JP2011193216A - Demodulation method, modulation method, demodulator and modulator - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an inexpensive and highly efficient communication system (demodulator and modulator). <P>SOLUTION: A demodulation method includes: a first step of receiving an analog signal to which frequency modulation is performed by a digital signal for transmission to perform sampling extraction of a plurality pieces of time series discrete data from the analog signal; and a second step of demodulating the analog signal to the digital signal by performing mode analysis of the plurality of pieces of discrete data. In addition, the modulation method includes: a first step of inputting the digital signal for transmission; and a second step of performing frequency modulation for changing frequencies of a carrier signal on the basis of the input signal. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a signal modulation technique and a demodulation technique in digital communication.

  Until now, in order to improve the communication speed of digital communication, in order to secure the bandwidth used for communication, the frequency of the carrier signal used for communication between the modulation device on the transmission side and the demodulation device on the reception side (hereinafter referred to as carrier frequency) It was necessary to increase the

  Communication is performed by setting a certain bandwidth within the carrier frequency range, and the spectral efficiency (bit transfer rate [bps] / bandwidth [Hz]) is, for example, high-efficiency IEEE802.11n. The maximum is about 7 [bps / Hz] (= 300 Mbps / 40 MHz). Since the carrier frequency used in the IEEE 802.11n standard is 2.4 GHz / 5 GHz (see Non-Patent Document 1), the amount of information transmitted per cycle of the carrier signal is about 0.13 [bit / cycle] (= 300 Mbps / 2.4 GHz).

Japanese Patent No. 3836847

“IEEE 802.11”, free encyclopedia “Wikipedia”, [online], [searched on March 9, 2010], Internet <URL: http://en.wikipedia.org/wiki/IEEE_802. 11>

  That is, since an advanced technology in an extremely high frequency band is required, it has been difficult to easily realize a high communication speed. Further, the amount of information that can be transmitted per cycle of the carrier signal is small and inefficient.

  The present invention has been made in view of the above problems, and an object of the present invention is to provide an inexpensive and highly efficient communication method.

  The present invention according to claim 1 is a first step of receiving an analog signal frequency-modulated by a digital signal to be transmitted, and sampling and extracting a plurality of time-series discrete data from the analog signal; And a second step of demodulating the digital signal by performing modal analysis on discrete data.

  According to the present invention, since a signal is demodulated using mode analysis, an inexpensive and highly efficient communication method can be provided.

According to the second aspect of the present invention, in the second step, the unique bit string associated with the frequency used for modulation by the modulation device is stored in a storage unit, and the discrete data S _n (where, order n is chronologically.) linear difference equations and _{a k} undetermined coefficients for _{S n = Σ k a k S} n-k ( where, k = 1~K, K is the order of the linear differential equations )), The undetermined coefficient is determined by fitting the linear difference equation to the discrete data, and S _n = Σ _k e ^* (where * = C _k + (2πif) _k + λ _k ) nΔT, k = 1 to K, e ^C is the amplitude, i is the imaginary unit, f is the frequency, λ is the signal attenuation rate, and ΔT is the sampling period). Find the frequency used and respond to that frequency And acquires a bit sequence that from the storage means.

  The present invention according to claim 3 is characterized in that the second step performs the fitting by a least square method.

  According to a fourth aspect of the present invention, there is provided a first step of inputting a digital signal to be transmitted, and frequency modulation for changing a frequency of a carrier signal based on the input digital signal. And a second step performed in a period shorter than one cycle.

  According to the present invention, since the frequency modulation is performed in a period shorter than one cycle of the frequency of the carrier signal, the amount of information transmitted per one cycle (cycle) of the carrier can be increased.

  According to the fifth aspect of the present invention, in the second step, the frequency modulation is performed by generating an analog signal transmitted by using a plurality of sine waves having different frequencies with the frequency of the carrier signal as an upper limit. It is characterized by performing.

  According to the present invention, the frequency modulation is performed by generating an analog signal that is transmitted using a plurality of sine waves having different frequencies up to the frequency of the carrier signal. The amount of information transmitted per one cycle can be maximized, and a highly efficient communication method can be provided.

  According to a sixth aspect of the present invention, in the second step, a bit string specific to each frequency of the plurality of sine waves is allocated and stored in the storage means, and the bit string of the input digital signal is stored in the storage means. A corresponding frequency is acquired from the storage means, and the analog signal is generated using a sine wave having the acquired frequency.

