# Are there any advantages to collecting data at a sampling rate higher than a recording device can physically record?

Background:

As an example, the Swift recording device can record at a sampling rate up to 96 kHz (with a corresponding effective rate of 48 kHz). However, the highest frequency response that the device's microphone can collect is 16kHz. See faq #8 and #9 at https://www.birds.cornell.edu/ccb/swift-frequently-asked-questions/

It seems to me that - in this example - collecting at a sampling rate greater than 32 kHz (effective rate of 16 kHz) would be overkill, due to the microphone's 16 kHz limit.

Question:

Are there any advantages to collecting data at a sampling rate higher than a recording device can physically record?

• I have not used a Swift before, but from their user guide it seems like the microphone is detachable meaning you can potentially change the microphone for one with a higher response frequency if you wish to do so. Jun 13, 2023 at 18:28
• Ah yes, Jure, I had overlooked that option. Jun 13, 2023 at 23:17

## 3 Answers

As you know, the minimum sampling frequency is twice the highest frequency of interest. If you can afford, you could sample at least 3 times the highest frequency improving the signal waveform close to Nyquist. More than 4 times highest frequency is only useful when you wanted to do phase processing (array of sensors)

Edit: While I said highest frequency of interest, I should have said highest frequency available in your data. In addition to be able to reconstruct data with frequencies less than Nyquist, one should keep in mind that sampling always require a low pass filter as an anti-aliasing filter. Real implementations of anti-aliasing filters never completely suppress signals with frequencies above corner frequency, so a higher sampling frequency is always helpful to avoid residual aliasing.

• Interesting! It was my understanding that there was no advantage to recording at a sampling rate > 2x the highest frequency pitch of the subject to be recorded. I was unaware of the 3x sampling that you mention. Would you please direct me to a source that further describes that 3x phenomenon? Jun 13, 2023 at 22:57
• I know ~nothing of acoustics, but if the microphone can pick up 16khz, then it can also probably pick up 15khz, but if you're only sampling at 32khz, then those would be nearly identical, rather than a full note lower. You'd need a higher sampling rate than 32khz in order to clearly tell those apart, wouldn't you? Which is, I assume, why the device samples up to 96khz? Jun 14, 2023 at 4:22
• @MooingDuck actually no, even with 32 kHz sample rate you would still be able to clearly tell 15 kHz and 16 kHz apart. The 15 kHz would look like 16 kHz with a 1 kHz envelope in the raw data, but proper sinc interpolation would reconstruct this as a single 15 kHz sinuoid. Jun 14, 2023 at 11:52
• @MooingDuck: No, if you can assume band-limited input (no frequency components at or above the Nyquist frequency), you can in theory perfectly reconstruct any band-limited input signal. (Err, at least if you have infinite bit-depth in your samples. Since you don't, some frequency headroom probably helps?) Monty (the Vorbis and Opus codec developer) posted wiki.xiph.org/Videos/Digital_Show_and_Tell a few years ago, about digital sampling and bit-depth, including some real demos with a signal generator and oscilloscope. Worth a watch. Jun 14, 2023 at 18:06

However, the highest frequency response that the device's microphone can collect is 16kHz.

This isn't really true, at least it's not true for typical microphones. The maximum rated frequency is the maximum that the microphone can capture reliably and with reasonably low distortion, not the maximum it can capture at all.

(What's “reasonable”? – it depends a lot on the application. There probably are standards for this, but not all specs might refer to the same standard.)

At any rate, it's fair to assume the microphone outputs a significant amount of signal components above 16 kHz, quite possibly even above 22 kHz.

Are these parts of the signal useful? Not necessarily, but even if you don't want them at all you couldn't just ignore them at this stage. If you sampled this straight to 32 kHz, it would result in aliasing, which can be quite notable in audio because it creates signal artifacts way below the Nyquist frequency. This could be avoided by adding analogue filters, but that has its own problems: these filters would cause additional distortion, at least phase mismatches, in the passband. Also, if the manufacturer does this then it definitely precludes any use of the extra frequencies.

Fast ADCs are readily available, and letting the ADC run at 96 kHz reliably avoids introducing audible aliasing in the process.

Once you have this high sampled signal, you can decide what to do with it. Keeping it at 96 kHz may not make any sense at all if the intention is playback for humans, but downsampling digitally is very easy in a way that reliably avoids aliasing. It might make sense however if the signal is processed further.

For bird song I could certainly see the extra frequencies being useful. They will probably need a lot of boosting, which would incur a lot of noise, and of course you can't rely on amplitude let alone phase correctness, but you might at least try to see whether that's good enough for you.

Yes, as WMXZ has mentioned the Nyquist rate determines the maximum frequency that can be reproduced with fidelity, but I think that's only part of the story here.

If one wants to avoid aliasing, then one must also ensure that there is no signal present at frequencies greater than half the Nyquist rate as well. Typically, this is accomplished with an anti-aliasing filter, i.e. a low-pass filter with a corner frequency or cutoff frequency near the half the Nyquist rate. However, the attenuation provided by low-pass filters rolls off with a finite slope (as would the frequency response of your microphone). So an ever-so slightly more nuanced answer would be: depending on the frequency response of your microphone and anti-aliasing filter, using a sample rate more than Nyquist rate might help improve the signal at and near Nyquist frequency.