Please contact me if you find any mistakes and errors in the book; I will add them to this (hopefully slowly) growing list of corrections for the 1st edition.

Section | Page | Wrong | Corrected |
---|---|---|---|

2.1.3.1 | 10 | A sampled signal can only be reconstructed without loss of information if the sample rate $f_{\mathrm{S}}$ is higher than twice the highest frequency $f_{\mathrm{max}}$ in the sampled audio signal. | A sampled signal can only be reconstructed without loss of information if the sample rate $f_{\mathrm{S}}$ is higher than twice the bandwidth $f_{\mathrm{max}}$ of the audio signal. |

2.1.4.1 | 13 | The abscissa of a PDF plot represents all possible amplitude values of the signal $x$ and their probability is plotted on the ordinate. | The abscissa of a PDF plot represents all possible (amplitude) values of the signal $x$ and their probability density is plotted on the ordinate. |

2.2.3 | 20 | `\Delta\Omega = \frac{2\pi}{\mathcal{K}\cdot T_{\mathrm{S}}}` | `\Delta\Omega = \frac{2\pi}{\mathcal{K}}` |

20 | `f(k) = ` | `f(k) = \frac{\Delta\Omega}{2\pi}k f_{\mathrm{S}} = \frac{k}{\mathcal{K}}f_{\mathrm{S}}` | |

2.2.4 | 24 | Q adjusts the desired frequency resolution per octave c, while ... | Q adjusts the desired frequency resolution and can be derived from c, the desired number of frequency bins per octave, while ... |

2.2.6.4 | 28 | `r_{xx}(\tau) &=& \int\limits_{-\infty}^{\infty}{x(\tau)\cdot x(t+\tau), d\tau} \\ &=& x(\tau) \ast x(-\tau)` | `r_{xx}(` |

3 | 32 | Envelope of excerpts from a typical speech recording (left), a string quartet recording (mid), and a pop recording (right) with a length of \unit[15]{s} | Waveform of excerpts from a pop recording (left), a string quartet recording (mid), and a speech recording (right) with a length of \unit[15]{s}, respectively |

3.2 | 35 | Various methods describing the properties of a (time-invariant) properties of a signal... | Various methods describing the properties of a (stationary) signal... |

3.3.3.1 | 46 | denominator: `\sum\limits_{k = 0}^{N/2-1}{}` | denominator: `\sum\limits_{k = 0}^{` |

3.3.3.1 | 47 | denominator: `\sum\limits_{k = 0}^{N/2-1}{}` | denominator: `\sum\limits_{k = 0}^{` |

3.5.2.1 | 66 | As a rule of thumb, distributions with a skewness smaller than 2 are... | As a rule of thumb, distributions with a skewness between -2 and 2 are... |

4.3.2 | 76 | `|x(i)| \leq v_{\mathrm{PPM}}(i-1)` | `|x(i)| ` |

5.5.2.1 | 113 | Various key profile templates, normalized to a sum of 1 | Various key profile templates, normalized to a vector length of 1 |

6.4 | 134 | Beat histogram of a piece of popular music (left) and of a string quartet performance (right) | Beat histogram of a string quartet performance (left) and of a piece of popular music (right) |

10 | 169 | Here, it requires a performer or a group of performers who ``self-consciously enacts music for an audience'' \cite{sloboda85}. The performers render the composer's work | Here, it requires a performer who ``self-consciously enacts music for an audience'' \cite{sloboda85}. The performer or a group of performers render the composer's work |

10.2.2.3 | 179 | has been studied by Dixon, who ... | The regularity of the beat pulse for tempo perception of a music performance has been studied by Dixon et al., who ... |

A.2 | 181 | Changing the order of operands does change the result... | Changing the order of operands does not change the result... |

B.4.1.3 | 195 | Blackman-Harris window $w_{\mathrm{BH}}(t)$:\\ $b_0 = 0.4243801, b_1 = 0.4973406, b_2 = 0.0782793$ | Blackman-Harris window $w_{\mathrm{BH}}(t)$:\\ $b_0 = 0.35875, b_1 = 0.48829, b_2 = 0.14128, b_3 = 0.01168$ |

B.4.1.4 | 195 | alternative Blackman window $w_{\mathrm{AB}}(t)$:\\ $\beta = 0$ | alternative Blackman window $w_{\mathrm{AB}}(t)$:\\ $\beta = 4$ |

Double check equation:

2.42 –> shouldn’t it be X(k) ?

2.45 –> shouldn’t it be 2pi*fs ?

2.47 –> missing fs ?

Thanks for pointing this out. After I thought a bit about it, I removed the $X(j\Delta\Omega)$ from equation 2.42 (which is unnecessary, confusing, and missing a k: it should have been $X(jk\Delta\Omega)$). But more importantly, $f_S$ should be removed from Eq. (2.43). I added two changes to the errata above; note that the same changes apply to the appendix as well.

PS: edited because previous answer was incomplete.

In 2.2.6.4, equation (2.72) I think there is a little mistake.

Original: r_{xx}(\tau)&=\int_{-\infty}^{\infty}{x(\tau)\cdot x(t+\tau}d\tau

Shouldn’t it be: r_{xx}(\tau)&=\int_{-\infty}^{\infty}{x(t)\cdot x(t+\tau}dt ?

Yes, you are correct! Thanks for the heads up, I will add it to the page right away.

Thanks for correcting it!

But please compare it with for example http://www.marga.com.ar/6615/wiener-khinchin.pdf. I think “x(\tau)” should also replaced by “x(t)”.

Right, I should think more carefully before correcting anything. Now that I thought about it I believe the point here was to write r(t) = int x(tau)x(t+tau) dtau

Yes, now its right, thanks ðŸ™‚

(Only nitpicking: On the wrong side is a backslash missing in “x(-tau)”)

Very instructive book. Nitpick in 10.2.2.3, p.179. The beginning of the second to last paragraph is missing: “has been studied by Dixon[…]”.

Ah! Thanks for that, I added it to the list of errata above.

Best,

Alexander