  The present invention according to claim 7 is characterized in that the sine wave is a combination of a plurality of sine waves having different frequencies.

  The present invention according to claim 8 is a signal receiving means for receiving an analog signal frequency-modulated by a digital signal to be transmitted, sampling a plurality of discrete data in time series from the analog signal, and the plurality of discrete signals Signal demodulating means for demodulating the digital signal by mode analysis of data.

  According to the present invention, since a signal is demodulated using mode analysis, an inexpensive and highly efficient communication method can be provided.

In the present invention according to claim 9, the signal demodulating means stores a unique bit string associated with the frequency used for modulation by the modulation device in the storage means, and the discrete data S _n (where n order of when the order along the sequence.) linear difference equations and _{a k} undetermined coefficients for _{S n = Σ k a k S} n-k ( where, k = 1~K, K is linear difference equations. ), The undetermined coefficient is determined by fitting the linear difference equation to the discrete data, and S _n = Σ _k e ^* (where * = C _k + (2πif _k + Λ _k ) nΔT, k = 1 to K, e ^C is the amplitude, i is the imaginary unit, f is the frequency, λ is the signal attenuation factor, and ΔT is the sampling period. Is determined and the corresponding frequency is obtained. And acquires the bit string from said storage means.

  According to a tenth aspect of the present invention, the signal demodulating means performs the fitting by a least square method.

  The present invention according to claim 11 is a signal input means for inputting a digital signal to be transmitted, and frequency modulation for changing the frequency of the carrier signal based on the inputted digital signal, and the frequency of the carrier signal is 1 And a signal modulation means for performing a period shorter than the period.

  According to the present invention, since the frequency modulation is performed in a period shorter than one cycle of the frequency of the carrier signal, the amount of information transmitted per one cycle (cycle) of the carrier can be increased.

  The invention according to claim 12 is characterized in that the signal modulation means performs the frequency modulation by generating an analog signal transmitted using a plurality of sine waves having different frequencies with the frequency of the carrier signal as an upper limit. It is characterized by performing.

  According to the present invention, the frequency modulation is performed by generating an analog signal that is transmitted using a plurality of sine waves having different frequencies up to the frequency of the carrier signal. The amount of information transmitted per one cycle can be maximized, and a highly efficient communication method can be provided.

  According to a thirteenth aspect of the present invention, the signal modulation means allocates a bit string specific to each frequency of the plurality of sine waves and stores it in the storage means, and corresponds to the bit string of the input digital signal. The frequency to be acquired is acquired from the storage means, and the analog signal is generated using a sine wave of the acquired frequency.

  The present invention according to claim 14 is characterized in that the sine wave is a combination of a plurality of sine waves having different frequencies.

  According to the present invention, an inexpensive and highly efficient communication method can be provided.

It is a figure which shows the whole structure of a modulation / demodulation system. It is a figure which shows the code table memorize | stored with the modulation apparatus of Example 1. FIG. It is a figure explaining the frequency modulation in the signal modulation part of Example 1. FIG. It is a figure explaining the frequency demodulated by the signal demodulation part of Example 1. FIG. It is a figure which shows the code table memorize | stored with the modulation apparatus of Example 2. FIG. It is a figure explaining the frequency modulation in the signal modulation part of Example 2. FIG.

  Hereinafter, an embodiment for carrying out the present invention will be described with reference to the drawings.

  FIG. 1 is a diagram illustrating the overall configuration of the modulation / demodulation system according to the first embodiment. The present modulation / demodulation system modulates a digital signal to be transmitted into an analog signal and transmits it, and receives the analog signal transmitted from the modulator 1 and demodulates it into the digital signal. The device 3 is configured to be communicable via a wired or wireless communication network.

  First, the modulation device 1 will be described. The modulation device 1 includes a signal input unit 11 that inputs a digital signal to be transmitted, a signal modulation unit 12 that modulates the input digital signal into an analog signal, and a signal that outputs the modulated analog signal to the communication network. It is comprised with the transmission part 13. FIG. Hereinafter, each functional unit of the modulation device 1 will be described in detail.

