cqt

ketos.audio.utils.misc.cqt(x, rate, step, bins_per_oct, freq_min, freq_max=None, window_func='hamming')[source]

Compute the CQT spectrogram of an audio signal.

Uses the librosa implementation,

https://librosa.github.io/librosa/generated/librosa.core.cqt.html

To compute the CQT spectrogram, the user must specify the step size, the minimum and maximum frequencies, $f_{min}$ and $f_{max}$ , and the number of bins per octave, $m$ . While $f_{min}$ and $m$ are fixed to the input values, the step size and $f_{max}$ are adjusted as detailed below, attempting to match the input values as closely as possible.

The total number of bins is given by $n = k \cdot m$ where $k$ denotes the number of octaves, computed as

$k = ceil(log_{2}[f_{max}/f_{min}])$

For example, with $f_{min}=10$ , $f_{max}=16000$ , and $m = 32$ the number of octaves is $k = 11$ and the total number of bins is $n = 352$ . The frequency of a given bin, $i$ , is given by

$f_{i} = 2^{i / m} \cdot f_{min}$

This implies that the maximum frequency is given by $f_{max} = f_{n} = 2^{n/m} \cdot f_{min}$ . For the above example, we find $f_{max} = 20480$ Hz, i.e., somewhat larger than the requested maximum value.

Note that if $f_{max}$ exceeds the Nyquist frequency, $f_{nyquist} = 0.5 \cdot s$ , where $s$ is the sampling rate, the number of octaves, $k$ , is reduced to ensure that $f_{max} \leq f_{nyquist}$ .

The CQT algorithm requires the step size to be an integer multiple $2^k$ . To ensure that this is the case, the step size is computed as follows,

$h = ceil(s \cdot x / 2^k ) \cdot 2^k$

where $s$ is the sampling rate in Hz, and $x$ is the step size in seconds as specified via the argument winstep. For example, assuming a sampling rate of 32 kHz ( $s = 32000$ ) and a step size of 0.02 seconds ( $x = 0.02$ ) and adopting the same frequency limits as above ( $f_{min}=10$ and $f_{max}=16000$ ), the actual step size is determined to be $h = 2^{11} = 2048$ , corresponding to a physical bin size of $t_{res} = 2048 / 32000 Hz = 0.064 s$ , i.e., about three times as large as the requested step size.