CN112929030A - Noise shaping method for direct alignment detection DMT system - Google Patents
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Abstract
本发明属于光通信系统、高速光信号处理技术领域，更具体地，涉及一种直调直检DMT系统的噪声整形方法。本发明针对传统DMT信号PAPR高以及低位宽DAC量化噪声高的问题，提出了噪声整形技术。噪声整形技术可以同时对裁剪噪声和量化噪声起整形的作用。通过把信号带内的噪声推到信号带外，降低信号带内的量化噪声，提升SQNR，近而改善整个系统的性能。
The invention belongs to the technical fields of optical communication systems and high-speed optical signal processing, and more particularly, relates to a noise shaping method of a direct modulation and direct detection DMT system. Aiming at the problems of high PAPR of traditional DMT signals and high quantization noise of low-bit-width DACs, the present invention proposes a noise shaping technology. Noise shaping techniques can simultaneously shape clipping noise and quantization noise. By pushing the noise in the signal band to the outside of the signal band, the quantization noise in the signal band is reduced, the SQNR is improved, and the performance of the entire system is improved.
Description
Technical Field
The invention belongs to the technical field of optical communication systems and high-speed optical signal processing, and particularly relates to a noise shaping method of a direct alignment direct detection DMT system.
Background
To meet the requirement of high transmission rate, multi-carrier modulation techniques have been proposed instead of single carrier communication systems. DMT, as shown in fig. 1, is a multi-carrier modulation technique, which is formed by aggregating a plurality of non-interfering sub-carriers with different frequencies, and the sub-carriers can flexibly adopt different modulation formats. In recent years, with the rapid development of communication technology, people have higher and higher requirements on data capacity, and DMT signals are widely applied to high-capacity short-distance transmission systems with the advantages of high-efficiency spectrum utilization rate and strong resistance to inter-channel interference. In the dc-dc system, a low quantization bit width DAC generates a large amount of quantization noise during the digital-to-analog conversion of the DMT signal, and the signal strength of the DMT signal is insufficient due to a high PAPR, so that the quantization signal-to-noise ratio (SQNR) is low.
Chinese patent CN111131122A, published as 20200508, discloses an equalizing method and device for an optical transmission system based on DMT modulation and beat frequency detection, which removes the imaginary part of the DMT signal, reduces the noise of the DMT signal, and greatly improves the performance of the DMT signal under the condition of beat frequency detection; however, this method cannot solve the problem of low total signal power caused by high peak-to-average power ratio (PAPR) of discrete multi-tone (DMT) signals in the dc-dc system, and the problem of a large amount of quantization noise caused by low bit width digital-to-analog conversion (DAC) devices at the transmitting end.
Disclosure of Invention
The present invention overcomes at least one of the above-mentioned drawbacks of the prior art, and provides a noise shaping method for a direct alignment DMT system, which effectively improves the SQNR of the transmitted signal, thereby improving the performance of the entire direct alignment DMT system.
In order to solve the technical problems, the invention adopts the technical scheme that: a method of noise shaping in a direct alignment DMT system, comprising the steps of:
s1, generating DMT signal with frequency band of 0-omegasIn a range of storing signals, frequency band omegas-a null subcarrier within a range of-pi;
s2, the signal passes through a cutter and a quantizer, and the whole signal spectrum generates relatively large noise;
s3, in order to reduce quantization noise, the noise shaping modulator brings 0-omega of signal bandsIs pushed out of band by omegasA range of-pi;
and S4, filtering noise outside the signal band by using a low-pass filter to obtain a signal with higher SQNR.
The invention provides a noise shaping technology aiming at the problems of high PAPR (peak-to-average power ratio) of the traditional DMT signal and high quantization noise of a low-bit-width DAC (digital-to-analog converter). The noise shaping technique may simultaneously shape clipping noise and quantization noise. By pushing the noise in the signal band out of the signal band, the quantization noise in the signal band is reduced, the SQNR is improved, and the performance of the whole system is improved.
Further, the generation of DMT signals specifically includes: DMT signals were generated offline in MATLAB; firstly, a pseudo-random bit sequence is mapped to 32-QAM/64-QAM constellation points on a frequency domain, then, a frequency domain signal is converted into a time domain through IFFT, a real DMT signal is generated by using a Hermite symmetric algorithm, and finally, a cyclic prefix is added to prevent intersymbol interference.
