Question about sampling rate… but not what you think!!

[blinkofani]

So, today is the day i ask the question that’s been haunting me for a long time. I could have ask in any audio-related forum but since the ratio of smart people is rather high here, I thought it would be a good place!!

So, we often hear that it’s doesn’t make that much of a difference to record above 44.1KHz because of « I don’t remember the name of » the law you divide by 2, that makes that frequencies above 20KHz won’t be captured or something and most human ears can’t hear above 20K. Right? It’s just useful to dogs to use a higher sampling rate, bla bla bla.

But, when we talk about frequencies the human can hear, we’re talking about frequencies related to pitch. When we talk about sampling frequencies we talk about the number of samples(recordings) a converter will make every second. What relation does it have with the highest frequencies a human ear can hear? In another kind of sampling, if I take 4 pictures a second of someone walking in front of me, and then 16 pictures a second, the later will give a smoother idea of the walk but I won’t see less content in the pictures, no? Don’t know if I’m making myself clear? 

What’s the relation between the frequencies in Hz that the ear can hear(pitch) and the frequencies of a recording(number of samples captured every second)? Thanks for any explanation.

[David Nahmani]

You're talking about the Nyquist–Shannon sampling theorem

14 minutes ago, blinkofani said:

if I take 4 pictures a second of someone walking in front of me, and then 16 pictures a second, the later will give a smoother idea of the walk but I won’t see less content in the pictures, no?

Yes. 

However with sound, keep in mind that you're going to route the digital audio signal through a low-pass filter, which will reconstruct the signal in its smooth form. You need limited information about the value of the audio signal certain positions in order to recreate the smooth analog signal. For example in the image below, in the DAC, the reconstructed squared signal fed to a low-pass filter will result in the smooth sine wave like the original signal. 

 

[blinkofani]

So, you’re saying more samples(recordings) will not render the original signal that much better because of the rounding off of the filter? This i kind of understand, but why are people saying that it’s related to the frequencies the human ear can hear?

[David Nahmani]

9 minutes ago, blinkofani said:

you’re saying more samples(recordings) will not render the original signal that much better because of the rounding off of the filter?

Yes. Well...it's not me saying it, it's Nyquist and Shannon. And in your sentence, you can replace "that much better" with "any better at all". 

Check out this oscilloscope view of a square waveform (produced by a synth). It's only two values, but when I run it through a low-pass filter, it ends up being a sine wave: 

Before I cut off the high frequencies, you can see all the higher frequency harmonics in the EQ Analyzer, that are responsible for those angled edges in the waveform, that give you a square wave. Now imagine that those are above 20 kHz, meaning you can't hear them. Once you run that reconstructed signal into a low pass filter at the right frequency, you get a sine wave at 20 kHz, the limit of human hearing. Meaning you got rid of anything unnecessary and end up with the same smooth waveform you had originally recorded. 

[blinkofani]

Thanks for your explanation, but I still don’t see how the sampling frequency(the number of recordings every second) has anything to do with this. When we use an EQ(filter) it’s for manipulating the content of high/low frequencies into the sound. When we change the sampling frequency when recording, it’s affects the number of recordings happening every second, nothing to do with the timbre of the recording. Anyway, have to go to bed now!! But i appreciate your time. Maybe it’s me who’s not smart enough to see the link here.

[David Nahmani]

10 hours ago, blinkofani said:

I still don’t see how the sampling frequency(the number of recordings every second) has anything to do with this.

If you're trying to record a 20 kHz sine wave with a 40 kHz sample rate then you'll record only two alternative values, one high and one low. After reconstructing an analog signal with the DAC, you'll get a square wave, however when you filter off the high frequencies you're back to the original sine wave. 

[blinkofani]

So, the number of recordings per second(sample rate) has an impact on the quality of the end result depending how many cycle a pitch have(your example of a sine wave cycling at 20K)? But most sounds in life are more complex than a sine wave.

