JP4497116B2 - Signal generation circuit - Google Patents

Description

  The present invention relates to a signal generation circuit that generates a signal having a peak level larger than an average level by synthesizing phase modulation signals.

For example, there is an amplitude / phase modulation circuit disclosed in Patent Document 1 described below, which generates an arbitrary signal by combining phase modulation signals. Next, the technique of Patent Document 1 will be briefly described.
Japanese Patent No. 3427952

  FIG. 7 shows a block configuration of the circuit in the above-mentioned Patent Document 1, in which data to be transmitted is input and a modulation signal is output. 100 is an input data string, 101 is a serial-parallel converter, 102 is a memory, 103 is a conversion circuit that converts input data into phase information, 104 is a phase modulation circuit, 105 is a carrier generation circuit, 106 is phase information, and 107 is a synthesis The circuit 108 is a phase modulation signal, and 109 is an amplitude phase modulation signal. Further, a time change of the value of the phase information 106, a real time waveform of the phase modulation signal 108, and a real time waveform of the amplitude phase modulation signal 109 are shown.

The basic operation will be described below.
The conversion circuit 103 is a circuit that converts input data into phase information of two phase modulation signals, and includes a series-parallel converter 101 and a memory 102. The memory 102 stores in advance the relationship of the phase information of the phase modulation signal with respect to the preceding and following data including an arbitrary symbol. The input data 100 is sequentially input to the serial-parallel converter 101, the output of the serial-parallel converter 101 is input as an address of the memory 102, and the memory 102 outputs two pieces of phase information 106. The two phase modulation circuits 104 phase-modulate the carrier of the carrier generation circuit 105 with the respective phase information 106, and two phase modulation signals 108 are generated. The two generated phase modulation signals 108 are analog-added and synthesized by a synthesis circuit 107, and an amplitude phase modulation signal 109 is generated as a final output.

  FIG. 8 shows a principle in which the two phase modulation signals 108 are converted into the amplitude phase modulation signal 109 in the synthesis circuit 107, and is represented by a signal space diagram. In the signal space diagram, the angle around the center represents the phase of the modulation signal, the distance from the center represents the amplitude of the modulation signal, and the vector represents the amplitude and phase of the modulation signal. The angle 201 and the angle 202 are the phase information θ1 and θ2 at the time t of the two phase modulation signals S1 = E · sin (ωt + θ1) and S2 = E · sin (ωt + θ2), respectively. Is the angle. The angle 200 is the angle θ0 at the time t of the amplitude phase modulation signal R = A · sin (ωt + θ0), which is the final output signal corresponding to the input data, and is the angle of the vector 109.

Here, in the memory 102, for example, when θ1 and θ2 are output for inputs corresponding to A and θ0, θ1 and θ2 are determined so that the following expression (1) is established.
θ0 = (θ1 + θ2) / 2, A = cos (θ1-θ0) + cos (θ0-θ2) (1)
In the signal space diagram of FIG. 8, equation (1) represents the following. That is, θ0 is the average value of θ1 and θ2, and the amplitude A is the sum of two lengths cos (θ1-θ0) and cos (θ0-θ2) obtained by projecting the two vectors 108 onto the vector 601. is there. Thus, the vector 109 is equal to the combined vector of the two vectors 108. Since this relationship is established at each time, the combination of the phase modulation signals S1 and S2 generated so as to satisfy the expression (1) becomes the amplitude phase modulation signal R.

  A circuit for synthesizing a phase modulation signal as in the conventional example is advantageous in terms of element variation and power consumption because it is converted into a phase modulation signal and processed, but compared to the average level. Since there is a problem when a signal having a large peak level is generated, this will be described.

  An example of a signal having a large peak level value relative to the average level is an OFDM signal (Orthogonal Frequency Division Multiplexing). When the levels of the frequency channels match, there is an instantaneously large peak level. For example, the peak level is about 10 dB larger than the average level.

  FIG. 5 shows an example of a real-time waveform of the OFDM signal, and FIG. 6 shows the probability density and effective value of the OFDM signal level. As can be seen from FIGS. 5 and 6, the OFDM signal has a higher peak level and a lower probability density than the average level.

