Patent Publication Number: US-10763969-B2

Title: Waveform generator

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This U.S. non-provisional patent application claims priority under 35 U.S.C. § 119 of Korean Patent Application No. 10-2018-0067712, filed on Jun. 12, 2018, the entire contents of which are hereby incorporated by reference. 
     BACKGROUND 
     The present disclosure herein relates to an opto-electronic device, and more particularly to, a waveform generator configured to generate a signal having an intended characteristic. 
     With the development of wireless communication systems, devices for processing data that is transmitted/received at high speed are being required. A radio frequency arbitrary waveform generator (RF AWG) is a device for generating RF signals having arbitrary waveforms. The RF AWG requires a broadband RF filter to handle broadband signals. 
     The RF AWG configured to generate an arbitrary signal on the basis of an electronic signal includes an analog-to-digital converter (ADC). The analog-to-digital converter may operate normally within a restricted bandwidth. The analog-to-digital converter may include noise due to surrounding environments such as a temperature change, etc. Therefore, a signal-to-noise ratio (SNR) of a signal output from the RF AWG on the basis of the electronic signal may be low. 
     The noise included in an optical signal due to the surrounding environments may be lower than the noise included in an electronic signal. Therefore, when the RF AWG uses an optical signal rather than an electronic signal, the signal-to-noise ratio of the signal output from the RF AWG may increase. Accordingly, RF AWGs for generating signals on the basis of optical signals are being actively developed. 
     SUMMARY 
     The present disclosure provides a waveform generator configured to generate a signal having a characteristic according to an instruction from a user. 
     An embodiment of the inventive concept provides a waveform generator including an optical signal generating circuit, a controlling circuit, a waveform shaping circuit, and an output circuit. The optical signal generating circuit may generate a first optical signal including pulses. The controlling circuit may generate a control signal indicating a first pulse to be attenuated among the pulses. The waveform shaping circuit may attenuate a magnitude of the first pulse on the basis of the control signal and the first optical signal, and may generate a second optical signal including pulses corresponding to the pulses included in the first optical signal and the first pulse having the attenuated magnitude. The output circuit may output an electric signal of bands corresponding to differences between frequencies of the pulses included in the second optical signal on the basis of the second optical signal. A band corresponding to the first pulse among the bands of the electric signal may be adjusted as the magnitude of the first pulse is attenuated. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The accompanying drawings are included to provide a further understanding of the inventive concept, and are incorporated in and constitute a part of this specification. The drawings illustrate example embodiments of the inventive concept and, together with the description, serve to explain principles of the inventive concept. In the drawings: 
         FIG. 1  is a block diagram illustrating a waveform generator according to an embodiment of the inventive concept; 
         FIG. 2  is a block diagram illustrating an example configuration of the waveform shaping circuit of  FIG. 1 ; 
         FIG. 3  is a block diagram illustrating an example configuration of the output circuit of  FIG. 1 ; 
         FIG. 4  is a graph illustrating an example optical signal generated by the optical signal generating circuit of  FIG. 1 ; 
         FIG. 5  is a graph illustrating an example optical signal generated by the AGC amplifying circuit of  FIG. 2 ; 
         FIG. 6  is a graph illustrating an example optical signal generated by the pulse shaping circuit of  FIG. 2 ; 
         FIG. 7  is a graph illustrating an example optical signal generated by the optical modulation circuit of  FIG. 2 ; 
         FIG. 8  is a graph illustrating an example optical signal generated by the coupling circuit of  FIG. 2 ; 
         FIG. 9  is a graph illustrating an example signal generated by the OE converting circuit of  FIG. 3 ; 
         FIG. 10  is a flowchart illustrating an example operation of the waveform generator of  FIG. 1 ; 
         FIG. 11  is a block diagram illustrating a waveform generator according to an embodiment of the inventive concept; 
         FIG. 12  is a graph illustrating an example optical signal generated by the frequency interval adjusting circuits of  FIG. 11 ; 
         FIG. 13  is a graph illustrating an example signal generated by the output circuit of  FIG. 11 ; 
         FIG. 14  is a flowchart illustrating an example operation of the waveform generator of  FIG. 11 ; and 
         FIG. 15  is a block diagram illustrating a waveform generator according to an embodiment of the inventive concept. 
     
    
    
     DETAILED DESCRIPTION 
     Example embodiments of the inventive concept will be described in detail and clearly so that the present invention can be easily carried out by those skilled in the art. 
       FIG. 1  is a block diagram illustrating a waveform generator according to an embodiment of the inventive concept. 
