The Fourier Transform- Part I

A short tutorial video on how the Fourier Transform works. The video is designed for those who know what a Fourier Transform is but need to understand at a basic level how it converts time domain signals into the frequency domain.

Category:

Education

Tags:

• electrical
• engineering
• fourier
• transform
• time
• domain
• frequency
• signal
• analysis

[kridnix]

I think if you try to think of a physical analogy for a complex number you get confused. A complex number is a mathematical tool that is needed to solve a large class of algebraic equations such as x^2 = -1.

The way I think about it is that there is energy in a sinusoidal wave. Where is that energy at the exact moment(s) the wave amplitude passes through zero? If you represent a wave as having complex amplitude the magnitude is always constant, sometimes the energy is in "imaginary space".

[kridnix]

I am afraid I don't have any videos on those topics. I am not a signal processing person and most of my videos are on photonics and optics. I am trying to get a series on electromagnetics together, but it is going more slowly than I would like.

[kridnix]

O.k. There are three questions

1) You only measure the real part. In the complex eq. A and B themselves are complex which allows you to change the phase of the wave.

2) Orthogonal functions form a set from which any other function can be built. The most common example are the unit vectors, xhat, yhat, and zhat, from which any point in space can be represented. They are orthogonal because changing xhat doesn't affect yhat for example. Move in x, y does not change.

[78uttam]

i do not understand why a time signal is represented by a complex form. what will happen if we simply add cos & sin i.e. Acoswt+Bsinwt instead of Acoswt+jBsinwt?

They say sin and cos are orthogonal. Can you briefly give an intuitive idea about orthogonal functions?

Also, fourier transform definition says that any aperiodic signal can be obtained by summing infinite no. of sinosoidal waves. But why is that the data I receive from customer has limited no. of freq in freq domain?

[kridnix]

@78uttam For the third question, they are using a numerical Fourier transform and the frequency spacing will be inversely proportional to the sampling rate and proportional to the duration they measured the data for. You can't have an infinite number of frequencies in a time limited window.

[kridnix]

You can do it either way as long as you are consistent. Different books define it different ways.

[kridnix]

I don't just play a professor on YouTube, I actually teach electrical engineering at Oklahoma State University. I did these videos so I don't have to lecture in class anymore. It bored the students more than it bored me. Now we build things instead. Much more fun and my students can watch the videos at home.

[BoomBaaamBoom]

Math like BOSS!!! Thanks alot!

[TranceTips]

additive synthesis, a good example of this.

[JoaoPedroBorlido]

Best explanation I found!! Thank you very much!!! =D

[JugurthaHadjar]

@kridnix Cool video, we need more of those. You should check the sign in your exponential in the definition. I think it's exp(-jwt) not exp(jwt). Also in the definition, I think you wanted to write "exp(-jwt).dt" and not "exp(-jwt)delta(t)". The delta sign is used in another context of differentiation as you know. ("partial" and "spacial" as keywords).

Salutations d'Alger.

[pluterday]

buena explicacion.

[Nexus2Eden]

Is this the Cat Yoddeler? You sound like Paul the Cat Wrangler...are you he?

[12345soa]

tq very much bro.i'm a student interested for this particular topic

[MatrixOfDynamism]

I am VERY CONFUSED as to how the "Imaginary " sine wave is related to something real in the real world.

[surprizerrr]

excellent video....

very informative and eye opener for amatuers in this field and even for those who are just mugging up things whithout even caring to know what the thing is doing....

thanks a lot for this video ,.....

hope to expect more of such videos in future from u.........