11–20 of 105 posts
EDIT: I mixed up high vs low frequencies, as the reply pointed out, so I've edited this to be correct now. The reason we can get away with throwing away low frequencies in JPEG is because humans are prone to notice significant details rather than tiny details. High frequencies of a Fourier transform of an image == tiny detail (like being able to distinguish individual hairs) Low frequencies of a Fourier transform of…
Hi Hacker News - I'm the author of the piece, also on twitter @aatishb. Look forward to hearing your thoughts. I encourage you to share your thoughts and insights with other readers by leaving a comment on the post, particularly if you know of other interesting applications about the Fourier transform. Cheers!
OK, since you asked: > The sound wave produced by a piano note is a simple sine wave. No, it's not. A piano note is a complicated stack of overtones (some of which are harmonic and some of which aren't) and transients. If it was just a sine wave, it would sound like a sine wave and not like a piano. This is part of why things like Shazam are so difficult: musical notes aren't just a single frequency in the FFT, they…
So, Nice enough article for slipping into the topic - now give me more! harder! faster!
Hi Hacker News - I'm the author of the piece, also on twitter @aatishb. Look forward to hearing your thoughts. I encourage you to share your thoughts and insights with other readers by leaving a comment on the post, particularly if you know of other interesting applications about the Fourier transform. Cheers!
OK, since you asked: > The sound wave produced by a piano note is a simple sine wave. No, it's not. A piano note is a complicated stack of overtones (some of which are harmonic and some of which aren't) and transients. If it was just a sine wave, it would sound like a sine wave and not like a piano. This is part of why things like Shazam are so difficult: musical notes aren't just a single frequency in the FFT, they…
EDIT: I mixed up high vs low frequencies, as the reply pointed out, so I've edited this to be correct now. The reason we can get away with throwing away low frequencies in JPEG is because humans are prone to notice significant details rather than tiny details. High frequencies of a Fourier transform of an image == tiny detail (like being able to distinguish individual hairs) Low frequencies of a Fourier transform of…
To illustrate, here is an example of zeroing the lowest frequencies: http://imgur.com/a/wVjYk
This is a great post, but it's a little bit misleading when talking about MP3s and lossy compression and conflates analog fourier analysis with discrete analysis. When you're talking about a digital signal, it is the sample rate that determines the maximum frequency you can represent. It's not MP3s that "throw out the really high notes" -- it's any digital signal. A discrete fourier transform actually is lossless, bu…
Yes, any digital signal has a limited bandwidth However, MP3s throw more high frequencies than the digital signal at that given sampling rate allows.
Once you understand the FT, you basically understand how a signal is structured. By converting (or transforming) a time signal to the frequency domain, one can clearly see what frequency components (or harmonics) contribute to said signal. If one were to try the same in the time domain, it would be much more difficult to visualize.
This is a great post, but it's a little bit misleading when talking about MP3s and lossy compression and conflates analog fourier analysis with discrete analysis. When you're talking about a digital signal, it is the sample rate that determines the maximum frequency you can represent. It's not MP3s that "throw out the really high notes" -- it's any digital signal. A discrete fourier transform actually is lossless, bu…
Thanks for your feedback. Sure, any digital signal is by definition finite in its resolution (the sample rate or bits). I was trying to address the distinction between wave files of the type stored on audio CDs, and MP3s - both digital signals. I agree that the Fourier transform is in principle lossless, but it's particularly useful to use it in a lossy way, i.e. to throw out the least important (to us) components of…
Also, the the word "note" is confusing in the context of music, since really low notes usually contain a lot of high frequency information.
Elegantly explained. Does anyone know of similar posts on other transforms like Z, etc?
Earlier quoted context omitted.
To illustrate, here is an example of zeroing the lowest frequencies: http://imgur.com/a/wVjYk
Oh, so your brain can still mostly recreate the shape even with no low frequencies!
Hi Hacker News - I'm the author of the piece, also on twitter @aatishb. Look forward to hearing your thoughts. I encourage you to share your thoughts and insights with other readers by leaving a comment on the post, particularly if you know of other interesting applications about the Fourier transform. Cheers!
OK, since you asked: > The sound wave produced by a piano note is a simple sine wave. No, it's not. A piano note is a complicated stack of overtones (some of which are harmonic and some of which aren't) and transients. If it was just a sine wave, it would sound like a sine wave and not like a piano. This is part of why things like Shazam are so difficult: musical notes aren't just a single frequency in the FFT, they…
In a way, it's twice as many, since they have both real and imaginary components.
