Video duration: 646 seconds
Global video hits: 13010
We begin our study on the work of Joseph Fourier (1768-1830) with the definition of the Fourier Series - a way of expressing functions as infinite sums or integrals or trigonometry functions.
Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.
Video duration: 474 seconds
Global video hits: 1173
A discussion on the Convergence Theorem of a Fourier Series, a very important theorem in Fourier Analysis. How do we know when the Fourier Series converges to the function f(x).
Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.
Video duration: 609 seconds
Global video hits: 2026
Let's look at the graphs of various Fourier Series. To illustrate the series, we will be taking the Nth partial sum. It is also here where we notice some interesting behaviour of some Fourier Series.
Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.
Video duration: 457 seconds
Global video hits: 2119
Reference: http://FreedomUniver sity.tv
This simple demo shows how a square wave can be represented as other functions such as a sine wave using matlab. This video also serves as a Matlab and/or simulink tutorial as applied to the concept of the Fourier seriesI will post a more thorough discussion on the Fourier Transform.
Video duration: 511 seconds
Global video hits: 1390
Using the even property of a function, we'll find the Fourier Series of x^2 on [-3, 3] which serves as a example of why certain functions NEED NOT agree with its Fourier Series. A Convergence theorem is needed.
Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.
Video duration: 648 seconds
Global video hits: 2929
Using our previous definitions, here is an example of how you write a Fourier Series from a graph of a function, a 'broken' function in this case.
Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.
Video duration: 3437 seconds
Global video hits: 1690
Lecture Series on Digital Signal Processing by Prof.S. C Dutta Roy, Department of Electrical Engineering, IIT Delhi. For More details on NPTEL visit http://nptel.iitm.ac .in
Video duration: 3679 seconds
Global video hits: 1578
Lecture Series on Digital Signal Processing by Prof.S. C Dutta Roy, Department of Electrical Engineering, IIT Delhi. For More details on NPTEL visit http://nptel.iitm.ac .in
Video duration: 642 seconds
Global video hits: 1410
We shall take advantage of certain properties of odd and even functions to simplify our work in finding the Fourier Series.
ERRATA: For odd functions, -f(x)=f(-x). Apologies for the mistake.
Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.
Video duration: 443 seconds
Global video hits: 1403
With our definitions of a Fourier Series on [-L, L], let us look at a simple example, this time a function integrable on [-3, 3].
Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.
Video duration: 650 seconds
Global video hits: 1256
We now extend the basic ideas we have of Fourier Series and look at a periodic functions, ones which repeats itself after a period T.
Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.
Video duration: 483 seconds
Global video hits: 1218
We will revise some basic definitions of limits and derivatives of piecewise continuous functions which are needed in learning the convergence theorem of Fourier Series.
Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.
Video duration: 359 seconds
Global video hits: 1606
Using a simple substitution, we extend the definition of a Fourier Series of a function, this time integrable from -L to L.
Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.
Video duration: 3130 seconds
Global video hits: 657
Lecture Series on Networks and Systems by Prof. V.G.K.Murti, Department of Electrical Engineering,IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac .in
Video duration: 558 seconds
Global video hits: 863
We find the Fourier Series of a periodic function g(x), write it in its phase angle form and glimpse at its amplitude spectrum.
Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.
Video duration: 3154 seconds
Global video hits: 367
Lecture Series on Networks and Systems by Prof. V.G.K.Murti, Department of Electrical Engineering,IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac .in
Video duration: 2918 seconds
Global video hits: 353
Lecture Series on Networks and Systems by Prof. V.G.K.Murti, Department of Electrical Engineering,IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac .in
Video duration: 2894 seconds
Global video hits: 335
Lecture Series on Networks and Systems by Prof. V.G.K.Murti, Department of Electrical Engineering,IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac .in
Video duration: 3100 seconds
Global video hits: 396
Lecture Series on Networks and Systems by Prof. V.G.K.Murti, Department of Electrical Engineering,IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac .in
Video duration: 255 seconds
Global video hits: 835
Using the convergence theorem, we have another looking at the Fourier Series of a simple function f(x) = 2x on [-pi, pi].
Please check out www.gaussianmath.com for a deeper look into this or other mathematics topics.
![Fourier Analysis 6: Fourier Series of x^2 [MAY NOT = f(x)]](http://img.youtube.com/vi/UBr9dfYPmGI/2.jpg "Fourier Analysis 6: Fourier Series of x^2 [MAY NOT = f(x)]")
![Fourier Analysis 2: Fourier Series of a \](http://img.youtube.com/vi/CK9NaHBe2CE/2.jpg "Fourier Analysis 2: Fourier Series of a \")
![Fourier Analysis 4: Example of Fourier Series on [-L, L]](http://img.youtube.com/vi/JgYx5jTYv4s/2.jpg "Fourier Analysis 4: Example of Fourier Series on [-L, L]")
![Fourier Analysis 3: Fourier Series of function on [-L, L]](http://img.youtube.com/vi/M7HLT3cwJPI/2.jpg "Fourier Analysis 3: Fourier Series of function on [-L, L]")