  The signal input unit 11 has a function of inputting a digital signal to be transmitted and sending it to the signal modulation unit 12 as a bit string consisting of 1 or 0.

The signal modulation unit 12 has a carrier signal frequency (hereinafter referred to as a carrier frequency) used for communication with the demodulation device 3 as an upper limit, and is unique to four modulation frequencies f _k (k = 1 to 4) having different frequencies. A code table to which bit sequences (00, 01, 10, 11) are assigned is stored in a storage unit (not shown), and a modulation frequency f _k corresponding to the 2-bit bit sequence transmitted from the signal input unit 11 is stored. It has a function of modulating the carrier frequency using a sine wave obtained from the code table and having the obtained modulation frequency _fk .

Specifically, for example, when the code table shown in FIG. 2 is stored in a storage unit (not shown) and the bit string sent from the signal input unit 11 is “0010011101”, as shown in FIG. Then, one period of the carrier frequency is divided into five by the time throttle, a sine wave of the modulation frequency f ₁ corresponding to the first two bits “00” is embedded in the time throttle of the first divided section, and the next two bits “10” the sine wave modulation frequency f ₃ corresponding to "performing frequency modulation of the carrier frequency by repeating the process of embedding the time the throttle of the next divided section, and generates an analog signal. That is, a signal encoded with a sine wave is generated and analogized in a period (each divided section divided into five) shorter than one cycle (cycle) of the carrier frequency.

  The signal transmission unit 13 has a function of outputting the analog signal generated by the signal modulation unit 12 to the outside by wire or wireless.

That is, according to the modulation device 1 of the first embodiment, a code table in which unique bit strings are respectively assigned to four modulation frequencies f _k (k = 1 to 4) with the carrier frequency as an upper limit is stored in advance. The modulation frequency f _k corresponding to 2 bits in the signal sequence of the input digital signal is obtained from the code table, and the obtained modulation frequency f is used for the time throttle of each divided section obtained by dividing one cycle of the carrier frequency into five. _Since the frequency modulation of the carrier frequency is performed by embedding _k sine waves, 10 [bit / cycle] (= 2 bits × 5 time throttle) can be embedded per cycle of the carrier signal. This makes it possible to transmit an information amount approximately 80 times the information amount that can be transmitted by the conventional IEEE802.11n described in the background art.

In the first embodiment, 2 bits are used as the number of bits in the bit string and 4 are used as the number of modulation frequencies _fk . However, the number of bits is n bits (n is an integer of 1 or more). It is also possible to set the number of modulation frequencies f _k to 2 ⁿ .

  In the first embodiment, the number of divisions of the carrier frequency has been described as five. However, even in the case of N division (N is an arbitrary real number larger than 1 and is not limited to an integer), the same applies. An effect can be obtained.

  Next, the demodulator 3 will be described. The demodulating device 3 includes a signal receiving unit 31 that receives an analog signal frequency-modulated by a digital signal to be transmitted, a signal demodulating unit 32 that demodulates the received analog signal into the digital signal, and an external demodulated digital signal. And a signal output unit 33 for outputting the signal. Hereinafter, each functional unit of the demodulator 3 will be described in detail.

The signal receiving unit 31 receives the frequency-modulated analog signal, and uses the analog waveform of the received analog signal at a sampling frequency sufficiently higher than the carrier frequency (in other words, the sampling period ΔT is set to (1 / ( 2ΔT)) >> Sampling is performed so that the carrier frequency is obtained, and discrete data extracted by the sampling is digitized as time-series data S _n (n is an order along the time series) and transmitted to the signal demodulator 32. It has a function to do.

Signal demodulator 32 has a function of demodulating the digital signal by modal analysis series data S _n when sent from the signal receiving unit 31. An example of mode analysis will be described later.

  The signal output unit 33 has a function of outputting an intended digital signal demodulated by the signal demodulation unit 32.

  Next, as an example of mode analysis by the signal demodulator 32, an analysis method using fitting by a linear difference equation will be described with reference to FIG.

Signal demodulation unit 32, to the series data S _n when extracted by the sampling, make a linear difference equations with undetermined coefficients in order to perform the fitting to be described later and a _k (Equation (1)).

なお、Ｋは線形差分方程式の次数を示す。

K represents the order of the linear difference equation.