     Referring to  FIG. 1 , a waveform generator  100  may include an optical signal generating circuit  110 , a waveform shaping circuit  130 , an output circuit  140 , and a controlling circuit  150 . 
     The optical signal generating circuit  110  may generate an optical signal S 1 . For example, the optical signal S 1  may include an optical comb signal. The optical comb signal may include one or more pulses diffused so as to have different frequencies in a frequency domain. Each of the one or more pulses included in the optical comb signal may have a specific frequency. 
     Intervals between the pulses included in the optical comb signal may be substantially equal in a frequency domain. The term “interval” between pulses is used herein. The term “interval” may represent a difference between frequencies of pulses in a frequency domain. 
     For example, the frequencies of the pulses included in the optical comb signal may include first to third frequencies. The interval between the first frequency and the second frequency may be substantially equal to the interval between the second frequency and the third frequency. However, the inventive concept may include any embodiment in which at least two of the intervals between the pulses of the optical comb signal are different. The optical signal S 1  including the optical comb signal will be described in more detail with reference to  FIG. 4 . The optical signal generating circuit  110  may output the optical signal S 1  including the optical comb signal to the waveform shaping circuit  130 . 
     For example, the optical signal generating circuit  110  may include a light emitting element (e.g., a laser diode) configured to generate a semiconductor laser. 
     The waveform shaping circuit  130  may receive the optical signal S 1  from the optical signal generating circuit  110 . The waveform shaping circuit  130  may receive the optical comb signal included in the optical signal S 1 . The waveform shaping circuit  130  may receive a control signal C 2  from the controlling circuit  150 . 
     The waveform shaping circuit  130  may operate normally on the basis of an optical signal having a magnitude within a reference range. The waveform shaping circuit  130  may obtain information related to the reference range from the control signal C 2 . For example, when the magnitudes of the pulses included in the optical signal S 1  are outside the reference range, the waveform shaping circuit  130  may adjust the magnitude of the optical signal S 1  on the basis of the control signal C 2 . For example, the waveform shaping circuit  130  may adjust the magnitudes of the pulses included in the optical signal S 1  on the basis of the control signal C 2 . The waveform shaping circuit  130  may generate a new optical signal by adjusting the magnitude of the optical signal S 1 , and may operate normally on the basis of the new optical signal. 
     The waveform shaping circuit  130  may adjust, on the basis of the control signal C 2 , characteristics (e.g., pulse magnitude, pulse phase, interval between pulses, the number of pulses) of the new optical signal generated based on the optical signal S 1 . For example, the waveform shaping circuit  130  may decrease the magnitudes of the pulses included in the optical signal S 1  on the basis of the control signal C 2 . The waveform shaping circuit  130  may adjust phases of the pulses included in the optical signal S 1  on the basis of the control signal C 2 . Therefore, the waveform shaping circuit  130  may generate pulses corresponding to the pulses included in the optical signal S 1  and having magnitudes and phases that are different from the magnitudes and phases of the pulses included in the optical signal. 
     The waveform shaping circuit  130  may generate an optical signal S 3  including pulses having adjusted characteristics. The waveform shaping circuit  130  may output the optical signal S 3  to the output circuit  140 . A configuration and operation of the waveform shaping circuit will be described in more detail with reference to  FIG. 2 , and  FIGS. 5 to 8 . 
     The output circuit  140  may receive the optical signal S 3  from the waveform shaping circuit  130 . The output circuit  140  may disperse the optical signal S 3  in a time domain. The output circuit  140  may perform frequency-time conversion on the optical signal S 3  by dispersing the optical signal S 3 . For example, the output circuit  140  may include an optical fiber or the like to perform the frequency-time conversion. 
     The output circuit  140  may photoelectrically convert the dispersed optical signal S 3  to generate a signal S 4 . For example, the output circuit  140  may include a photoelectric conversion element for converting the optical signal S 3 . An example configuration and operations of the output circuit  140  will be described in more detail with reference to  FIG. 3 . 
     The signal S 4  may be an electric signal transmitted through wire. Alternatively, the signal S 4  may be transmitted wirelessly. For example, the signal S 4  may be a radio frequency (RF) signal. For example, in the case where the waveform generator  100  is a component of an electronic device (e.g., a mobile device or computing device), the signal S 4  may be transmitted to other components (e.g., communication devices such as an antenna, etc.) of the electronic device. The signal S 4  may then be transmitted from the electronic device to another electronic device. 
     The signal S 4  may have at least one frequency band. For example, the magnitude of the signal S 4  may be related to the magnitudes of the pulses included in the optical signal S 3 . Bandwidths of the frequency bands of the signal S 4  may be related to the number of pulses included in the optical signal S 3 . The frequency band of the signal S 4  may be related to the intervals between the pulses included in the signal S 3 . 
