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It is super to easy to find resources on HOW the FT works. But I find it very difficult to find resources on WHY we need it and WHERE it is useful to have. Does anybody have some good sources that explain the practical applications and how it is useful on real world usage?
It is super to easy to find resources on HOW the FT works. But I find it very difficult to find resources on WHY we need it and WHERE it is useful to have. Does anybody have some good sources that explain the practical applications and how it is useful on real world usage?
Hacker news folks seem to enjoy it :)
Another thought on the "why": many things in the real world operate on frequencies, sound being the most obvious but also electrical signals, mechanical systems like springs, etc. Doing the analysis representing a signal as a bunch of frequencies makes more sense, and Fourier transforms lets us do that
It is super to easy to find resources on HOW the FT works. But I find it very difficult to find resources on WHY we need it and WHERE it is useful to have. Does anybody have some good sources that explain the practical applications and how it is useful on real world usage?
Making convolution faster.
So what real world problems we have right now that depend on making convolution faster?
It is super to easy to find resources on HOW the FT works. But I find it very difficult to find resources on WHY we need it and WHERE it is useful to have. Does anybody have some good sources that explain the practical applications and how it is useful on real world usage?
Source: PCA and Fourier Analysis (2010) J Banfelder, Weill Cornell Medical College
> "A beautiful example of how this knowledge can be used in medicine is found in the cochlear implant. This device is used in patients with inner ear damage. The entire mechanical transduction mechanism is bypassed when the device is implanted. Instead, a microphone worn on the outer ear records sound that is digitized and sent to a signal processor. Here an FFT and an array of bandpass filters are applied. Results are passed to the implanted device, which electrically stimulates the neurons in the cochlea. Typical devices divide the frequency range of 0 to 4 kHz into about 15 or 20 bands, and stimulate neurons accordingly. However, profoundly deaf patients have recovered their hearing and have been able to understand speech even when as few as five bands are used."
See also:
https://allsignalprocessing.com/lessons/the-four-fourier-rep...
It is super to easy to find resources on HOW the FT works. But I find it very difficult to find resources on WHY we need it and WHERE it is useful to have. Does anybody have some good sources that explain the practical applications and how it is useful on real world usage?
From TFA: Stop. Here's where most tutorials excitedly throw engineering applications at your face. Don't get scared; think of the examples as "Wow, we're finally seeing the source code (DNA) behind previously confusing ideas". If earthquake vibrations can be separated into "ingredients" (vibrations of different speeds & amplitudes), buildings can be designed to avoid interacting with the strongest ones. If sound wave…
For example I would love to find an article that starts with "let's make a wav file smaller". And then somewhere in the middle it just says "and here we will use FT to achieve X".
Just a nit. The pair of equations the author showed at the beginning of the article are not the equations of the Fourier Transform and its inverse. The Transform is a continuous function operating on an infinite input. The equation for the Transform involves the use of the integral taken over +/- infinity. What is shown, using the summation operator, is a discrete form on the Transform where the input is a limited ti…
It is super to easy to find resources on HOW the FT works. But I find it very difficult to find resources on WHY we need it and WHERE it is useful to have. Does anybody have some good sources that explain the practical applications and how it is useful on real world usage?
Your cell phone wouldn't exist without the Fourier Transform, or the discrete fourier transform, to be correct. Image compression is another application, albeit, a 2-dimensional version. Software defined radios, or SDR, are completely dependent on the DFT. Radar processing. Earthquake analysis. The list goes on and on. Basically, our technological society would not exist in its current form without the fourier transf…
Yes that is great to know. But where can I find an article that explains how exactly FT helps in my cell phone? What exactly do we do with FT in a cell phone?
The short explanation of the DFT that I like the most is that it projects the signal vector on to the vector room with the exponential functions as basis vectors. Then you can see how much of the signal that each basis vector, corresponding to a frequency, can explain. It's intuitive to see if you start with a 2D vector space (the regular euclidian plane) and a 2D vector, and then you can expand the definition of vec…
Minor point, it's not a projection because you don't lose dimensions.
P^2 = P is the definition. not losing dimensions