Lecture 10, Discrete-Time Fourier Series | MIT RES.6.007 Signals and Systems, Spring 2011

Lecture 10, Discrete-Time Fourier Series
Instructor: Alan V. Oppenheim
View the complete course: ocw.mit.edu/RES...
License: Creative Commons BY-NC-SA
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[@BunkerSquirrel]

Oh, this is the guy who made my textbook. Okay.

[@blockhet]

Ironic that so much aliasing occurs in this video.

[@danialdunson]

This guy. The subtle enthusiasm. Thank you for this gem. :)

[@ahmedatifabrar7698]

Assuming he'd given lectures with his last edition of the textbook (1997), it'd maintain more 'symmetry' with the book and the least compressed 'ripples' in coherent understanding if MIT taped those ones. Nevertheless, it is laced with the elements of a modern day classic.

[@birullino]

These lectures are timeless.

[@mferreira1231]

Best explanation directly from the best in the business!

[@MrJITMANO]

amazing...Doesn't get any better than this.....

[@j50313j50313]

I still do not understand why the discrete-time Fourier series's synthesis step only requires k from 0 to N-1 and not negative infinity to infinity because in the continuous-time case, the synthesis step equation's index is from negative infinity to infinity.

[@adarshsrivastav3991]

Since the coefficients are periodic, it would repeat itself

[@elonmusk4267]

The God off signals and systems

[@Calligraphy1054]

Plz me with how the integral of the discrete fourier transform synthesis equation takes place over 2pi?

[@windandrain98]

What a class! Thank you!!

[@khivasara007]

At 46:00 equation, k limit is 0 to N-1 or - infinite to +infinite?

[@MrQwertymnb]

At 30:50, there is an Omega_0 right at the end of the synthesis equation. Where did that Omega_0 come from? It isn't in the original synthesis equation of Discrete-time Fourier Series.

[@PhooGiSucky]

He didn't work through the math this time but if you go back to the earlier lecture where he derives the Fourier Transform from the Continuous Time Fourier Series it's more clear. Basically he replaced a_k with 1/N * X(k Omega_0), but remember that N = 2 pi / Omega_0 so you get Omega_0 / 2 pi in front of the X(k Omega_0). He leaves the 1/(2 pi) and puts the Omega_0 at the end in anticipation of taking the limit as Omega_0 goes to zero thus converting the sum to a Reimann integral.

[@thetradefloor]

where can I get my vhs copy?

[@mitocw]

+k8 www.worldcat.org/title/signals-and-systems/oclc/18284377

[@lbhwilliams]

For the synthesis equation in DFS, why do we only add-up k during one period? i mean in this case, the high-frequency components would be lost i think?

[@thebigVLOG]

+Bohan Li You've probably solved this by now but it's because in discrete time the exponential signals start to repeat once k is greater than N-1. Imagine you have a circular track with 2 racers on it. It takes Racer One 300 seconds to do a lap whilst Racer Two can do a lap in 150 seconds. Now say you sample each racers location every 300 seconds, both racers will be in the same position and you have no information regarding which racer has done the most laps. N = 150 seconds.

[@mohacirday5884]

thebigVlog bro can you mssg me private coz i have a problem about this please?

[@heshamqaba9807]

take speed as 1.5 so that you save your life :))))))))))

[@rohitborra2507]

2x is better

[@ECEGrishmaKarekar]

Bro but there are some concepts which might be bit tough to understand For that switching back to normal speed helps!!

[@tashi2009]

good lecture but super slow

[@danialdunson]

Tashi Rabten there’s a speed button

[@faisalmuhamad4893]

2x is still bearable

[@canned_heat1444]

take it easy speedracer