     The phases of the optical signal S 3  may be related to a filtering characteristic of the signal S 4 . For example, the phases of the optical signal S 3  may be related to a skirt characteristic of the signal S 4 . The skirt characteristic of the signal S 4  may correspond to a shape factor of the signal S 4 . For example, the signal S 4  may have characteristics of a filter. Therefore, the signal S 4  may have a transition band in a frequency domain. The magnitude of the signal S 4  may vary in the transition band. In the transition band, a change rate of the magnitude of the signal S 4  depending on a frequency (i.e., a gradient of the magnitude of the signal S 4  in a frequency domain) may correspond to the shape factor of the signal S 4 . For example, as the shape factor of the signal S 4  increases, the change rate of the magnitude of the signal S 4  according to a frequency may increase. A relationship between the signal S 4  and the optical signal S 3  will be described in more detail with reference to  FIGS. 3 and 9 . 
     The controlling circuit  150  may generate the control signal C 2  for controlling the waveform shaping circuit  130 . For example, the controlling circuit  150  may determine characteristics of pulses to be included in the optical signal S 3 , on the basis of a command received from a user or a device (e.g., a processor, a memory device, or the like) outside the waveform generator  100 . The controlling circuit  150  may generate the control signal C 2  for transferring information associated with the determined characteristics. The controlling circuit  150  may output the control signal C 2  to the waveform shaping circuit  130 . 
     For example, the controlling circuit  150  may determine pulses to be attenuated among the pulses included in the optical signal S 1 . The controlling circuit  150  may generate the control signal C 2  indicating the pulses determined to be attenuated. The controlling circuit  150  may output the control signal C 2  to the waveform shaping circuit  130 . 
     The controlling circuit  150  may determine the reference range. For example, the controlling circuit  150  may store data indicating information related to the reference range. The controlling circuit  150  may determine the reference range on the basis of the stored data. For example, the controlling circuit  150  may obtain data related to the reference range on the basis of a command received from a user or another device outside the waveform generator  100 . The controlling circuit  150  may determine the reference range on the basis of the obtained data. The controlling circuit  150  may generate the control signal C 2  for transferring the data related to the reference range. The controlling circuit  150  may output the control signal C 2  to the waveform shaping circuit  130 . 
       FIG. 2  is a block diagram illustrating an example configuration of the waveform shaping circuit of  FIG. 1 . 
     Referring to  FIG. 2 , the waveform shaping circuit  130  may include an automatic gain control (AGC) amplifying circuit  131 , a pulse shaping circuit  132 , an optical modulation circuit  133 , an oscillator  134 , an optical filter circuit  135 , and a combining circuit  136 . 
     The AGC amplifying circuit  131  may receive the optical signal S 1  from the optical signal generating circuit  110  of  FIG. 1 . The AGC amplifying circuit  131  may receive the control signal C 2  from the controlling circuit  150  of  FIG. 1 . 
     As described above with reference to  FIG. 1 , the waveform shaping circuit  130  may operate normally on the basis of an optical signal having a magnitude within a reference range. In more detail, the pulse shaping circuit  132  included in the waveform shaping circuit  130  may operate normally on the basis of an optical signal M 1  including pulses having magnitudes within the reference range. For example, the reference range may be related to characteristics of circuit elements included in the pulse shaping circuit  132 . 
     The AGC amplifying circuit  131  may obtain data related to the reference range from the control signal C 2 . The AGC amplifying circuit  131  may adjust the magnitudes of the pulses included in the optical signal S 1  on the basis of the obtained data. The AGC amplifying circuit  131  may generate the optical signal M 1  including pulses having adjusted magnitudes. The AGC amplifying circuit  131  may output the optical signal M 1  to the pulse shaping circuit  132 . An example operation of the AGC amplifying circuit  131  will be described in more detail with reference to  FIG. 5 . 
     The pulse shaping circuit  132  may receive the optical signal M 1  from the AGC amplifying circuit  131 . The pulse shaping circuit  132  may receive the control signal C 2  from the controlling circuit  150  of  FIG. 1 . The pulse shaping circuit  132  may obtain, from the control signal C 2 , information related to characteristics (e.g., magnitude, phase, interval between pulses, and the number of pulses) of pulses. 
     The pulse shaping circuit  132  may generate an optical signal M 2  on the basis of the optical signal M 1  and the control signal C 2 . For example, the pulse shaping circuit  132  may adjust, on the basis of the control signal C 2 , the magnitudes, phases, and number of and interval between the pulses included in the optical signal M 1  so as to generate the optical signal M 2 . 
