Not to discount the historical importance, but the MOST important algorithm in that respect is not really the FFT, so much as the DWT (or Discrete Wavelet Transform). Not only do wavelets extract more useful information from the signal, the algorithm itself is much less complex. Some can even be implemented with nothing but integer maths. The Haar wavelet for example, which deconstructs the signal by recursively calculating integrals and derivatives via simple sums and differences.

 

I think any part of science, engineering, or life that claims to be the "most important" forgets about the "most overlooked". It's like asking, what's the most important part of the body? Most people would answer either brain or heart, but without a colon, you'd just be full of you-know-what.

Also, an algorithm is, by definition, a list of instructions to meet an objective or solve a problem. In that case, algorithms to find food, find water, or reproduce, would be just a few that are way more important than a FFT.

 

Not to discount the historical importance, but the MOST important algorithm in that respect is not really the FFT, so much as the DWT (or Discrete Wavelet Transform). Not only do wavelets extract more useful information from the signal, the algorithm itself is much less complex. Some can even be implemented with nothing but integer maths. The Haar wavelet for example, which deconstructs the signal by recursively calculating integrals and derivatives via simple sums and differences.

More useful (lose frequency precision to gain temporal information) information from the signal might not be optimal if you're looking for absolute precision for one aspect of the signal like frequency.

"most important"
It's the usually non-factual click-bait headline from a YT video.

 

More useful (lose frequency precision to gain temporal information) information from the signal might not be optimal if you're looking for absolute precision for one aspect of the signal like frequency.

"most important"
It's the usually non-factual click-bait headline from a YT video.

All well-produced videos are designed to be clickbait- the creator wants you to click&view it so YouTube pays them for the content they create. In this case, the non-factual "most Important" algorithm claim worked for them.

 

More useful (lose frequency precision to gain temporal information) information from the signal might not be optimal if you're looking for absolute precision for one aspect of the signal like frequency.

Actually, FFT's are no different. They ALSO lose granularity in the frequency domain as the frequency of the signal increases toward the Nyquist limit. Wavelets are somewhat different in that, as the frequencies decrease, the resolution improves. (Albeit while the temporal domain becomes less certain.) So nothing is lost by using wavelets instead. There are also literally an infinite set of wavelets to choose from. The FFT on the other hand can essentially only do one thing well: deconstruct the signal into simple sine waves (including its phase information) over the complex plane. It does a fine job in most situations, but it is nonetheless somewhat limited if you are looking for MUCH finer detail.

 

wonder what we would do without the number zero ?

 

wonder what we would do without the number zero ?

We'd never run out of anything. Life got so much more complicated (and dangerous) after zero was invented.

 

The world would be a better place if we eliminated a lot of zeros.

If there were no zeros we would never have to deal with a division with zero.

 

If there were no zeros we would never have to deal with a division with zero.

Then we get infinity of stuff and too much ain't good either.

 

Then we get infinity of stuff and too much ain't good either.

If there were no zeros then there would be no infinity.

 

If there were no zeros then there would be no infinity.

That's what I said.