  In general, a circuit that generates and transmits a signal tends to increase power consumption in accordance with the peak level. In particular, when a linear class A amplifier is used, the power use efficiency is low, and the power consumption increases when the output signal level is increased. In order to faithfully generate a signal such as an OFDM signal waveform that has a high peak level relative to the rms value but a low probability of existence of the peak level, it is necessary to generate very small level fluctuations faithfully. In addition, since a large output level is required, the use of a class A amplifier has a drawback that the power use efficiency of the entire signal generation circuit is lowered. A signal generation circuit that transmits signals such as OFDM signals with high power while increasing power utilization efficiency is required.For example, when generating and transmitting OFDM signals in portable devices with many power consumption restrictions Especially problematic.

On the other hand, when an OFDM signal is regarded as one amplitude-phase modulation signal, it is possible to generate an OFDM signal by converting and synthesizing into two phase-modulation signals as in the above-described prior art example.
If converted to a phase modulation signal in this way, the phase modulation signal has a constant amplitude and the peak level is generally close to the average level. Therefore, the circuit that handles the phase modulation signal has the advantage that the power can be effectively used. If the amplitude of the signal is 1, the peak level of the signal that can synthesize two phase-modulated signals is 2 or less, so that the above-described conventional technique has a problem that it can only generate an OFDM signal having an amplitude of 2 or less. It was.

An object of the present invention is to provide a circuit that synthesizes phase-modulated signals and that can effectively use power and generates a signal with a high peak level.
It is another object of the present invention to provide a signal generation circuit capable of generating or transmitting a signal having a high peak level such as an OFDM signal in a portable device that cannot increase power consumption.

In order to solve such a problem, the present invention has means for synthesizing an arbitrary modulation signal by increasing or decreasing the number of phase modulation signals to be converted according to the level of the input signal.
Phase conversion means for converting an input signal into n pieces of phase information, where n is an integer of 2 or more, phase modulation means for generating n phase modulation signals based on the n pieces of phase information, and the n pieces And a synthesizing means for adding the phase modulation signals.

  In the phase conversion unit, the phase modulation unit, and the synthesis unit, when a level range of a signal to be output is divided into a predetermined number of level sections of n or less and there is a signal level to be output in the level section including a peak level. When there is no signal level to be output in the level section including the peak level, m (n or less integer) for each of the level sections. ), And converted to m phase modulation signals and combined to generate an arbitrary modulation signal.

  For example, a circuit that considers an OFDM signal as one amplitude-phase modulation signal, converts it into a phase modulation signal, and synthesizes it, and converts it into two phase modulation signals when the OFDM signal level is below a specific value. A period for which the OFDM signal level is equal to or greater than a specific value is synthesized and converted into four phase modulation signals and synthesized to generate an OFDM signal.

  Since the present invention uses a plurality of phase modulation signals in a circuit that generates a signal with a high peak level such as an OFDM signal, the amplitude level of the phase modulation signal is substantially constant and the peak level is generally close to the average level. There is an advantage that power can be used effectively.

  In particular, when the level of the signal to be output is close to the peak level, for example, it is converted into four phase modulation signals and synthesized, and when the level is low, for example, it is converted into two phase modulation signals and synthesized. As described above, compared with the conventional technique of converting into two phase modulation signals and combining them, a signal having a high peak level such as an OFDM signal can be generated by effectively using power.

  Furthermore, the present invention can increase the number of phase modulation signals to be synthesized, so that a signal with a high peak level can be generated, and the number of phase modulation signals to be synthesized is increased or decreased, so that the number of drive circuits can be controlled. . That is, when the number of phase modulation signals to be combined is small, the power consumption of unnecessary circuits can be reduced, so that the power consumption of the entire signal generation circuit can be reduced. For example, when the circuit is composed of CMOS elements, there is a two-digit difference between the power consumption during gate drive and the power consumption during stop in the CMOS element, and if the drive of each element is stopped, the power consumption can be greatly reduced.

In this way, according to the present invention, it is possible to generate a high peak level signal while making effective use of electric power.
Furthermore, since power consumption cannot be increased in a portable device, it has been difficult to use an OFDM signal with a high peak level in a portable device. However, according to the present invention, since an effective use of power is achieved, an OFDM signal is used. It can be applied to portable devices.

One mode for carrying out the present invention will be described below.
FIG. 1 shows an example of a block configuration of a signal generation circuit of the present invention. Reference numeral 501 denotes data input corresponding to a signal to be output, for example, symbol data to be simultaneously modulated in each OFDM frequency channel. Alternatively, although not shown, a digital signal obtained by sample quantization of an analog input signal such as an AD converter may be used.

