Recent content by room_

##n>>1##, ##n\sim100## and above I guess can be considered as large.

As the paper present, this algorithm works for large ##n## and small ##\alpha##, whereas in this case we have ##(\alpha) = (n) > n-1##. They suggest that the input parameters are ##-1\leq \alpha \leq 5, \ n\geq 0##, which allows us to compute as much as ##L_{4}^{5}(\omega_c t)##. This result can...

Sorry, the formula has to be $$h_n(t)= 2^n\omega_c^n \frac{(n-1)!}{(2n-1)!}t^n e^{-\omega_c t} L_{n-1}^{(n)}(\omega_c t),$$

##(7)## can be expressed in terms of generalized Laguerre polynomials (here I add ##2^n## factor) $$h_n(t)= 2^n\omega_c^n \frac{(n-1)!}{(2n-1)!}t^n e^{-\omega_c t} L_{n-1}^{(n)}(t),$$ I guess there are procedures for computing them, hope it helps.

It is clear now how the impulse behaves with the growth of ##n##. What would you recommend to try to compute ##(7)## formula in the post? As previously mentioned, Matlab spits out 0 for ##n>30##, but I really want to see if it's the same as your results for ##n=100,200,400##.

How many filters can you add more? Is it possible to go for ##n=100,200##? It would be very interesting to see.

There was no limitation seen in Multisim, 49 is just an example, yet it was the biggest I went because it's quite hard for my PC to run simulation with that many filters. Speaking of Matlab, I think it's the "large numbers" limitation, since it is clear that all of derivatives exist and can be...

What it has to do with the Gibbs phenomenon in this case? I may be missing the point. Would you please describe it in a little simpler manner? I don't understand why the matching cannot be satisfied and what does that mean. I don't work with real network here, I only play around with the ideal...

I consider the band-pass filter of the following configuration (the ##u_m## is a voltage controlled voltage source): The transfer function is $$K_1(p)=\hat{U}_o(p) = \frac{p}{RC(p+1/RC)^2} = \frac{\omega_c p}{(p+\omega_c)^2}, \quad \omega_c=\frac{1}{RC}.\qquad (1)$$ Now I connect ##n## such...

Thank you for your response. I had and idea to write it out using exponential shift theorem, so here is my reasoning $$ \frac{d^{n-1}}{dt^{n-1}} (e^{-\omega_c t}t^{2n-1}) = D^{n-1}(e^{-\omega_c t}t^{2n-1})= e^{-\omega_c t}(D-\omega_c)^{n-1} t^{2n-1} = \\ = e^{-\omega_c...

I struggle to find an appropriate inverse Laplace transform of the following $$F(p)= 2^n a^n \frac{p^{n-1}}{(p+a)^{2n}}, \quad a>0.$$ WolframAlpha gives as an answer $$f(t)= 2^n a^n t^n \frac{_1F_1 (2n;n+1;-at)}{\Gamma(n+1)}, \quad (_1F_1 - \text{confluent hypergeometric function})$$ which...