**Properties of** ZCR**:**

The ZCR properties can be summarized as follow.

## 1.**The Principle of Dominant Frequency**

The dominant frequency of a pure sinusoid is the only value in the spectrum. This value of frequency is equal to the ZCR of the signal in one period. If we have a non-sinusoidal periodic signal, its dominant frequency is frequency with the largest amplitude. The dominant frequency (*ω*0) can be evaluated as follow.

$$
\alpha\_o = \frac{\pi E \{ D\_o \}}{N - 1} \tag{2}
$$

4.**Measure of Periodicity**

[44–47, 55–57, 130]*.*

*3.1.2 The STE algorithm*

**Figure 13.**

**103**

*Music and audio sharing some values [65].*

**The Ratio of High ZCR** (RHZCR)

one-window, and can be defined as follow.

RHZCR <sup>¼</sup> <sup>1</sup>

2*N*

*N* X�1 *n*¼0

ZCR*av* ¼

in an audio signal is greater than that of a music, as shown in **Figure 13**.

A signal is said to be purely periodic if and only if.

*Classification and Separation of Audio and Music Signals*

*DOI: http://dx.doi.org/10.5772/intechopen.94940*

Using Eq. (6), it was found that music is more periodic or than audio

It was found that the variation of the ZCR is more discriminative than the exact ZCR, so the RHZCR can be considered as one feature [78]. The RHZCR is defined as the ratio of the number of frames whose ZCR are above 1 over the average ZCR in

> *N* X�1 *n*¼0

where *N* is the number of frames per one-window, *n* is the index of the frame, sgn[.] is a sign function and ZCR(*n*) is the zero-crossing rate at the *n*th frame. In general, audio signals consist of alternating voiced and unvoiced sounds in each syllable rate, while music does not have this kind of alternation. Therefore, from Eq. (7) and Eq. (8), we may observe that the variation of the ZCR (or the RHZCR)

The amplitude of the audio signal varies appreciably with time. In particular, the amplitude of unvoiced segments is generally much lower than the amplitude of voiced segments. The STE of the audio signal provides a convenient representation

*<sup>E</sup>* <sup>1</sup>*<sup>D</sup>* � � <sup>¼</sup> *<sup>E</sup>* <sup>2</sup>*<sup>D</sup>* � � (6)

½sgn ZCR ð Þ ð Þ� *n* ZCR*av* þ 1 (7)

ZCRð Þ *n* (8)

where *N* is the number of intervals, *E*{.} is the expected value, and *Do* is the ZCR per interval.

## 2.**The Highest frequency**

Since *D0* denotes the ZCR of a discrete-time signal *Z*(*i*), let us assume that *Dn* denotes the ZCR of the *nth* derivative of *Z*(*i*), i.e., *D*<sup>1</sup> is the ZCR of the first derivative of *Z*(*i*), *D*<sup>2</sup> is the ZCR of the second derivative of *Z*(*i*), and so on. Then, the highest frequency *ωmax* in the signal can be evaluated as follow.

$$\rho\_{\text{max}} = \lim\_{i \to \infty} \frac{\pi \, E\{D\_i\}}{N - 1} \tag{3}$$

where *N* is the number of samples. If the sampling rate equals 11 KHz, then the change in *ωmax* can be ignored for *i* > 10.

#### 3.**The Lowest frequency**

Assuming that the time period between any two samples is normalized to unity, the derivative of *Z*(*i*) can be defined as *Z*(*i*) *= Z*(*i*) *– Z*(*i*–1). Then, the ZCR of the *n*th derivative of *Z*(*i*) is defined as *Dn.* Now, let us define ∇ <sup>+</sup> as the +ve derivative of *Z*(*i*), then ∇ <sup>+</sup> [*Z*(*i*)] can be defined as follow.

$$\nabla^{+}[Z(i)] = Z(i) + Z(i-1) \tag{4}$$

Now, let us define the ZCR of the *n*th + ve derivative of *Z*(*i*) by the symbol *nD*. Then we can find the lowest frequency *ωmin* of a signal as follow.

$$\mathcal{W}\_{\min} = \lim\_{i \to \infty} \frac{\pi \, E\{\_i D\}}{N - 1} \tag{5}$$

## 4.**Measure of Periodicity**

when *x*(*n*) < 0. An essential not is that the sampling rate must be high

The ZCR properties can be summarized as follow.

1.**The Principle of Dominant Frequency**

unvoiced audio.

**Properties of** ZCR**:**

*Multimedia Information Retrieval*

evaluated as follow.

ZCR per interval.

follow.

follow.

**102**

2.**The Highest frequency**

3.**The Lowest frequency**

enough to catch any crossing through zero. Another important note before evaluating the ZCR is to normalize the signal by subtracting its average value. It is clear from Eq. (1) that the value of the ZCR is proportional to the sign change in the signal, i.e., the dominant frequency of *x*(*n*). Therefore, we may find that the ZCR of music is, in general, higher than that of audio, but not sure at the

The dominant frequency of a pure sinusoid is the only value in the spectrum. This value of frequency is equal to the ZCR of the signal in one period. If we have a non-sinusoidal periodic signal, its dominant frequency is frequency with the largest amplitude. The dominant frequency (*ω*0) can be

*<sup>ω</sup><sup>o</sup>* <sup>¼</sup> *<sup>π</sup> E D*f g*<sup>o</sup>*

where *N* is the number of intervals, *E*{.} is the expected value, and *Do* is the

Since *D0* denotes the ZCR of a discrete-time signal *Z*(*i*), let us assume that *Dn* denotes the ZCR of the *nth* derivative of *Z*(*i*), i.e., *D*<sup>1</sup> is the ZCR of the first derivative of *Z*(*i*), *D*<sup>2</sup> is the ZCR of the second derivative of *Z*(*i*), and so on. Then, the highest frequency *ωmax* in the signal can be evaluated as

where *N* is the number of samples. If the sampling rate equals 11 KHz, then

Assuming that the time period between any two samples is normalized to unity, the derivative of *Z*(*i*) can be defined as *Z*(*i*) *= Z*(*i*) *– Z*(*i*–1). Then, the ZCR of the *n*th derivative of *Z*(*i*) is defined as *Dn.* Now, let us define ∇ <sup>+</sup> as the +ve derivative of *Z*(*i*), then ∇ <sup>+</sup> [*Z*(*i*)] can be defined as

Now, let us define the ZCR of the *n*th + ve derivative of *Z*(*i*) by the symbol *nD*.

*π E <sup>i</sup> D*

Then we can find the lowest frequency *ωmin* of a signal as follow.

*Wmin* ¼ *lim*

*i*!∞

*π E D*f g*<sup>i</sup>*

∇þ½ �¼ *Z i*ð Þ *Z i*ðÞþ *Z i*ð Þ � 1 (4)

*ωmax* ¼ lim *i*!∞

the change in *ωmax* can be ignored for *i* > 10.

*<sup>N</sup>* � *<sup>1</sup>* (2)

*<sup>N</sup>* � <sup>1</sup> (3)

*<sup>N</sup>* � <sup>1</sup> (5)

A signal is said to be purely periodic if and only if.

$$E\{\_1D\} = E\{\_2D\} \tag{6}$$

Using Eq. (6), it was found that music is more periodic or than audio [44–47, 55–57, 130]*.*
