3 ms·

Basically, the sampling theorem says you can reconstruct the exact waveform with a certain number of samples. Adding a bunch more samples bulks up the file, but

Basically, the sampling theorem says you can reconstruct the exact waveform with a certain number of samples. Adding a bunch more samples bulks up the file, but you didn't need them to restore the exact waveform. However, the unnecessary samples are in the file between you and the next sample you do need. At high enough levels of waste this creates an I/O bottleneck that hampers performance. Another way to look at is that digital audio is not like digital imaging. There aren't pixels. Increasing the data rate does not continue to make the waveform more and more detailed to human auditory perception in the way that raising the pixel density does for human visual perception. To describe it intuitively, forget your intuition that audio is like visual and start from "there is no metaphor between these two things."

sitharus 9y ago
> Increasing the data rate does not continue to make the waveform more and more detailed to human auditory perception in the way that raising the pixel density does for human visual perception. Early low data rate codecs - such as the one used for GSM mobiles - are obviously inferior, but still functional. I think a better analogy is that an iPhone 7 has a 1 megapixel screen, so there's no difference between a 1 megapixel image and a 5 megapixel image, except one is much larger. Of course visually you can zoom in (or move closer in real life), but audibly you can't.
- fusiongyro 9y ago
  I get what you're saying, that if you remove the ability to zoom you can equalize things, but without that twist I think this preserves the essential problem with the analogy that Monty works so hard to correct. If your data rate is too low, you don't have enough samples to recreate the waveform. So you create an approximate. But there is a finite number of samples that you need to recreate all of the information in the waveform, so once you have that, there isn't any additional information there for you to obtain if you continue to increase the sample rate.
- DigitalJack 9y ago
  To be fair, phone audio signals have until recently been bandlimited to just a few KHz in centered around 3KHz.
willglynn 9y ago
Digital imaging definitely has sampling concerns too: https://en.wikipedia.org/wiki/Aliasing https://en.wikipedia.org/wiki/Aliasing Even analog imaging has concerns that are better described in the frequency domain than the spatial domain: https://en.wikipedia.org/wiki/Airy_disk https://en.wikipedia.org/wiki/Airy_disk https://en.wikipedia.org/wiki/Optical_transfer_function https://en.wikipedia.org/wiki/Optical_transfer_function
- fusiongyro 9y ago
  Interesting!
astrange 9y ago
Images and audio are pretty similar, and sampling theory works for both - a low-pass filter on audio and a blur filter on images is the same. The difference is audio is "actually" bandlimited and frequency-based, but images are "actually" spatial. When you try using frequency math on images you get artifacts called ringing, which are easy to see with JPEGs or sharp scalers like Lanczos. Of course audio isn't really frequency-based either, or else it would just be one sound repeated forever. So there's still ringing artifacts (called "pre-echo") and cymbals are the first to go in an MP3.
- dom0 9y ago
  > The difference is audio is "actually" bandlimited and frequency-based, but images are "actually" spatial. I.e. audio is sampled along one dimension, while images are sampled along two dimensions. Note that frequency-domain considerations play a crucial role in all optical design, including imaging sensors.
  - astrange 9y ago
    It's a little more than that. A sine wave originates in the frequency domain but actually sounds like something, but images originating in the frequency domain are just noise and not pictures of anything.
josteink 9y ago
> Another way to look at is that digital audio is not like digital imaging. There aren't pixels. For the mathematically inclined, this would probably be a good time to repeat: pixels are not little squares[1]. [1] http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf

sitharus 9y ago

> Increasing the data rate does not continue to make the waveform more and more detailed to human auditory perception in the way that raising the pixel density does for human visual perception. Early low data rate codecs - such as the one used for GSM mobiles - are obviously inferior, but still functional. I think a better analogy is that an iPhone 7 has a 1 megapixel screen, so there's no difference between a 1 megapixel image and a 5 megapixel image, except one is much larger. Of course visually you can zoom in (or move closer in real life), but audibly you can't.

fusiongyro 9y ago
I get what you're saying, that if you remove the ability to zoom you can equalize things, but without that twist I think this preserves the essential problem with the analogy that Monty works so hard to correct. If your data rate is too low, you don't have enough samples to recreate the waveform. So you create an approximate. But there is a finite number of samples that you need to recreate all of the information in the waveform, so once you have that, there isn't any additional information there for you to obtain if you continue to increase the sample rate.
DigitalJack 9y ago
To be fair, phone audio signals have until recently been bandlimited to just a few KHz in centered around 3KHz.

willglynn 9y ago

Digital imaging definitely has sampling concerns too: https://en.wikipedia.org/wiki/Aliasing https://en.wikipedia.org/wiki/Aliasing Even analog imaging has concerns that are better described in the frequency domain than the spatial domain: https://en.wikipedia.org/wiki/Airy_disk https://en.wikipedia.org/wiki/Airy_disk https://en.wikipedia.org/wiki/Optical_transfer_function https://en.wikipedia.org/wiki/Optical_transfer_function

fusiongyro 9y ago
Interesting!

astrange 9y ago

Images and audio are pretty similar, and sampling theory works for both - a low-pass filter on audio and a blur filter on images is the same. The difference is audio is "actually" bandlimited and frequency-based, but images are "actually" spatial. When you try using frequency math on images you get artifacts called ringing, which are easy to see with JPEGs or sharp scalers like Lanczos. Of course audio isn't really frequency-based either, or else it would just be one sound repeated forever. So there's still ringing artifacts (called "pre-echo") and cymbals are the first to go in an MP3.

dom0 9y ago
> The difference is audio is "actually" bandlimited and frequency-based, but images are "actually" spatial. I.e. audio is sampled along one dimension, while images are sampled along two dimensions. Note that frequency-domain considerations play a crucial role in all optical design, including imaging sensors.
- astrange 9y ago
  It's a little more than that. A sine wave originates in the frequency domain but actually sounds like something, but images originating in the frequency domain are just noise and not pictures of anything.

josteink 9y ago

> Another way to look at is that digital audio is not like digital imaging. There aren't pixels. For the mathematically inclined, this would probably be a good time to repeat: pixels are not little squares[1]. [1] http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf http://alvyray.com/Memos/CG/Microsoft/6_pixel.pdf