  Reference numeral 502 denotes a memory for converting input data into phase information, and corresponds to phase conversion means. Reference numeral 503 denotes a phase modulation circuit for phase-modulating a carrier of a carrier generation circuit (not shown) with the phase information. Reference numeral 504 denotes a phase modulation signal. A synthesis circuit 505 performs analog addition. Reference numeral 506 denotes an output. An antenna is used for wireless transmission in a portable device or the like, but it is also possible to easily output by wire.

The operation of the circuit of FIG. 1 is as follows.
[1] First, data 501 corresponding to a signal to be output is input. In the example of FIG. 1, symbol data to be simultaneously modulated in each frequency channel for each OFDM subcarrier is input in parallel.

[2] The data 501 is used as the address of the memory 502, and the phase information supplied to the four phase modulation circuits 503 is stored in advance in the memory 502, and the four pieces of phase information are output.
As the contents of the memory 502, for example, an OFDM signal corresponding to the data 501 is regarded as an arbitrary modulation signal related to one center frequency, that is, an amplitude phase modulation signal B · sin (ωt + θ0). The peak level of this amplitude phase modulation signal is A. In order to decompose into four phase modulation signals, phase information θ1, θ2, θ3, and θ4 satisfying the following conditions are stored in advance.

Here, the peak level means a level at which the absolute value of the signal level is maximum with respect to the level of zero (so-called Zero to Peak).
The memory 502 outputs phase information and inputs the phase information to the phase modulation circuit 503. The phase modulation circuit 503 generates a phase modulation signal 504 based on the phase information, and the synthesis circuit 505 analog-adds the four phase modulation signals 504.

[3] When the level of the amplitude / phase modulation signal represented by the input is A / 2 or less, the memory 502
B ≦ A / 2, θ0 = (θ1 + θ2) / 2, B = (A / 4) cos (θ1−θ0) + (A / 4) cos (θ0−θ2)
... Formula (2)
Two pieces of phase information θ1 and θ2 satisfying the above relationship are generated. The phase modulation circuit 503 has two phase modulation signals by θ1 and θ2.
S1 ＝ (A / 4) ・ sin (ωt + θ1) 、 S2 ＝ (A / 4) ・ sin (ωt + θ2)
And output to the synthesis circuit 505 (S1, S2).

[4] When the level of the amplitude phase modulation signal represented by the input is A / 2 or more and A or less, the memory 502
θ0 = θ1 = θ2 (3)
Two pieces of phase information θ1 and θ2 satisfying the above relationship are generated. The phase modulation circuit 503 has two phase modulation signals by θ1 and θ2.
S1 ＝ (A / 4) ・ sin (ωt + θ1) 、 S2 ＝ (A / 4) ・ sin (ωt + θ2)
And then convert
B ≦ A, θ0 = (θ3 + θ4) / 2, B = (A / 2) + (A / 4) cos (θ3−θ0) + (A / 4) cos (θ0−θ4)
... Formula (4)
Two pieces of phase information θ3 and θ4 satisfying the above relationship are generated. The phase modulation circuit 503 has two phase modulation signals by θ3 and θ4.
S3 = (A / 4) ・ sin (ωt + θ3), S4 = (A / 4) ・ sin (ωt + θ4)
And a total of four phase modulation signals are output to the synthesis circuit 505 (S1, S2, S3, S4).

[5] In the synthesizing circuit 505, as a result of analog addition of the two phase modulation signals S1 to S2 in the case of [3] or the four phase modulation signals S1 to S4 in the case of [4], the amplitude phase modulation signal 506 is obtained. Generated.
For example, when the level of the OFDM signal is low, the signal is generated using only S1 and S2, and when the level of the OFDM signal is high, the signal is generated using four phase modulations of S1, S2, S3, and S4. .

  Here, when it is sufficient to decompose into two phase modulation signals S1 and S2 as shown in [3], the power consumption of the circuit handling S3 and S4 is four phase modulation signals S1 to S4 as shown in [4]. Compared to the case of conversion to S4, the power consumption of the entire circuit can be reduced because the configuration can be reduced. For example, power consumption can be reduced by configuring a circuit with CMOS elements.