Further, in step S2, the clipper sets a desired peak threshold M in the time domain, and inputs the signal S [ n ]]Limiting the amplitude exceeding M to M, keeping the original signal without the signal exceeding M, and outputting the signal
Expressed as:
further, the noise shaping process needs the noise of the signal to be uncorrelated, but the noise generated by the clipping process is nonlinear noise, and the clipping noise needs to be decorrelated. Obviously, the signal after clipping
The gaussian distribution is no longer satisfied and therefore the clipping noise is non-linear noise. In order to make the clipping noise be Gaussian white noise, the signal after clipping is processed
And the original signal s [ n ]]Performing correlation processing to output signal
Wherein the correlation coefficient
Noise of cutting
The clipping noise is white gaussian noise at this time and is uncorrelated with the signal.
Further, in the step S2, the quantization process is an amplitude classification process, and due to the limitation of the quantization bit width, a certain error may exist in the quantization process; suppose the quantization bit width of the quantizer is N and the reference voltage is Vref，hiFor each bit of the quantizer output, eqTo quantify noise, VinFor the input quantized signal, the output to input relationship is then obtained:
further, the output V of the modulator is represented as:
V＝U+(G+1)E
＝U+NTF×E
where U is the input signal, E is noise, and the Noise Transfer Function (NTF) ═ G + 1; it can be seen from the above formula that the modulator does not affect the signal, but only acts on the noise; in order to make the NTF have high-pass properties, the structure of the function G is designed as an FIR filter;
the function G is represented in the z-domain as:
G(z)＝h1z-1+h2z-2+…hnz-n
where n is the number of taps of the FIR filter, hiAre tap coefficients.
Furthermore, the number of the taps is 10-13. Simulation shows that the more the taps of the FIR filter are, the stronger the shaping capability is, and more noise can be pushed out of band, but when the number of taps is large enough, the shaping capability is not improved any more.
Further, in order to obtain the minimum value of quantization noise in a signal band, assuming that the square value of NTF is represented by P, it is necessary to determine the tap coefficient h when P is the minimum value in the bandi(ii) a According to z ═ e-jωIn the frequency band 0-omegasThe minimum value of P of (a) is:
suppose that the signal is between 0 and omegasThe frequency range is divided into t parts: { omega [ [ omega ] ]1，ω2，…ωt}, the above formula can be written as:
The minimum value of the quantization noise within the signal band is expressed as:
furthermore, the amplitude-frequency characteristic of the NTF causes uneven distribution of quantization noise in the signal band, so that a frequency domain pre-emphasis technique is required to ensure that the signal is in a range from 0 to ωsAn internal flat distribution; equally dividing the DMT signal into s parts in the 0-pi frequency band, wherein the signal band has a frequency band of 0-omegasAccounts for t parts; the squared value P of NTF is written as:
introducing a weight matrix W
Thus, the optimal problem becomes:
min‖W(1+Eh)‖2
in the formula, W1＝W2＝…Wt，Wt+1＝Wt+2＝…Ws，R＝Wt/WsThe value of (2) is in direct proportion to the shaping capability, and when the value of R is overlarge, the feedback noise is overlarge, so that the modulator is easily overloaded; a clipper is added to the feedback loop to prevent overload caused by excessive quantization noise of the feedback. But excessive clipping by the clipper results in significant nonlinear noise. Simulation shows that when R is 24, the clipping degree is 10dB, and the shaping capacity reaches the upper limit.
Further, the step S4 specifically includes: after the quantized signal is output from DAC, low-pass filter is used to take out the signal band by omegasThe noise in the range of-pi is filtered out and the signal is then modulated onto a carrier for transmission.
Compared with the prior art, the beneficial effects are: on one hand, the invention provides a noise shaping method of a direct alignment direct detection DMT system, which cuts signals by using a cutter, and carries out noise shaping on the cut noise to improve the total power of the signals; and on the other hand, the quantization noise generated by the DAC at the transmitting end is shaped, so that the quantization noise in the signal band is reduced. The SQNR of the transmitted signal is improved from the two aspects, so that the performance of the whole DMT direct alignment detection system is improved.
