Literally, bandwidth is a frequency span. Beyond that definition, its meaning will depend somewhat on context. For example, the bandwidth of a bandpass filter is the upper cutoff frequency minus the lower cutoff frequency (cutoff frequency being the filter’s -3 dB point). The audio bandwidth is generally given as 20 Hz to 20,000 Hz, although there are harmonic components of audio that extend far above the 20k point. In most situations where bandwidth is given as an audio spec, the wider the frequency range the better. Be sure that when comparing bandwidth on different devices, that the same spec is being expressed. For example, some effects devices cite their bandwidth spec based on the dry, or unprocessed signal, while others give the bandwidth of the actual processed sound. These difference between these two specs (both listed as “bandwidth”) can be substantial!
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