Fourier Transform Example Rectangular Pulse

[crumblewolf]

could you explain the reason you times by 2 and a a bit better. that's the part my lecturer skipped over as well and its the part that confuses me about these transforms. Thanks mate.

[marcodigio77]

hi...great explanation...helped me a lot! But what would happen if the amplitude of x is 3 and not 1?

[DarrylMorrell]

@marcodigio77 The Fourier transform X(jw) is 3 times larger than in the video.

[marcodigio77]

@DarrylMorrell thank you for your reply! I must have done something wrong because I got it six times larger. :-)

[SHITONASTICK1100]

it was great up until the bit where we just start to randomly times the equation by numbers.

[DarrylMorrell]

The random numbers are to put the equation into a specific form that leads to the sinc function. If you have not seen this derivation or the sinc function before, it probably would not occur to you to do this. Still, it is necessary to get things into the form we need.

[warriorrabbit]

Thank you for the video, but you make it sound so boring.

[RyanMMXII]

If integrating zero gives you an arbitrary constant "C", then evaluate that constant at the upper limit and subtract the value of the constant at the lower limit. In this case, C(Infinity) - C(a) or C(-a) - C(-Infinity) which both equal C - C = 0. This is the process for evaluating definite integrals.

[squarepusher303]

Isn't it "illegal" to ignore the zero? Because integrating zero yields an unknown constant.

[NaqashHaider]

Sorry to bother you again, the biggest problem that I am facing these days as I am reading Discrete Time Signal processing ( Oppenheim ) is that its hard for me to solve summation of infinite sequences 0 to infinity,-infinity to + finity,and these types of things. would you tell me the name of the book which can help me.

thanks

[rchandos]

Would you please comment on the physical significance of the Fourier transform of a transient signal like this pulse.

With a Fourier series (for a periodic signal), the line spectrum tells you what you how much signal amplitude you would measure on a spectrum analyzer at each of the harmonic frequencies, continuously. What does the FT spectrum tell you in this case? At what point(s) in time would you actually measure the ordinate values in that spectrum? Thank you.

[Holyfrik1]

what would happen if the rectangular pulse is periodic now?, will you just get infinity?

[DarrylMorrell]

@Holyfrik1 If the rectangular pulse is periodic, you will get a Fourier Series rather than a Fourier transform. My video "Fourier Analysis: Overview" explains this. My video "Fourier Series Example: Square Wave Part 1 & 2" shows the computation of the Fourier series coefficients for a periodic pulse.

[lukmackul]

What is the handwritten drawing program u are using?

[DarrylMorrell]

@lukmackul Paintbrush for the Mac

[xTimmAx]

Wow, this was incredibly helpful, thank you so much!

[gugolplex]

thanks a LOT, man! nice video

[brenskeee]

good video mate