Drawings
Figure 1 is a DMT signal formation process.
FIG. 2 is a schematic diagram of the operation of the noise shaping modulator of the present invention; (a) for the DMT signal spectrum, (b) for the spectrum that produces noise after clipping and quantization, (c) for the noise-shaped signal spectrum, and (d) for the low-pass filtered recovered signal spectrum.
FIG. 3 is a schematic diagram of the present invention, wherein FIG. 3(a) shows the cropping process and FIG. 3(b) shows a linear model thereof.
Fig. 4 is a block diagram of a noise shaping modulator of the present invention.
Fig. 5 is a block diagram of the FIR filter structure of the present invention.
FIG. 6 is a graph of the number of taps of the FIR filter versus the SQNR boost level in an embodiment of the present invention.
Fig. 7 is an amplitude-frequency characteristic curve of a noise transfer function in the embodiment of the present invention.
Fig. 8 is a noise shaping modulator with a clipper added to the feedback loop in an embodiment of the present invention.
Fig. 9 is an amplitude-frequency characteristic of the in-band flat noise-shaping modulator NTF in an embodiment of the present invention.
FIG. 10 is a block diagram of a Digital Signal Processing (DSP) flow and a diagram of an experimental setup in an embodiment of the present invention; (a) DMT signal spectrum, (b) signal spectrum after noise shaping.
FIG. 11 is a BER simulation curve corresponding to white Gaussian noise with different power added in the embodiment of the present invention; (a) a signal modulated by a modulator of 5-bit quantization bit width, and (b) a signal modulated by a modulator of 6-bit quantization bit width.
Fig. 12 is a BER curve corresponding to different received powers and a constellation diagram when the received power is 3dBm in the embodiment of the present invention.
Detailed Description
The drawings are for illustration purposes only and are not to be construed as limiting the invention; for the purpose of better illustrating the embodiments, certain features of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted. The positional relationships depicted in the drawings are for illustrative purposes only and are not to be construed as limiting the invention.
As shown in fig. 2, a method for noise shaping in a direct tone DMT system includes the steps of:
s1, generating DMT signal with frequency band of 0-omegasIn a range of storing signals, frequency band omegas-a null subcarrier within a range of-pi; the frequency spectrum is shown in fig. 2 (a);
s2, the signal passes through a clipper and a quantizer with the quantization bit width of 5-bit, and the whole signal spectrum generates large noise; as shown in FIG. 2 (b);
s3, in order to reduce quantization noise, the noise shaping modulator brings 0-omega of signal bandsIs pushed out of band by omegasA range of-pi; as shown in FIG. 2 (c);
s4, filtering noise outside the signal band by using a low-pass filter to obtain a signal with higher SQNR, as shown in figure 2 (d).
The invention provides a noise shaping technology aiming at the problems of high PAPR (peak-to-average power ratio) of the traditional DMT signal and high quantization noise of a low-bit-width DAC (digital-to-analog converter). The noise shaping technique may simultaneously shape clipping noise and quantization noise. By pushing the noise in the signal band out of the signal band, the quantization noise in the signal band is reduced, the SQNR is improved, and the performance of the whole system is improved.
In one embodiment, the generation of the DMT signal specifically includes: DMT signals were generated offline in MATLAB; first, a pseudo-random bit sequence is mapped to 32-QAM/64-QAM constellation points in the frequency domain, then the frequency domain signal is transformed to the time domain by IFFT, a real DMT signal is generated using hermite symmetry algorithm, and finally a Cyclic Prefix (CP) is added to prevent inter-symbol interference (ISI).
In step S2, the generation of the clipping noise specifically includes the steps of:
the clipper is to set a desired peak threshold M in the time domain, and input the signal s [ n ]]The amplitude exceeding M is limited to M, and the signal not exceeding M is kept as it is, as shown in FIG. 3(a), and the output signal
Expressed as:
the noise shaping process needs the noise of the signal to be uncorrelated, but the noise generated by the clipping process is nonlinear noise, and the clipping noise needs to be decorrelated. Display deviceThen, the signal after clipping
The gaussian distribution is no longer satisfied and therefore the clipping noise is non-linear noise. In order to make the clipping noise be Gaussian white noise, the signal after clipping is processed
And the original signal s [ n ]]Performing a correlation process, wherein a schematic diagram is shown in fig. 3, fig. 3(a) is a clipping process, and fig. 3(b) is a linear model thereof; output signal
Wherein the correlation coefficient
Noise of cutting
The clipping noise is white gaussian noise at this time and is uncorrelated with the signal.
