Hello professor, THANK YOU, i really appreciate this series, i studied (as tech elective) Laplace transforms and Fourier series in college and I am studying Fourier transforms now (32 years after graduating) so my question is: what does an i in the result mean? Sometimes all the i cancel out and sometimes not, sometimes there is an i in the exponent. In this lecture there remains an i in the denominator. The problem I want to solve is the FT of the N-wave of a sonic boom (sudden rise in pressure followed by linear decline to negative pressure and then a sudden rise to ambient pressure) but it troubles me that there can remain an i in the result, it would seem that every i should resolve in to a sin or cos term. Best regards, John in Michigan.
And how do we graph it now that the result is a complex number? Do we take the absolute value? And if so, is this absolute value the amplitude of the sinusoids that sum up to make up the function?
Teaching is skills. you really have got the skills man
Clear and helpful explanation. Thanks a lot
Glad it was helpful!
Hello professor, THANK YOU, i really appreciate this series, i studied (as tech elective) Laplace transforms and Fourier series in college and I am studying Fourier transforms now (32 years after graduating) so my question is: what does an i in the result mean? Sometimes all the i cancel out and sometimes not, sometimes there is an i in the exponent. In this lecture there remains an i in the denominator. The problem I want to solve is the FT of the N-wave of a sonic boom (sudden rise in pressure followed by linear decline to negative pressure and then a sudden rise to ambient pressure) but it troubles me that there can remain an i in the result, it would seem that every i should resolve in to a sin or cos term. Best regards, John in Michigan.
Can the constant a have negative values, that is a
Sir. what is the difference between the pulse and impulse ?
clearly and helpful. Thanks a lot.
Cool! I guess the key to these problems is to know your techniques of integration! ....and your algebra! 😮 😊
Definitely the foundation to a lot of things.
And how do we graph it now that the result is a complex number? Do we take the absolute value? And if so, is this absolute value the amplitude of the sinusoids that sum up to make up the function?
I would consider to graph |F(w)| vs w!
How is the answer if it is this way? f(t)=e^a|t|
And thanks
awesome thanx.. :)
3:12 It makes me thinking the Laplace transform...
Thank you!
Welcome!