Chapter 5, PSYCHOACOUSTIC PRINCIPLES Video Solutions, Audio Signal Processing and Coding

Problem 1

Describe the difference between a Mel scale and a Bark scale. Give tables and itemize side-by-side the center frequencies and bandwidth for $0-5 \mathrm{kHz}$. Describe how the two different scales are constructed.

Morgan Thompson

Numerade Educator

05:17

Problem 2

In Figure 5.12, the solid line indicates the just noticeable distortion (JND) curve and the dotted line indicates the absolute threshold in quiet. State which of the tones A, B, C, or D would be audible and which ones are likely to be masked. Explain.

Alexander Allen

Numerade Educator

01:21

Problem 3

In Figure 5.13, state whether tone B would be masked by tone A. Explain. Also indicate whether tone $\mathrm{C}$ would mask the narrow-band noise. Give reasons.

Khoobchandra Agrawal

Numerade Educator

01:21

Problem 4

In Figure 5.14, the solid line indicates the JND curve obtained from the psychoacoustic model 1. A broadband noise component is shown that spans
Figure 5.12. JND curve for Problem 5.2.
FIGURE CANT COPY
Figure 5.13. Masking experiment, Problem 5.3.
from 3 to 11 Barks and a tone is present at 10 Barks. Sketch the portions of the noise and the tone that could be considered perceptually relevant.

Manik Pulyani

Numerade Educator

Problem 5

Design a 3-band equalizer using the peaking filter equations of Chapter 2 . The center frequencies should correspond to the auditory filters (see Table 5.1) at center frequencies $450 \mathrm{~Hz}, 1000 \mathrm{~Hz}$, and $2500 \mathrm{~Hz}$. Compute the Q-factors associated with each of these filters using, $Q=f_0 / B W$, where $f_0$ is the center frequency and $B W$ is the filter bandwidth (obtain from Table 5.1). Choose $g=5 \mathrm{~dB}$ for all the filters. Give the frequency response of the 3-band equalizer in terms of Bark scale.

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00:59

Problem 6

Write a program to plot the absolute threshold of hearing in quiet Eq. (5.1). Give a plot in terms of a linear $\mathrm{Hz}$ scale.

Amy Jiang

Numerade Educator

00:46

Problem 7

Use the program of Problem 5.6 and plot the absolute threshold of hearing in a Bark scale.

Lucas Finney

Numerade Educator

Problem 8

Generate four sinusoids with frequencies, $400 \mathrm{~Hz}, 1000 \mathrm{~Hz}, 2500 \mathrm{~Hz}$, and $6000 \mathrm{~Hz} ; f_s=44.1 \mathrm{kHz}$. Obtain $s(n)$ by adding these individual sinusoids as follows,
$$
s(n)=\sum_{i=1}^4 \sin \left(\frac{2 \pi f_i n}{f_s}\right), n=1,2, \ldots, 1024 .
$$
FIGURE CANT COPY
Figure 5.14. Perceptual bit-allocation, Problem 5.4.

Give power spectrum plots of $s(n)$ (in $\mathrm{dB}$ ) in terms of a Bark scale and in terms of a linear Hz scale. List the Bark-band numbers where the four peaks are located. (Hint: see Table 5.1 for the bark band numbers.)

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00:39

Problem 9

Extend the above problem and give the power spectrum plot in dB SPL. See Section 5.7.1 for details. Also include the absolute threshold of hearing in quiet in your plot.

Chai Santi

Numerade Educator

Problem 10

Write a program to compute the perceptual entropy (in bits/sample) of the following signals:
a. ch5_malespeech.wav ( $8 \mathrm{kHz}, 16 \mathrm{bit})$
b. ch5_music.wav ( $44.1 \mathrm{kHz}, 16 \mathrm{bit})$

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Problem 11

FFT-based perceptual audio synthesis using the MPEG 1 psychoacoustic model 1.
In this computer exercise, we will consider an example to show how the psychoacoustic principles are applied in actual audio coding algorithms. Recall that in Chapter 2, Computer Exercise 2.25, we employed the peak-picking method to select a subset of FFT components for audio synthesis. In this exercise, we will use the just-noticeable-distortion (JND) curve as the "reference" to select the perceptually important FFT components. All the FFT components below the

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