  FIG. 3 shows the principle that four phase modulation signals 602 and 603 are converted into an output amplitude phase modulation signal 601 and is represented by a signal space diagram. The two vectors 602 correspond to the phase modulation signals S1 and S2, respectively, and the angles are θ1 and θ2, respectively. The two vectors 603 correspond to the phase modulation signals S3 and S4, respectively, and their angles are θ3 and θ4. A vector 601 is an output 506 which is an amplitude phase modulation signal, and an angle is θ0.

  When combining in S1 to S4, a vector obtained by combining two vectors 602 satisfying θ0 = θ1 = θ2 as shown in Expression (3) has an angle equal to the vector 603. This corresponds to a combined signal of S1 + S2, and the amplitude of each is A / 4, so the amplitude of S1 + S2 is A / 2. For the convenience of illustration, the vectors 601 and 602 are displayed in a shifted manner, but the angles of the vectors 601 and 602 are equal.

  A vector obtained by combining two vectors 603 with θ0 = (θ3 + θ4) / 2 corresponds to a combined signal S3 + S4, but has an average angle of the two vectors 603. A broken line indicates a combination of two vectors 603. Since the sum of components obtained by projecting the two vectors 603 in a direction orthogonal to the vector 601 is zero, the angle is equal to the vector 601. Further, the sum of the lengths of two vectors 603 projected onto the vector 601 is (A / 4) cos (θ3−θ0) + (A / 4) cos (θ4−θ0). When the sum A / 2 of the lengths of two vectors 602 having the same angle is added to the vector 601 as shown in Expression (4), a vector 601 is obtained. Therefore, the sum of the vectors of the combined signal S1 + S2 + S3 + S4 is the vector 601, which is the amplitude / phase modulation signal to be output.

  When combining only S1 and S2, it is the same as in FIG. 8, and the combined signal vector has an angle of θ0 = (θ1 + θ2) / 2, and the sum of the lengths projected onto the combined vector (A / 4) It has a length of cos (θ1−θ0) + (A / 4) cos (θ0−θ2). Therefore, the combined signal S1 + S2 is the amplitude / phase modulation signal to be output.

Since such a relationship is established at each time, the synthesis of the phase modulation signals S1 and S2 or the synthesis of the phase modulation signals S1 to S4 becomes the amplitude phase modulation signal B · sin (ωt + θ0).
The specific method of vector decomposition and synthesis described here is not the only method, but an example has been described.

  FIG. 4 shows the four phase modulation signals and the finally generated OFDM signal simultaneously in real time waveforms in the circuit of FIG. The upper real-time waveform is the output OFDM signal, and S1 to S4 correspond to the time. During the low level period, the output is synthesized only by S1 and S2, and during the high level period, S3 and S4 are generated, and the output is synthesized by S1 to S4. A broken line is a time when the number of phase modulation signals to be combined is switched.

Next, another embodiment of the present invention will be described.
In the embodiment so far, the amplitude phase modulation signal is generated by converting into two or four phase modulation signals and combining them according to the level.

  As an embodiment of the present invention, it is possible to configure a circuit that converts n to n phase modulation signals and synthesizes them with n being an integer of 2 or more. FIG. 2 shows an example of a block diagram of the circuit configuration of this embodiment. 501 is an input of data corresponding to a signal to be output, 502 is a memory for performing phase conversion from input data to n pieces of phase information, 503 is a phase modulation circuit, 504 is a phase modulation signal, 505 is a synthesis circuit, 506 is an output is there.

  As for the contents of the memory 502, for example, n pieces of phase information θ1 to θn satisfying specific conditions are stored in advance in order to decompose a signal corresponding to the data 501 into n phase modulation signals. The n pieces of phase information are input to n phase modulation circuits 503, and n pieces of phase modulation signals S1 = (A / n) · sin (ωt + θ1), S2 = (A / n) · sin (ωt + θ2),... Sn = (A / n) · sin (ωt + θn) is output, and the n phase modulation signals are synthesized by addition in the synthesis circuit 505 and output signal B · sin (ωt + θ0 ) Is obtained.