In step S2, the generation of quantization noise specifically includes the steps of:
the quantization process is a process of classifying the amplitude, and due to the limitation of the quantization bit width, a certain error exists in the quantization process; suppose the quantization bit width of the quantizer is N and the reference voltage is Vref，hiFor each bit of the quantizer output, eqTo quantify noise, VinFor the input quantized signal, the output to input relationship is then obtained:
in step S3, a noise feedback loop is designed to form a closed loop, thereby shaping noise. Figure 4 shows a linear model of a noise-shaping modulator.
The output V of the modulator is represented as:
V＝U+(G+1)E
＝U+NTF×E
where U is the input signal, E is noise, and the Noise Transfer Function (NTF) ═ G + 1; it can be seen from the above formula that the modulator does not affect the signal, but only acts on the noise; in order to make the NTF have high-pass properties, the structure of the function G is designed as an FIR filter; the structural block diagram is shown in fig. 5.
The function G is represented in the z-domain as:
G(z)＝h1z-1+h2z-2+…hnz-n
where n is the number of taps of the FIR filter, hiAre tap coefficients.
Simulation shows that the more the taps of the FIR filter are, the stronger the shaping capability is, and more noise can be pushed out of band, but when the number of taps is large enough, the shaping capability is not improved any more. Fig. 6 is a graph showing the number of taps of the FIR filter and the SQNR lifting degree. After the number of taps exceeds 13, the SQNR lifting is not obvious any more, and preferably, the number of taps is taken to be 13.
Further, in order to obtain the minimum value of quantization noise in a signal band, assuming that the square value of NTF is represented by P, it is necessary to determine the tap coefficient h when P is the minimum value in the bandi(ii) a According to z ═ e-jωIn the frequency band 0-omegasThe minimum value of P of (a) is:
suppose that the signal is between 0 and omegasThe frequency range is divided into t parts: { omega [ [ omega ] ]1，ω2，…ωt}, the above formula can be written as:
let 1 ═ 11 … 1]T,h＝[h1 h2 … hn]T，
The minimum value of the quantization noise within the signal band is expressed as:
since E is a low rank matrix, the least squares problem that minimizes (Eh +1) will have an infinite number of solutions, where (h ═ E '× (-1)) found by solving the generalized pseudo-inverse matrix E' of E is a norm less than any other solution.
The obtained tap coefficient hiThe amplitude-frequency characteristic curve of the NTF is obtained by substituting the NTF, as shown in fig. 7.
Further, as shown in fig. 7, the amplitude-frequency characteristic of NTF causes uneven distribution of quantization noise in the signal band, so that it is necessary to adopt frequency domain pre-emphasis technique to ensure that the signal is in the range of 0 to ωsAn internal flat distribution; equally dividing the DMT signal into s parts in the 0-pi frequency band, wherein the signal band has a frequency band of 0-omegasAccounts for t parts; the squared value P of NTF is written as:
introducing a weight matrix W
Thus, the optimal problem becomes:
min‖W(1+Eh)‖2
in the formula, W1＝W2＝…Wt，Wt+1＝Wt+2＝…Ws，R＝Wt/WsThe value of (2) is in direct proportion to the shaping capability, and when the value of R is overlarge, the feedback noise is overlarge, so that the modulator is easily overloaded; as shown in fig. 8, a clipper can be added to the feedback loop to prevent overload due to excessive quantization noise in the feedback. But excessive clipping by the clipper results in significant nonlinear noise. Simulation shows that when R is 24, the clipping degree is 10dB, and the shaping capacity reaches the upper limit.
H is to beiThe amplitude-frequency characteristic curve of the NTF of the in-band flat noise shaping modulator is obtained by substituting the NTF, as shown in fig. 9.
The low-pass filter filters out-of-band noise:
the step S4 specifically includes: after the quantized signal is output from DAC, low-pass filter is used to take out the signal band by omegasThe noise in the range of-pi is filtered out and the signal is then modulated onto a carrier for transmission.
