You only get the Gaussian if you take the limit correctly.
In the visualization as you increase the number of bins, the Gaussian approximation becomes more and more squeezed, and by the weak law of large numbers the limit is a Dirac delta.
In order to get the Gaussian you'd need to be looking at a window whose width is proportional to the square root of the number of bins.
The copyright issue can be a bit tricky. Assuming that Instagram goes on and sells users' pictures - who's liable if somebody uploads a picture which he/she doesn't own, and then Instagram goes on and sells that to a third party?
The phase portion isn't actually just the imaginary part, it's just the piece of information lost when one goes from real+imag -> magnitude, i.e. it's the argument of the complex number.
This is a nice way to see how the DFT is computed, however I find the view of the FT as a change of basis as even more important - generalizes easily to other bases and and one can understand easily wavelets and their advantages. Basically, the sinusoids form a basis of the vector space of functions (every 'non-pathological' function can be written as a possibly infinite sum of them) and the numbers computed by the FT are coefficients for the respective basis vectors - the magnitude of these coefficients is interpreted as the strength of the corresponding wave in the original signal.
Another way to see the FT is as the basis where the convolution operators are diagonal - this is used in image processing, where computing the FFT of a filter + entry-wise multiplication can be much faster than running the convolution at each pixel of the input image.
vist a museum and read the 'Agony and the Ecstasy' and 'Lust for Life' by Irving Stone. The first book is on Michealangelo and the second is on the life of Vincent Van Gogh.
Well not quite. While SVMs gained a lot of popularity for having nice properties e.g.
1) a convex problem which means a unique solution and a lot of already existing technology can be used
2) the "kernel trick" which enables us to learn in complicated spaces without computing the transformations
3) can be trained online, which makes them great for huge datasets (here the point 2) might not apply - but there exist ways - if someone's interested I can point out some papers)
There is an ongoing craze about deep belief networks developed by Hinton et al. (who is teaching this course) who came up with an algorithm that can train them reasonably well (there exist local optima and such, so it's far from ideal). Some of the reasons they're popular
1) they seem to be winning algorithm for many competitions / datasets, ranging from classification in computer vision to speech recognition and if I'm not mistaken even parsing. They are for example used in the newer Androids.
2) DBNs can be used in an unsupervised mode to _automatically_ learn different representations (features) of the data, which can be then used in subsequent stages of the classification pipeline. This makes them very interesting because while labelled data might be hard to get by, we have a lot of unlabelled datasets thanks to the Internet. As what they can do - see the work by Andrew Ng when they automatically learned a cat detector.
3) DBS are "similar" to biological neural networks, so one might think they have the necessary richness for many interesting AI applications.
"SVMs. . .3)can be trained online, which makes them great for huge datasets (here the point 2) might not apply - but there exist ways - if someone's interested I can point out some papers)"
Please do. I want to read some about SVMs since i haven't heard that much about them.
[†] x is where it is centered.