Anyway, I’m not trying to argue with you and what you write(it seems to sound like that!!), I just don’t understand the link there can be between the speed of sampling and the pitches that will be retained!! For me, it seems logical that the more recordings every second, the more precise the rendering and that it has no impact on the frequency spectrum captured.

I hope I make sense. Being french Canadian, it’s already a bit of a chalenge trying to explain myself in that topic!! Thanks David.

[David Nahmani]

1 hour ago, blinkofani said:

But most sounds in life are more complex than a sine wave.

A sound that is more complex than a sine wave can be deconstructed in the sum of multiple harmonics that are sine wave. That was the work of Joseph Fourrier: Fourrier analysis. It's similar to how any color can be deconstructed in a sum of Red, Green, and Blue values. 

If a complex sound has harmonics above 20 kHz and you sample the sound with a sample rate of 40 kHz, then you'll record all harmonics up to 20 kHz, but you won't record any of the harmonics that are above 20 kHz. However, since you can't hear them anyway, you don't need to record them!

Think of every sound as a sum of pure sine waves. You can't hear any of the sine waves that are above 20 kHz, so if you filter them out, it won't make any  difference to you. Take any record, and run it through an EQ that filters out everything above 20 kHz, and you won't hear any difference at all. 

So the idea behind the Nyquist-Shannon sampling theorem is that if you need to be able to record all kinds of sine waves (in order to reproduce any sound, no matter how complex) up to a certain frequency, you need to sample at twice that frequency. 

[Atlas007]

 

As mentioned here:

Recording digital audio at higher bit depths and sampling rates offers several benefits, but there can also be drawbacks if you go to extremes. Let's explore both sides:

Benefits of Higher Bit Depth (e.g., 24-bit):

Greater Dynamic Range: Higher bit depths provide a wider dynamic range, meaning you can capture both very soft and very loud sounds without losing detail. This is particularly important in music production and audio recording.

Reduced Quantization Noise: Increased bit depth reduces quantization noise, making the audio signal cleaner and less susceptible to distortion.

Better Signal-to-Noise Ratio (SNR): Higher bit depths result in a higher SNR, which means the recorded audio is less noisy, especially in quiet passages.

Improved Editing Flexibility: When you work with higher bit depth audio, you have more headroom for processing and editing without introducing artifacts or degrading the quality.

Benefits of Higher Sampling Rate (e.g., 96 kHz or 192 kHz):

Extended Frequency Response: Higher sampling rates capture a wider range of audio frequencies, potentially capturing ultrasonic frequencies that may affect the perceived quality of audio equipment.

Reduced Aliasing: Higher sampling rates reduce the risk of aliasing, which is a distortion that occurs when high-frequency sounds are improperly captured or reproduced.

Better Time Resolution: When you record at a higher sampling rate, you capture more "snapshots" of the audio waveform per second, improving the accuracy of transient sounds and fast-moving audio.

Drawbacks of Excessive Bit Depth and Sampling Rate:

File Size: Higher bit depths and sampling rates produce larger audio files. This can quickly eat up storage space, especially when working on long audio recordings or multiple tracks.

Processing Demands: Audio recorded at very high bit depths and sampling rates can be demanding on computer resources during recording and editing, requiring more powerful hardware.

Compatibility: Some playback devices and software may not support extremely high bit depths and sampling rates. Compatibility issues can arise when sharing or distributing audio files.

Diminishing Returns: The improvements in audio quality beyond a certain point may not be very noticeable, especially for most casual listeners. Higher bit depths and sampling rates may be more beneficial in professional or specialized contexts.

Conclusion:

Recording at higher bit depths and sampling rates can offer improved audio quality, especially in professional audio production. However, there are practical limitations and considerations, including larger file sizes and increased processing demands. It's essential to choose the right balance between quality and practicality based on your specific needs and equipment. For many everyday listening situations, standard bit depths (16 or 24 bits) and sampling rates (44.1 kHz or 48 kHz) are more than sufficient.