The following describes a specific implementation of the present invention, and the present invention is analyzed by simulation and experiment.
FIG. 10 shows a block diagram of a Digital Signal Processing (DSP) flow and a diagram of an experimental setup according to the present invention.
(1) And a transmitting end DSP:
in the DSP of the transmitting end, a pseudo-random bit sequence is firstly mapped into 32-QAM/64-QAM constellation points, and a real DMT signal is generated after modulation. After the receiving end estimates the channel by using the training sequence, the channel is used for the transmitting end to carry out pre-equalization. And then, cutting the signal after pre-equalization and shaping cutting noise, finally, quantizing the cutting signal by 5-bit/6-bit, shaping quantization noise, and inputting the obtained quantized signal into the DAC.
(2) Receiving end DSP
At the receiving end, the directly detected signals are synchronized first. And carrying out channel equalization on the received data by utilizing the training sequence. And finally, carrying out constellation point inverse mapping on the data, and calculating the bit error rate.
(3) Experimental device
The experimental system is a direct alignment detection experimental system, firstly, at a transmitting end, a signal generated by MATLAB off-line is loaded to a DAC with 80-GSa/s sampling rate, then, after out-of-band noise of the signal is filtered by a low-pass filter, the signal is amplified by an Electric Amplifier (EA) with a band limit of 30-GHz and a gain of 20 dB. Then, an electric absorption modulation laser (EML) with the wavelength of 1550nm is used for modulating an electric signal onto an optical carrier, the electric signal is transmitted through a few-mode optical fiber of 2-km, and then the power of the carrier is adjusted by an optical attenuator. At the receiving end, the signal received by the Photoelectric Detector (PD) is collected by an oscilloscope and is processed by MATLAB off line.
And (4) analyzing results:
by utilizing the test system to build simulation, DMT signals of 25GHz are respectively modulated by noise shaping modulators with 5-bit and 6-bit quantized bit widths, and then transmission with a modulation format of 32-QAM/64-QAM can be realized, and simulation results of the DMT signals are respectively shown in fig. 11(a) and fig. 11 (b). In practical experiments, after the DMT signal is modulated by the noise shaping modulator with 5-bit quantization bit width, the transmission of the 32-QAM modulation format can be realized, and fig. 12 shows experimental results.
As can be seen from fig. 11(a), at BER 3.8E-3, the performance of the 32-QAM DMT signal modulated by the modulator with 5-bit quantization bit width is improved by about 2.2dB over the conventional 32-QAM DMT signal. As can be seen from fig. 11(b), at BER 3.8E-3, the performance of the 64-QAM DMT signal modulated by the modulator with 6-bit quantization bit width is improved by about 1dB over the conventional 64-QAM DMT signal. Also, as can be seen in both fig. 11(a) and 11(b), the signal performance improvement through the noise shaping modulator is more pronounced as the white gaussian noise in the channel is reduced. This is because the noise sources within the channel include quantization noise and other noise, whereas noise shaping can only work on quantization noise. When quantization noise plays a leading role in the system, the noise shaping modulator obviously improves the system performance; the noise shaping modulator is less effective for system performance improvement when other noise is dominant within the system.
As can be seen from fig. 12, after signals are transmitted through a system of back-to-back (BTB) and 2-km Single Mode Fiber (SMF), the noise shaping modulator can bring about 2.5dB improvement to the system performance at BER 3.8E-3. Fig. 12(a) and (b) are the constellation diagrams of DMT signals at a received power (ROP) of 3dBm in transmission systems of 2-km SMF and BTB, respectively. FIGS. 12(c) and (d) are the constellation diagrams for noise shaped signals with ROP of 3dBm in 2-km SMF and BTB transmission systems, respectively.
Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention, and that variations, modifications, substitutions and alterations can be made to the above embodiments by those of ordinary skill in the art within the scope of the present invention.
It should be understood that the above-described embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Other variations and modifications will be apparent to persons skilled in the art in light of the above description. And are neither required nor exhaustive of all embodiments. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.
