<p>While the Nyquist theorem asks for &quot;at least twice the bandwidth  of your data&quot;, optimal sampling frequency may also be connected to processing, especially if you are using the Taeger-Kaiser operator (TKO) for detections. For this type of processing, best sampling frequency is 4-times the frequency of interest.</p>
<p>To see this, assume that signal of interest is a sine wave, then the TKO is given by</p>
<p>TKO(t) = P(t)^2 -P(t-dt)*P(t+dt) = P_0^2 * sin^2(omega * dt)</p>
<p>The sinus on the right hand side becomes 1 when omega * dt = pi/2 or f = 1/(4 * dt) = fs/4. For all other frequencies the TKO underestimates the signal.</p>

CC BY-SA 4.0
2022-06-25T04:54:40.847Z
2022-06-25T04:54:40.847Z
WMXZ
<p>The <a href="https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem" rel="noreferrer">Nyquist-Shannon sampling theorem</a> says that if <code>Fsampling</code> is the sampling rate, the highest frequency that can be reliable captured (Nyquist frequency, <code>Fnyquist</code>) is <code>Fsampling/2</code>. In your case, the sampling rate is 192 kHz, which means the the highest frequency that can be reliably recorded is 96 kHz. Parts of the bat call that are &gt;= 96 kHz will be aliased, where the higher frequencies get mirrored as lower frequencies. The obvious signs for bat calls are for example if an FM call (higher-lower frequency sweep) seems to start with a weird initial up-sweep (see image below).</p>
<p><a href="https://i.sstatic.net/ZgxGu.png" rel="noreferrer"><img src="https://i.sstatic.net/ZgxGu.png" alt="enter image description here" /></a></p>
<p>While all bat calls typically have multiple harmonics, many species have one harmonic that is dominant. You may get lucky if your species main energy lies &lt;= 96 kHz (e.g. Fpeak -20 dB range of the power spectrum is 20-90 kHz). A warning though: most sound cards have strong anti-aliasing filters, which remove frequencies above the Nyquist frequency - and so your calls may still have higher spectral content - which have been 'removed' pre-digitisation itself. At least for bat calls, aliasing is often only seen when the bats fly very close to the mics, and the received levels are high. Otherwise the higher frequencies are anyway absorbed easily over longer distances - and so are typically filtered out by the built-in anti-alias filters.</p>
<p>Ultimately, your best shot is to check for obvious signs of aliasing, and additionally record the same bats with higher (e.g. 384/500) sampling rates to see how the call measurements differ much spectrally.</p>

CC BY-SA 4.0
2022-06-23T12:28:47.747Z
2022-06-23T12:28:47.747Z
Thejasvi
<p>I will be performing echolocation call recordings of an understudied bat species that roosts in caves. Many studies use very high sampling rates (&gt;=384 kHz), but I currently only have a sound card with a max sampling rate of 192 kHz.</p>
<p>I see that there are a few studies that have used 192 kHz sampling rate for other bat species  and am wondering whether this will be enough to capture the echolocation calls of my bat? How will I know if my sampling rate is sufficient?</p>

<recording><fieldwork><experiment-design>
Will be recording vocalisation of an understudied species, with 192 kHz is my sampling rate high enough?
# Will be recording vocalisation of an understudied species, with 192 kHz is my sampling rate high enough?

(Asked by: username_0 on 2022-06-23)

I will be performing echolocation call recordings of an understudied bat species that roosts in caves. Many studies use very high sampling rates (>=384 kHz), but I currently only have a sound card with a max sampling rate of 192 kHz.

I see that there are a few studies that have used 192 kHz sampling rate for other bat species and am wondering whether this will be enough to capture the echolocation calls of my bat? How will I know if my sampling rate is sufficient?

**Tags:** recording, fieldwork, experiment-design


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## 2 answers

### Answer by username_0 on 2022-06-23. Score: 7 | Accepted answer

The [Nyquist-Shannon sampling theorem](https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem) says that if `Fsampling` is the sampling rate, the highest frequency that can be reliable captured (Nyquist frequency, `Fnyquist`) is `Fsampling/2`. In your case, the sampling rate is 192 kHz, which means the the highest frequency that can be reliably recorded is 96 kHz. Parts of the bat call that are >= 96 kHz will be aliased, where the higher frequencies get mirrored as lower frequencies. The obvious signs for bat calls are for example if an FM call (higher-lower frequency sweep) seems to start with a weird initial up-sweep (see image below).

[![enter image description here](https://i.sstatic.net/ZgxGu.png)](https://i.sstatic.net/ZgxGu.png)

While all bat calls typically have multiple harmonics, many species have one harmonic that is dominant. You may get lucky if your species main energy lies <= 96 kHz (e.g. Fpeak -20 dB range of the power spectrum is 20-90 kHz). A warning though: most sound cards have strong anti-aliasing filters, which remove frequencies above the Nyquist frequency - and so your calls may still have higher spectral content - which have been 'removed' pre-digitisation itself. At least for bat calls, aliasing is often only seen when the bats fly very close to the mics, and the received levels are high. Otherwise the higher frequencies are anyway absorbed easily over longer distances - and so are typically filtered out by the built-in anti-alias filters.

Ultimately, your best shot is to check for obvious signs of aliasing, and additionally record the same bats with higher (e.g. 384/500) sampling rates to see how the call measurements differ much spectrally.


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### Answer by username_1 on 2022-06-25. Score: 2

While the Nyquist theorem asks for "at least twice the bandwidth of your data", optimal sampling frequency may also be connected to processing, especially if you are using the Taeger-Kaiser operator (TKO) for detections. For this type of processing, best sampling frequency is 4-times the frequency of interest.

To see this, assume that signal of interest is a sine wave, then the TKO is given by

TKO(t) = P(t)^2 -P(t-dt)\*P(t+dt) = P\_0^2 \* sin^2(omega \* dt)

The sinus on the right hand side becomes 1 when omega \* dt = pi/2 or f = 1/(4 \* dt) = fs/4. For all other frequencies the TKO underestimates the signal.


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