculate overall transfer function of serie of N filters Hn(f) = H(f) x H(f) x ... x H(f) = [N(f)]^N
3. Calculate impulse response of overall filter by taking inverse Fourier transform F^-1{Hn(f)} = hn(t)
4. Let the N->inf in hn(t)
Regards (and let us know the results)