The level range of the signal to be output is divided into a predetermined number of level sections of n or less, and the number of phase modulation signals to be converted is increased or decreased within a range of n or less according to the level of the signal to be output. In the level section including the peak level A of the signal to be output, n phase modulation signals S1 = (A / n) · sin (ωt + θ1), S2 by n pieces of phase information θ1, θ2,. = (A / n) · sin (ωt + θ2), ... Sn = (A / n) · sin (ωt + θn), and n phase modulation signals are synthesized by addition to obtain an output . At this time, the n pieces of phase information are
B = (A / n) ・ cos (θ1−θ0) + (A / n) ・ cos (θ2−θ0) + ・ ・ + (A / n) ・ cos (θn−θ0),
0 = sin (θ1−θ0) + sin (θ2−θ0) + ・ ・ + sin (θn−θ0)
... Formula (5)
It is converted to satisfy the relationship. In the signal space diagram, the sum of the components of the phase modulation signal vector projected in the direction of the synthesized signal vector is the length of the synthesized signal vector, and the phase modulated signal vector is projected in the direction orthogonal to the synthesized signal vector. As described above, it means that the sum of the obtained components is zero.

Further, in the level section not including the peak level, the phase information is converted into m pieces of phase information θ1, θ2,. ) ・ Sin (ωt + θ1), S2 = (A / n) ・ sin (ωt + θ2), ... Sm = (A / n) ・ sin (ωt + θm), m phase modulation The signals are combined by addition to obtain an output. At this time, the m pieces of phase information are
B = (A / n) ・ cos (θ1−θ0) + (A / n) ・ cos (θ2−θ0) + ・ ・ + (A / n) ・ cos (θm−θ0),
0 = sin (θ1−θ0) + sin (θ2−θ0) + ・ ・ + sin (θm−θ0)
... Formula (6)
It is converted to satisfy the relationship. In the signal space diagram, for the same reason as described above.

  Further, the number of phase modulation signals to be combined is associated with each level section. For example, when n = 10, it has a memory for converting into 10 pieces of phase information, 10 phase modulation circuits, and a synthesis circuit for synthesizing 10 phase modulation signals, and the peak level of the signal to be output is A When the level section is divided into five. Assume that the amplitude of each phase modulation signal is A / 10. At this time, the number of phase modulation signals to be combined is made to correspond as follows.

  When the level of the signal to be output is 0 to A / 5, two phase modulation signals are synthesized, and when it is A / 5 to 2A / 5, four phase modulation signals are synthesized, and 2A / 5 to 3A / When 5 is 6, 6 phase modulation signals are combined, when 3A / 5 to 4A / 5, 8 phase modulation signals are combined, and when 4A / 5 to A, 10 phase modulation signals are combined. In other words, the number of phase modulation signals combined is associated with each level section.

  At this time, for example, in the same manner as described above, the average value of the two phase modulation signals is equal to the phase of the signal to be output, and the other phase modulation signals are the same as the signal to be output and the phase of the signal. May be synthesized so that they are equal.

However, when synthesizing the phase modulation signal, it is needless to say that the number of phase modulation signals to be synthesized is determined by defining the level interval based on the fact that the level that can be synthesized is limited.
When converting into m or n phase modulation signals, the level range of the corresponding output signal and the conditions satisfied by the respective phase information are designed by using a signal space diagram as described above. be able to.

  A large number of fine level ranges can be provided and each can be designed to be converted into an appropriate number of phase modulation signals and synthesized, so that the effective use of power can be further optimized. Depending on the probability density and peak level of the signal level desired to be output, the number of phase modulation signals should be examined and the optimum n or the like determined.

  Thus, in this embodiment, since n phase modulation signals are combined, the peak level that can be output is increased, and the number of phase modulation signals combined is increased or decreased as necessary. Effective use.

It is a block diagram which shows the circuit structure by one Embodiment of this invention. It is a block diagram which shows the circuit structure by other one Embodiment of this invention. It is a signal space diagram which shows the principle which synthesize | combines a phase modulation signal in one Embodiment of this invention, and obtains an output signal. It is a figure which shows an example of the real-time waveform of a phase modulation signal and an output signal in one Embodiment of this invention. It is a figure which shows an example of the real-time waveform of an OFDM signal. It is a figure which shows the probability density of the level of an OFDM signal. It is the block diagram which shows the circuit structure of a prior art, and the time waveform of each signal. It is a signal space diagram which shows the principle which synthesize | combines a phase modulation signal and obtains an output signal in a prior art.