Determining the unknown coefficients a _k by fitting the time-series data S _n the linear difference equations using a least square method. Thus, the linear differential equation corresponding to the time-series data S _n is determined. Then, by solving the determined linear difference equation, the modulation frequency used for modulation by the modulation device 1 can be obtained. Hereinafter, the process until the modulation frequency is derived from the linear difference equation will be described.

Since there is only one modulation frequency in each divided section shown in FIG. 3, the degree K of the linear difference equation may be 2 or more. This is because, in the first embodiment, one modulation frequency is calculated as a set of two frequencies (± f _k ) having different signs, and therefore the order K needs to be double the modulation frequency to be obtained. Because. Hereinafter, in order to facilitate understanding, a case where K = 2 will be described.

  When K = 2, the linear difference equation shown in Expression (1) becomes Expression (2).

ここで、定数ｂ_１を式（３）とし、定数ｂ_２を式（４）とし、ｃ_１，ｃ_２を別途Ｓ_ｎへのフィッティングによって定める定数とすると、

Here, the constants _{b 1} and Equation (3), the constant _{b 2} and Equation _(4), when constants determined by fitting the c 1, _{c 2} to separate _{S n,}

式（２）を式（５）で表現することができる。

Expression (2) can be expressed by Expression (5).

また、式（５）は、指数関数を用いて式（６）のように表現することができる。

Moreover, Formula (5) can be expressed like Formula (6) using an exponential function.

ここで、上記Ｓ_ｎを、変調用周波数を明示的に含む形で表記するため、式（７）〜式（１２）の定数を導入する。

Here, the S _n, for which appear in the form that includes explicitly modulation frequency, introduces a constant in equation (7) to (12).

すると、Ｓ_ｎは式（１３）に示すように表現できる。

Then, _{S n} can be expressed as shown in equation (13).

なお、定数ｂ_１，ｂ_２の定義よりλ_１＝λ_２、ｆ_１＝−ｆ_２が常に成立し、変調用周波数は、ｆ_１＝−ｆ_２として得ることが可能となる。

Note that λ ₁ = λ ₂ and f ₁ = −f ₂ are always established from the definitions of the constants b ₁ and b ₂ , and the modulation frequency can be obtained as f ₁ = −f ₂ .

  That is, since Equation (1) is linear, it can be easily solved using a known method such as the DKA (Durand-Kerner-Aberth) method. As a result, Equation (1) to Equation (1) 14) can be derived.

なお、ｅ^Ｃは振幅、ｉは虚数単位、ｆは周波数、λは信号減衰率、ΔＴは信号受信部３１でサンプリングしたサンプリング周期を示す。

Here, e ^C is the amplitude, i is the imaginary unit, f is the frequency, λ is the signal attenuation rate, and ΔT is the sampling period sampled by the signal receiving unit 31.

Then, the signal demodulating unit 32 stores the code table shown in FIG. 2 in a storage unit (not shown), obtains the modulation frequency f _k using the equation (14), and obtains the obtained modulation frequency f _k. Are obtained from the code table and sequentially output to the signal output unit 33.

Note that the method described in Patent Document 1 can be used to extract the modulation frequency f _k . Further, when the order K is set to 3 or more, f _k that maximizes the amplitude ‖e ^Ck ‖ may be adopted as an intended frequency.

  Generally, when modulation is performed using L sets of modulation frequencies simultaneously, the order K needs to be 2L or more, and the case of L = 1 (that is, the order K is 2) corresponds to the first embodiment. , L = 2 (that is, when the order K is 4) corresponds to Example 2 described later.

That is, according to the demodulator 3 of Example 1, the signal demodulation unit 32, since the demodulated series data S _n when sent from the signal receiving unit 31 into a digital signal by modal analysis, high efficiency at low cost A communication method can be provided.

  Hereinafter, a processing flow of the modulation / demodulation system according to the first embodiment will be described. First, a digital signal to be transmitted is input by the signal input unit 11 of the modulation device 1 and is transmitted to the signal modulation unit 12 as a bit string consisting of 1 or 0 (S1).

Next, the signal modulation unit 12 stores in the storage unit (not shown) a code table in which the carrier frequency of the carrier signal is set as the upper limit and the bit strings specific to the four modulation frequencies f _k having different frequencies are respectively assigned. Then, the modulation frequency f _k corresponding to the 2-bit bit string transmitted from the signal input unit 11 is acquired from the code table, and one cycle of the carrier frequency is divided into five using the acquired sine wave of the modulation frequency f _k Each divided section is modulated (S2).

