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  • 0 posts edited
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  • 57 votes cast
Sep
18
comment Integration of infinite series not giving expected result
The result now plots as expected. Thanks for your help!
Sep
18
comment Integration of infinite series not giving expected result
Ok, I went ahead and made the clarifications as suggested by your post!
Sep
18
comment Integration of infinite series not giving expected result
I'm using u(t) to represent the Heaviside function (edited to make this clearer). Let me go ahead and reformat using Mathjax and replace t with a different variable.
Sep
17
comment Solving integral of sinusoid involving unit step and dirac delta function
FWIW, my main mistake above was in the integration of the dirac function - which should integrate to u(t), not 1. Once that's fixed the integration method above "works" even though as per Dr. MV it may not be entirely sound mathematically.
Sep
17
comment Solving integral of sinusoid involving unit step and dirac delta function
Excellent, thanks!
Sep
17
comment Expressing a function in terms of sinc(t)
Right, so I guess I wasn't looking for a more explicit relation than what is possible. Thanks for pointing me in the right direction.
Sep
17
comment Solving integral of sinusoid involving unit step and dirac delta function
Also, the solution I am given doesn't have a negative sign.
Sep
17
comment Solving integral of sinusoid involving unit step and dirac delta function
I would like to accept but the solution (see question) doesn't involve this additional u(t) - that's part of what I don't understand.
Sep
16
comment Solving integral of sinusoid involving unit step and dirac delta function
Thank you for your help. What about the + 1 part from the derivative of the dirac function?
Sep
16
comment Expressing a function in terms of sinc(t)
Essentially everything I'm writing down simplifies to $sin(t) = sin(t)$ or $sin(t/\Delta)=sin(t/\Delta)$.
Sep
16
comment Expressing a function in terms of sinc(t)
Thanks for your help. This gives me $U(\Delta*s)=\Delta*S(s)$, but I can't seem to find a value of $s$ that results in relating $sin(t/\Delta)$ to $sin(t)$. Maybe I'm missing something obvious, or not aiming for the right thing here.
Sep
16
comment Expressing a function in terms of sinc(t)
So far, I've tried expanding each side into their complex exponential forms, then isolating t on both sides and trying to solve the equation. That's not been getting me anywhere.
Sep
16
comment Integrating an infinite series of the Dirac function
Ok, thanks a lot, I get it for 1! What about the 2nd part regarding tau?
Sep
16
comment Integrating an infinite series of the Dirac function
(Regarding 1, my programmer mind desperately wants to code this as n % T == 0 ? Inf : 0. But I'm trying to understand and use the notation above directly in Matlab and it doesn't seem to be making sense).
Sep
16
comment Integrating an infinite series of the Dirac function
Thanks for your answer. I understand the impulse train and the staircase function graphically, but I'm having trouble understanding the notation. Let me clarify my questions: 1) What does the summation sign mean/do in the first equation? 2) What does tau mean/do in the second equation?
Sep
11
comment Proof that absolute integrability does not imply square integrability
@Travis thanks, edited to reflect this clarification
Sep
11
comment Proof that absolute integrability does not imply square integrability
I want to accept this answer because it points in the right direction, but I'm afraid it brings me back to Cauchy-Schwartz, which was my unsuccessful starting point. I have near zero formal math background so a little more detail would be appreciated (I'm not looking for the actual proof/conditions).
Sep
11
comment Proof that absolute integrability does not imply square integrability
I'm a little bit confused by ||x||p+a ≤ ||x||p. That seems to imply that an absolutely integrable function will always be square integrable, with a solution smaller than for the absolute integration.
Nov
13
comment Why aren't there $+\infty^{+\infty}$ real numbers?
Ah-ha! Now I get it. Thanks for the re-statement / further explanations.
Nov
12
comment Why aren't there $+\infty^{+\infty}$ real numbers?
I understand this is correct symbolically, but I fail to rationalize to myself "why" this should be.