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When recording an audio signal one can have a high sampling frequency. To reduce the amount of data that is stored, and thereby the power consumption, I head that it is possible to use a high-pass filter to reduce storage.

For example a signal is sample with 600Hz, the signal of interest is between 100 and 150 Hz.

  1. Is a bandpass filter between 100 and 150 (or 95 and 155) sufficient or should the nyquist frequency also be taken into account and should one bandpass between 200 (190) and 300 (310) Hz?
  2. How can this method reduce data when only a highpass-filter is used? Than the signal is still sampled at the highest frequency so I do not understand how this consumes less data? For example a highpass filter for all frequencies above 450 Hz?
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    $\begingroup$ you can save memory in two ways: either reduce sampling frequency or decrease data bitness (or both). Often, you can decrease bitness w/o loosing useful information, if you record only high-frequency component. $\endgroup$
    – V.V.T
    Sep 18, 2023 at 15:51
  • $\begingroup$ I think you may be confusing things by your choice of terminology, and you may wish to edit your question. You say you have an audio signal, but you're only interested in the band from 100 to 150Hz. Usually when a signal-processing person hears "audio signal" they interpret that as meaning "signal meant to be listened to by a human". It may be better to say "audio frequency signal", or just "signal from 100 to 150Hz". $\endgroup$
    – TimWescott
    Sep 18, 2023 at 21:06
  • $\begingroup$ "I heard that it is possible to use a high-pass filter..." Please edit your question to cite your source, or at least give us an idea (a professor, a coworker, a wandering homeless person, etc.). Your source was probably assuming that you're already low-pass filtering for 150Hz, and suggesting you add high-pass filtering for 100Hz to end up with bandpass filtering. But this is not at all clear. $\endgroup$
    – TimWescott
    Sep 18, 2023 at 21:12
  • $\begingroup$ While you are editing your question, let us know if you just need to have adequate frequency amplitude response (as you would with audio), or if phase response is also important (i.e. if you need pulses to retain their shape rather than being spread out or have ringing on edges). $\endgroup$
    – TimWescott
    Sep 18, 2023 at 21:13

2 Answers 2

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The Nyquist theorem states that you need at least two samples per Hz of bandwidth. And yes, you can reduce the sample rate for properly band passed signals, which is called band-pass sampling. If your signal of interest is 100Hz to 150Hz, you can theoretically reduce the sample rate to 100Hz. In practice there are quite a few details you need to work out properly (margins, residual aliasing, properly centering the pass band, etc. ) and these details depend a lot on your specific data and the requirements of your application.

For audio signals, bandpass sampling is somewhat unusual, since narrow band audio signals are quite rare. If the signal is for human consumption, it might be much better to use a perceptual compression scheme (MP3, AAC, Ogg Vorbis, Opus, etc.). This encode only the parts of the sound file that are audible. If you have no energy in some frequency bands, the perceptual encoders will also not allocate any bits to these bands.

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The most straightforward way to realize memory savings when the signal of interest only takes up some of the bandwidth, is to resample the signal to a lower samplerate. To prevent aliasing when doing this, you must lowpass the data to remove any high frequency energy before changing samplerate (decimating).

As Hilmar mentions is it possible to utilize the fact that the bandwidth of the signal is lower than the highest frequency component of interest.

Another way to reduce memory usage would be to use compressed sensing. These kinds of techniques allows to sample at below Nyquist rates by exploiting structures/sparsity in the signal.

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