  Finally, the signal transmission unit 13 outputs the analog signal generated by the signal modulation unit 12 to the demodulation device 3 by wire or wireless (S3).

Next, the signal receiving unit 31 of the demodulator 3 receives the analog signal output from the modulator 1, samples extracted discrete data as time series data S _n (S4).

Then, the signal demodulator 32, modal analysis series data S _n when extracted by the signal receiving unit 31 (for example, analysis of using a fitting by linear difference equations discussed above) and demodulates a digital signal by (S5 ).

  Finally, the signal output unit 33 outputs the digital signal demodulated by the signal demodulation unit 32 (S6).

  Next, a second embodiment will be described. Hereinafter, the signal modulation unit 12 of the modulation device 1 and the signal demodulation unit 32 of the demodulation device 3 that are different from those of the first embodiment will be described. Since the characteristic functions of the other functional units are the same as those described in the first embodiment, a duplicate description is omitted here.

The signal modulation unit 12 uses the carrier frequency of the carrier signal used for communication with the demodulator 3 as an upper limit, and an arbitrary set of modulation frequencies (f _k (k = 1 to 4) and g _k (k = 1 to 4). Are stored in a storage unit (not shown), and are sent from the signal input unit 11. The code table in which unique bit strings (0000, 0001,. A set of modulation frequencies f _k and g _k corresponding to a bit string of bits is acquired from a code table, and the carrier frequency is modulated using the acquired sine wave of the modulation frequency f _k and sine wave of the modulation frequency g _k It has a function to do.

Specifically, for example, when the code table shown in FIG. 5 is stored in a storage unit (not shown) and the bit string transmitted from the signal input unit 11 is “00000001101111100100”, as shown in FIG. In addition, one cycle of the carrier frequency is divided into five by time throttle, and the synthesized wave of the sine wave of the modulation frequency f _{1 and} the sine wave of the modulation frequency g ₁ corresponding to the first 4 bits “0000” is divided first. Embedding in the time throttle of the section, and embedding the synthesized wave of the sine wave of the modulation frequency f ₂ and the modulation frequency g ₁ corresponding to the next 4 bits “0001” in the time throttle of the next divided section By repeating, frequency modulation of the carrier frequency is performed to generate an analog signal.

  Thus, according to the modulation device 1 of the first embodiment, 20 [bit / cycle] (= 4 bits × 5 time throttle) can be embedded per cycle of the carrier signal. That is, it is possible to transmit twice the amount of information that can be transmitted in the first embodiment.

  Note that although two modulation frequency groups have been described, three or more groups may be used.

On the other hand, the signal demodulator 32 differs from the first embodiment in that the degree K of the linear difference equation shown in the equation (1) is 4 or more. As a result, two modulation frequencies used for modulation are extracted for each divided section shown in FIG. When the order K is set to 5 or more, two f _k and g _k from the larger amplitude と し て e ^Ck ‖ may be adopted as intended frequencies.

  As described above, according to the first and second embodiments, the signal demodulator 32 demodulates the signal using the mode analysis, so that it is possible to provide an inexpensive and highly efficient communication method.

  According to the first and second embodiments, since the signal modulation unit 12 performs frequency modulation in a period shorter than one cycle of the frequency of the carrier signal, the amount of information transmitted per one cycle (cycle) of the carrier can be increased. .

  According to the first and second embodiments, the signal modulation unit 12 performs frequency modulation by generating an analog signal transmitted using a plurality of sine waves having different frequencies, with the frequency of the carrier signal as an upper limit. Using the lowest possible carrier frequency, the amount of information transmitted per one cycle of the carrier can be maximized, and a highly efficient communication method can be provided.

  According to the second embodiment, frequency modulation is performed using a composite wave composed of a plurality of modulation frequencies of a sine wave, so that the amount of information to be transmitted can be increased as compared with the first embodiment.

  Finally, according to the first and second embodiments, it is possible to realize digital communication in which the information density per carrier cycle is higher than that of the conventional technology.

