Lecture 5 | The Fourier Transforms and its Applications

Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood finishes up on Fourier series, then he talks about the transformation Fourier series compared to the Fourier Transformations and how one gets to the study of periodic phenomena to non periodic phenomena by means of a limiting process.

The Fourier transform is a tool for solving physical problems. In this course the emphasis is on relating the theoretical principles to solving practical engineering and science problems.

Complete Playlist for the Course:
http://www.youtube.com/view_play_list?p=B24BC7956EE040CD

EE 261 at Stanford University:
http://eeclass.stanford.edu/ee261/

Stanford University:
http://www.stanford.edu

Stanford University Channel on YouTube:
http://www.youtube.com/stanford

Category:

Education

Tags:

• Electrical
• engineering
• computers
• math
• physics
• geometry
• algebra
• calculus
• technology
• functions
• linear
• operations
• Fourier
• transformations
• periods
• heat
• flow
• series
• convolution
• non
• periodic
• phenomena

[leocmen]

Very good, very good...

Great support for whoever is investigating this subject...

[noobmartin]

This is a great complement to my regular studies in series and transforms.

[grunder20]

Spectacular lecture.

[zephyxj]

The way he ends his lectures halfway through explaining an important point reminds me of the Arabian Nights

[MrGreySuit]

Amazing videos

ha ha, I wonder how many people have written "Not Great" on their notes

[Reicouross]

Why does he integrate by dy when calculating the coefficients at 12:52? he is still doing an integral from 0 to 1 (1 period of the disk radial) so should he still be in x? what does the y variable represent?

[Reicouross]

Why does he integrate by dy when calculating the coefficients? he is still doing an integral from 0 to 1 (1 period of the disk radial) so should he still be in x? what does the y variable represent?

[iBradleyAllen]

@kevinatucla for me its the opposite, i have lots of application of the Fourier transform, years but need to see the underlying theory. Im SO grateful he started talking about the series first and starts to switch over in #5

u can imagine a series of analog samples in some memory array; now tell me the frequency components that series of numbers represents? impossible! well the Ft does it. how? you send thru different frequencies and see what resonates. show the math? I cant. yet.

[ibreakkidslegs]

"the rigor police are off-duty" haha

[FrankClautier]

@hai2410 It's because the absolute value of a sum is always less than or equal to the sum of the absolute values of the individual terms, e.g. abs(a+b)<=abs(a)+abs(b). Since a definite integral is a sum, the same principle applies. Also observe that the absolute value (the modulus) of the complex exponential equals 1 since exp(a*t*i) (with a=-2*pi*k*t/T) can be rewritten as cos(a*t)+i*sin(a*t), resulting in an absolute value of 1. Cheers!

[ralucada123]

excellent!!



[hai2410]

can anyone explain to me the part at 49:20 why the absolute value of the full integral is only less than or equal to the integral of the two separate absolute products- why isn't it precisely equal? Thanks