Explanation of symbols

100 input data
101 Series-parallel converter
102 memory
103 Conversion circuit
104 Phase modulation circuit
105 Carrier generation circuit
106 Phase information
107 Synthesis circuit
108 Phase modulation signal
109 Amplitude phase modulation signal
200 angle
201 angle
501 Input data
502 memory
503 Phase modulation circuit
504 Phase modulation signal
601 Amplitude phase modulation signal vector
602 Phase modulation signal vector
603 Phase modulation signal vector

Claims (2)

A circuit that generates an arbitrary modulation signal having a peak level A by converting an input signal into a phase modulation signal and synthesizing the signal,
The phase conversion means for converting the input signal into n pieces of phase information θ1, θ2,... Θn, where n is an integer of 2 or more, and n phase modulation signals S1 = ( A / n) · sin (ωt + θ1), S2 = (A / n) · sin (ωt + θ2), ... Phase modulation to generate Sn = (A / n) · sin (ωt + θn) And a combining means for adding the n phase modulation signals,
The arbitrary modulation signal is B · sin (ωt + θ0), and the range of the level of the arbitrary modulation signal is divided into a predetermined number of level sections of n or less,
When the level of the arbitrary modulation signal is in a level section including the peak level A among the level sections, n pieces of phase information θ1, θ2,.
B = (A / n) ・ cos (θ1−θ0) + (A / n) ・ cos (θ2−θ0) + ・ ・ + (A / n) ・ cos (θn−θ0),
0 = sin (θ1−θ0) + sin (θ2−θ0) + ・ ・ + sin (θn−θ0)
The phase modulation means generates n phase modulation signals based on the n pieces of phase information, and the synthesis means adds the n phase modulation signals to add the arbitrary modulation signal. Produces
When the level of the arbitrary modulation signal is not in the level section including the peak level A, the phase conversion means converts the phase information to m pieces of phase information θ1, θ2,. The m pieces of phase information are
B = (A / n) ・ cos (θ1−θ0) + (A / n) ・ cos (θ2−θ0) + ・ ・ + (A / n) ・ cos (θm−θ0),
0 = sin (θ1−θ0) + sin (θ2−θ0) + ・ ・ + sin (θm−θ0)
The phase modulation means generates m phase modulation signals based on the m pieces of phase information, and the synthesis means adds the m phase modulation signals to the arbitrary modulation signal. Produces
The signal generation circuit, wherein the arbitrary modulation signal is generated so that the number of the phase modulation signals combined corresponds to each of the level sections. N is 4, the arbitrary modulation signal is B · sin (ωt + θ0), and the range of the level of the arbitrary modulation signal is divided into two level sections;
The first level section is a level section between A / 2 and A that includes the peak level A, and when the level of the arbitrary modulation signal is in the first level section,
θ0 = θ1 = θ2
The phase conversion means generates two pieces of phase information θ1 and θ2 that satisfy the relationship: The phase modulation means outputs the phase modulation signal S1 = (A / 4) · sin (ωt + θ1), S2 = (A / 4 ) Sin (ωt + θ2), and the phase conversion means
B ≦ A, θ0 = (θ3 + θ4) / 2, B = (A / 2) + (A / 4) cos (θ3−θ0) + (A / 4) cos (θ0−θ4)
Two phase information θ3 and θ4 satisfying the above relationship are generated, and the phase modulation means outputs the phase modulation signal S3 = (A / 4) · sin (ωt + θ3), S4 = (A / 4) · sin (ωt + θ4) to generate the arbitrary modulation signal by analog addition of the four phase modulation signals S1, S2, S3, S4 by the combining means,
The second level section is a level section of A / 2 or less that does not include the peak level A, and when the level of the arbitrary modulation signal is in the second level section,
B ≦ A / 2, θ0 = (θ1 + θ2) / 2, B = (A / 4) cos (θ1−θ0) + (A / 4) cos (θ0−θ2)
The phase conversion means generates two pieces of phase information θ1 and θ2 that satisfy the relationship: The phase modulation means outputs the phase modulation signal S1 = (A / 4) · sin (ωt + θ1), S2 = (A / 4 2. The signal generating circuit according to claim 1, wherein the arbitrary modulation signal is generated by generating S) and sin (ωt + θ2) and analog-adding S1 and S2 by the synthesizing means.