Claims (10)
1. A method for noise shaping in a direct alignment DMT system, comprising the steps of:
s1, generating DMT signal with frequency band of 0-omegasIn a range of storing signals, frequency band omegas-a null subcarrier within a range of-pi;
s2, the signal passes through a cutter and a quantizer, and the whole signal spectrum generates relatively large noise;
s3, in order to reduce quantization noise, the noise shaping modulator brings 0-omega of signal bandsIs pushed out of band by omegasA range of-pi;
and S4, filtering noise outside the signal band by using a low-pass filter to obtain a signal with higher SQNR.
2. The method of claim 1, wherein the generating the DMT signal comprises: DMT signals were generated offline in MATLAB; firstly, a pseudo-random bit sequence is mapped to 32-QAM/64-QAM constellation points on a frequency domain, then, a frequency domain signal is converted into a time domain through IFFT, a real DMT signal is generated by using a Hermite symmetric algorithm, and finally, a cyclic prefix is added to prevent intersymbol interference.
3. The method of claim 1, wherein the step S2 is performed by setting a desired peak threshold M in the time domain and applying the input signal S [ n ] to the slicer]Limiting the amplitude exceeding M to M, keeping the original signal without the signal exceeding M, and outputting the signal
Expressed as:
4. the method of claim 3, wherein the noise-shaping of the DMT system is performed on the signal after clipping
And the original signal s [ n ]]Performing correlation processing to output signal
Wherein the correlation coefficient
Noise of cutting
The clipping noise is white gaussian noise at this time and is uncorrelated with the signal.
5. The noise shaping method of the dc-dc DMT system as claimed in claim 4, wherein in step S2, the quantization process is an amplitude classification process, and there is a certain error in the quantization process due to the limitation of quantization bit width; suppose the quantization bit width of the quantizer is N and the reference voltage is Vref，hiFor each bit of the quantizer output, eqTo quantify noise, VinFor the input quantized signal, the output to input relationship is then obtained:
6. the noise shaping method of the DMT system as claimed in any one of claims 1 to 5, wherein the output V of the modulator is expressed as:
V＝U+(G+1)E
＝U+NTF×E
where U is the input signal, E is noise, and the Noise Transfer Function (NTF) ═ G + 1; in order to make the NTF have high-pass properties, the structure of the function G is designed as an FIR filter;
the function G is represented in the z-domain as:
G(z)＝h1z-1+h2z-2+…hnz-n
where n is the number of taps of the FIR filter, hiAre tap coefficients.
7. The noise shaping method of the DMT system according to claim 6, wherein the number of taps is 10 to 13.
8. According to claim 6The noise shaping method of the direct alignment DMT system is characterized in that, in order to obtain the minimum value of quantization noise in a signal band, assuming that P represents the square value of NTF, it is necessary to determine the tap coefficient h when P is the minimum value in the bandi(ii) a According to z ═ e-jωIn the frequency band 0-omegasThe minimum value of P of (a) is:
suppose that the signal is between 0 and omegasThe frequency range is divided into t parts: { omega [ [ omega ] ]1，ω2，…ωt}, the above formula can be written as:
let 1 ═ 11 … 1]T,h＝[h1 h2 … hn]T，
The minimum value of the quantization noise within the signal band is expressed as:
9. direct tune according to claim 8Method for noise shaping in direct view DMT systems, characterized in that frequency domain pre-emphasis is used to ensure that the signal is in the range 0-omegasAn internal flat distribution; equally dividing the DMT signal into s parts in the 0-pi frequency band, wherein the signal band has a frequency band of 0-omegasAccounts for t parts; the squared value P of NTF is written as:
introducing a weight matrix W
Thus, the optimal problem becomes:
min‖W(1+Eh)‖2
in the formula, W1＝W2＝…Wt，Wt+1＝Wt+2＝…Ws，R＝Wt/WsThe value of (2) is in direct proportion to the shaping capability, and when the value of R is overlarge, the feedback noise is overlarge, so that the modulator is easily overloaded; a clipper is added to the feedback loop to prevent overload caused by excessive quantization noise of the feedback.
10. The noise shaping method of the DMT system according to claim 9, wherein the step S4 further comprises: after the quantized signal is output from DAC, low-pass filter is used to take out the signal band by omegasThe noise in the range of-pi is filtered out and the signal is then modulated onto a carrier for transmission.
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