# errata

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
2.1.3.110A 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.
2.1.4.113The 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.
2.2.320\Delta\Omega = \frac{2\pi}{\mathcal{K}\cdot T_{\mathrm{S}}}\Delta\Omega = \frac{2\pi}{\mathcal{K}}
20f(k) = \frac{\Delta\Omega}{2\pi}k = \frac{f_{\mathrm{S}}}{\mathcal{K}}kf(k) = \frac{\Delta\Omega}{2\pi}k f_{\mathrm{S}} = \frac{k}{\mathcal{K}}f_{\mathrm{S}}
2.2.424Q 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 ...
2.2.6.428r_{xx}(\tau) &=& \int\limits_{-\infty}^{\infty}{x(\tau)\cdot x(t+\tau), d\tau} \\ &=& x(\tau) \ast x(-\tau)r_{xx}(t) &=& \int\limits_{-\infty}^{\infty}{x(\tau)\cdot x(t+\tau), d\tau} \\ &=& x(t) \ast x(-t)
332Envelope 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
3.235Various methods describing the properties of a (time-invariant) properties of a signal...Various methods describing the properties of a (stationary) signal...
3.3.3.146denominator: \sum\limits_{k = 0}^{N/2-1}{}denominator: \sum\limits_{k = 0}^{\mathcal{K}/2-1}{}
3.3.3.147denominator: \sum\limits_{k = 0}^{N/2-1}{}denominator: \sum\limits_{k = 0}^{\mathcal{K}/2-1}{}
3.5.2.166As 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...
4.3.276|x(i)| \leq v_{\mathrm{PPM}}(i-1)|x(i)| < v_{\mathrm{PPM}}(i-1)
5.5.2.1113Various key profile templates, normalized to a sum of 1Various key profile templates, normalized to a vector length of 1
6.4134Beat 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)
10169Here, 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 workHere, 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
10.2.2.3179has 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.2181Changing the order of operands does change the result...Changing the order of operands does not change the result...
B.4.1.3195Blackman-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.4.1.4195alternative Blackman window $w_{\mathrm{AB}}(t)$:\\ $\beta = 0$alternative Blackman window $w_{\mathrm{AB}}(t)$:\\ $\beta = 4$

## 9 thoughts on “errata”

1. 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.

2. 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 ?

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

3. 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