# Search results

1. ### Find the following integral

can you help to find a general formula for the autocorrelation function Hermite polynomials. Thanks a lot!
2. ### Calling T.Engineer

1. you mean for arbitrary n,m. 2. what do you mean by z. 3. can you tell me how to evalute eq(15) to get this result: δ_n,m 2^n n! sqr(pi). if I you will know how they get this result for Hn, Hm, so I can also evaluted for my equation with Hn * cos (...) but this is my problem I dont know...
3. ### Calling T.Engineer

1. please, can tell me how to find the normalization coeffecient N_n? 2. you said different δ _n,m. I know thet δ _n,m is Kronecker delta function, how it can be changed? Thanks a lot!
4. ### Calling T.Engineer

do you mean with different N_n which is represented by eq(16)
5. ### Find the solution for the following equation

Homework Statement if H_n(t)= (-1)^n * e^(t^2) * d^n/dt^n * e^(-t^2) where n=1,2,...,N from the orthogonality property of Hermite polynomials we will have: \int^{\infty}_{-\infty} e^{-t^2} H_n(t) H_m(t)dt = \delta_n,m 2^n n! \sqrt{}pi this gives N_n=...
6. ### Calling T.Engineer

OK, I will. Thank you very much!
7. ### Calling T.Engineer

As I said to you: let assume that our function g(t) instead of H(t) So that, g(t)= (-1)^n * e^(t^2) * d^n/dt^n * e^(-t^2)* cos (2 pi fc t) we can say that g(t) can satisfied equations 15 and 17 because of its orthogonality properties. Is that true?
8. ### Calling T.Engineer

yes, why? I dont think that they have it.
9. ### Calling T.Engineer

No, I dont have it.
10. ### Calling T.Engineer

It is a reference which is : A. D. Poularikas, The Transforms and Applications Hand book CRC Press, Boca Raton, Fla, USA, 2nd edition, 2000.
11. ### Calling T.Engineer

according to the text that I have and I couldnt attached it here, the coeffecient C_m,n(t) is the the cross correlation function between nth and mth order pulses at point t.
12. ### Find the following integral

I am runing windows Xp.
13. ### Calling T.Engineer

let assume that our function g(t) instead of H(t) So that, g(t)= (-1)^n * e^(t^2) * d^n/dt^n * e^(-t^2)* cos (2 pi fc t) 1. we can say that g(t) can satisfied equations 15 and 17 because of its orthogonality properties. Is that true? 2. in equation 18, I didnt understand what...
14. ### Calling T.Engineer

for Hn(t)= (-1)^n * e^(t^2) * d^n/dt^n * e^(-t^2)* cos (2 pi fc t) where fc will be chosen such as to still keeping the orthogonality of Hn(t) for different integer values for n. so, Psi_n(t)= N_n * Hn(t) where N_n = \frac{1}{\sqrt{2^n*n!*\sqrt{pi}}} according to the definition as...
15. ### Calling T.Engineer

what about \int^{\infty}_{-\infty} Hn(t) Hm(t-d) dt where H(t)= (-1)^n * e^(t^2) * d^n/dt^n * e^(-t^2)* cos (2 pi fc t)

it is 1/2
17. ### Calling T.Engineer

I dont think it will be so easy? May be I should use a formula that it will help me to find the result of the integrals, or may be I should use a mathimatical program to find it out.

19. ### Calling T.Engineer

but I dont know how?
20. ### Calling T.Engineer

and what about equations 17, 18, and 19. will they still the same. when the new psi= old psi* cos (2 pi fc t) will eqations 17, 18 , and 19 give the same results?
21. ### Calling T.Engineer

Accroding to what, they implies 1/N^2 = I/\delta If I will apply it to my new function with cos (...) then how would I work. May be you can help me to make it more cleare to me,because till now I dont know how they get the result in eq(16) and according to what? Thanks alot!
22. ### Calling T.Engineer

this is if : Hn(t) = (-1)^n * e^(t^2)* d^n/dt^n * e^(-t^2) what about if : Hn(t)= (-1)^n * e^(t^2)* d^n/dt^n * e^(-t^2) * cos (2\pi fc t) where fc is a constant. will we get the same result?
23. ### Find the following integral

my question is how to find a general formula for the following F(d)= \int^{T_f}_{0}p(t)p(t-d) dt where p(t) = (-1)^n * e^(t^2) * d/dt * e^(-t^2) and n=1,2,...,N Thanks alot!
24. ### Calling T.Engineer

Why it is important to find the Normalization coefficient Nn which is represented by equation (16)
25. ### Find the following integral

I am sorry I didnt write it correctly p(t) = (-1)^n * e^(t^2) * d^n/dt^n * e^(-t^2) where n= 1,2,...,N I just want a general formula for the result
26. ### Find the following integral

can anybody find the result for the following equation: F(d)= \int^{T_f}_{0}p(t)p(t-d) dt where 916; = d but it doesnt appears very well and p(t) = (-1)^n * e^(t^2) * d/dt * e^(-t^2) thanks alot!
27. ### Calling T.Engineer

can you for example explain to me what it means each equation in the attached file, please. Thank you!
28. ### Calling T.Engineer

Actually they find the autocorrelation function for just Hn(t) \int^{\infty}_{-\infty} Hn(t)Hm(t) dt where m not equal to n. also Hm(t) is the first derivative function of Hn(t) And then they try to find the mean and variance. So, I believe we should get the autocorrelation function...
29. ### Calling T.Engineer

Let suppose we are going to find the mean for equation (2). Hn(t) = (-1)^n * cos(2π*fc*t) * e^(t^2) * d^n/dt^n e-^(t^2) The mean is defined as E(X)= \sum_{i} P_i X_i So how can I implemented to my function?
30. ### Calling T.Engineer

ok I will try to do somthing just give me little time? I think I find it "I hope so". Thanks alot!