DESCRIPTION OF SYMBOLS 1 ... Modulator 11 ... Signal input part 12 ... Signal modulator 13 ... Signal transmitter 3 ... Demodulator 31 ... Signal receiver 32 ... Signal demodulator 33 ... Signal output part S1-S6 ... Step

Claims (14)

A first step of receiving an analog signal frequency-modulated by a digital signal to be transmitted and sampling a plurality of time-series discrete data from the analog signal;
A second step of demodulating the digital signal by modal analysis of the plurality of discrete data;
The demodulation method characterized by having. The second step includes
A unique bit string associated with the frequency used for modulation by the modulation device is stored in the storage means, and an undetermined coefficient is a for the discrete data S _n (where n is an order in time series). linear difference equations and _{k S n = Σ k a k} S n-k ( where, k = 1 to K, K is the order. of linear difference equations) vertical and fitting the linear difference equations with the discrete data Thus, the undetermined coefficient is determined, and S _n = Σ _k e ^* (where * = C _k + (2πif _k + λ _k ) nΔT, k = 1 to K, e ^C is the amplitude, i is an imaginary unit, f is a frequency, λ is a signal attenuation rate, and ΔT is a sampling period.) A frequency analysis is used to obtain a frequency used for the frequency modulation, and a bit string corresponding to the frequency is stored in the storage unit. Characteristic to get from Demodulating method of claim 1,. The second step includes
The demodulation method according to claim 2, wherein the fitting is performed by a least square method. A first step of inputting a digital signal to be transmitted;
A second step of performing frequency modulation for changing a frequency of a carrier signal based on the input digital signal in a period shorter than one cycle of the frequency of the carrier signal;
A modulation method characterized by comprising: The second step includes
The modulation method according to claim 4, wherein the frequency modulation is performed by generating an analog signal transmitted using a plurality of sine waves having different frequencies with the frequency of the carrier signal as an upper limit. The second step includes
A bit string specific to each frequency of the plurality of sine waves is assigned and stored in the storage means, and a frequency corresponding to the bit string of the input digital signal is acquired from the storage means, and the sine of the acquired frequency is obtained. The modulation method according to claim 5, wherein the analog signal is generated using a wave. The sine wave is
The modulation method according to claim 5 or 6, wherein a plurality of sine waves having different frequencies are combined. A signal receiving means for receiving an analog signal frequency-modulated by a digital signal to be transmitted, and sampling and extracting a plurality of discrete data in time series from the analog signal;
A signal demodulating means for demodulating the digital signal by performing mode analysis on the plurality of discrete data;
A demodulating device comprising: The signal demodulating means includes
A unique bit string associated with the frequency used for modulation by the modulation device is stored in the storage means, and an undetermined coefficient is a for the discrete data S _n (where n is an order in time series). linear difference equations and _{k S n = Σ k a k} S n-k ( where, k = 1 to K, K is the order. of linear difference equations) vertical and fitting the linear difference equations with the discrete data Thus, the undetermined coefficient is determined, and S _n = Σ _k e ^* (where * = C _k + (2πif _k + λ _k ) nΔT, k = 1 to K, e ^C is the amplitude, i is an imaginary unit, f is a frequency, λ is a signal attenuation rate, and ΔT is a sampling period.) A frequency analysis is used to obtain a frequency used for the frequency modulation, and a bit string corresponding to the frequency is stored in the storage unit. Characteristic to get from Demodulator of claim 8. The signal demodulating means includes
The demodulator according to claim 9, wherein the fitting is performed by a least square method. A signal input means for inputting a digital signal to be transmitted;
Signal modulation means for performing frequency modulation for changing the frequency of a carrier signal based on the input digital signal in a period shorter than one cycle of the frequency of the carrier signal;
A modulation device comprising: The signal modulating means includes
12. The modulation device according to claim 11, wherein the frequency modulation is performed by generating an analog signal transmitted using a plurality of sine waves having different frequencies with the frequency of the carrier signal as an upper limit. The signal modulating means includes
A bit string specific to each frequency of the plurality of sine waves is assigned and stored in the storage means, and a frequency corresponding to the bit string of the input digital signal is acquired from the storage means, and the sine of the acquired frequency is obtained. The modulation apparatus according to claim 12, wherein the analog signal is generated using a wave. The sine wave is
The modulation device according to claim 12 or 13, wherein a plurality of sine waves having different frequencies are combined.

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