     The pulse shaping circuit  132  may generate the optical signal M 2  by adjusting the intervals between the pulses included in the optical signal M 1  on the basis of the control signal C 2 . For example, as described above with reference to  FIG. 1 , the control signal C 2  may indicate pulses to be attenuated among the pulses included in the optical signal S 1 . The pulses indicated by the control signal C 2  may be determined or selected in response to a request from a user or another device. 
     The pulse shaping circuit  132  may adjust the intervals between the pulses included in the optical signal M 2  by attenuating the magnitudes of pulses corresponding to pulses of the optical signal S 1  indicated by the control signal C 2  among the pulses included in the optical signal M 1 . For example, the pulse shaping circuit  132  may attenuate the magnitudes of specific pulses to “0” or approximately “0”. When the magnitude of a specific pulse is attenuated to “0” or approximately “0”, the interval between pulses on two sides of the specific pulse may appear to be increased. The pulse shaping circuit  132  may output the optical signal M 2  to the combining circuit  136 . 
     The pulse shaping circuit  132  may generate the optical signal M 2  by adjusting the number of the pulses included in the optical signal M 1  on the basis of the control signal C 2 . For example, the control signal C 2  may indicate pulses to be attenuated among the pulses included in the optical signal S 1 . 
     The pulse shaping circuit  132  may adjust the number of pulses by attenuating the magnitudes of pulses indicated by the control signal C 2  among the pulses included in the optical signal M 1 . For example, the pulse shaping circuit  132  may attenuate the magnitudes of pulses to “0” or approximately “0”. When the magnitude of a specific pulse is attenuated to “0” or approximately “0”, it may appear that the total number of pulses decreases. The pulse shaping circuit  132  may output the optical signal M 2  to the combining circuit  136 . An example operation of the pulse shaping circuit  132  will be described in more detail with reference to  FIG. 6 . 
     The optical modulation circuit  133  may receive the optical signal S 1  including the optical comb signal from the optical signal generating circuit  110  of  FIG. 1 . The optical modulation circuit  133  may receive a signal having a reference frequency “fs” from the oscillator  134 . 
     The optical modulation circuit  133  may adjust the frequencies of the pulses included in the optical signal S 1  on the basis of the signal received from the oscillator  134 . For example, the optical modulation circuit  133  may modulate the frequencies of the pulses so as to increase or decrease the frequencies of the pulses to the reference frequency fs. The optical modulation circuit  133  may generate an optical signal M 3  including the pulses of modulated frequencies. The optical modulation circuit  133  may output the optical signal M 3  to the optical filter circuit  135 . An example operation of the optical modulation circuit  133  will be described in more detail with reference to  FIG. 7 . 
     The optical filter circuit  135  may receive the optical signal M 3  from the optical modulation circuit  133 . The optical signal M 3  may include a noise while the frequency of the optical signal S 1  is modulated by the optical modulation circuit  133 . The optical filter circuit  135  may filter the noise included in the optical signal M 3  so as to generate an optical signal M 4 . Therefore, the optical signal M 4  may not include the noise of the optical signal M 3 , and thus may include components other than the noise. 
     For example, the optical filter circuit  135  may include at least one of a periodic optical filter or an arrayed grating filter to filter the noise of the optical signal M 3 . The optical filter circuit  135  may output the optical signal M 4  to the combining circuit  136 . The noise of the optical signal M 3  and an example operation of the optical filter circuit  135  will be described in more detail with reference to  FIG. 7 . 
     The combining circuit  136  may receive the optical signal M 2  from the pulse shaping circuit  132 . The combining circuit  136  may receive the optical signal M 4  from the optical filter circuit  135 . The combining circuit  135  may generate the optical signal S 3  by combining the optical signal M 2  and the optical signal M 4 . 
     For example, when the frequency of the pulse included in the optical signal M 2  is the same as the frequency of the pulse included in the optical signal M 4 , the combining circuit  136  may generate the optical signal S 3  including pulses having a magnitude obtained by adding the pulses included in the optical signal M 2  and the pulses included in the optical signal M 4  (i.e., through operation of vector summation). For example, when the frequency of the pulse included in the optical signal M 2  is different from the frequency of the pulse included in the optical signal M 4 , the combining circuit  136  may generate the optical signal S 3  including both the pulses. 
     Therefore, the number of the pulses included in the optical signal S 3  may be larger than the number of the pulses included in the optical signal M 2 . Furthermore, the number of the pulses included in the optical signal S 3  may be larger than the number of the pulses included in the optical signal M 4 . The combining circuit  136  may output the optical signal S 3  to the output circuit  140  of  FIG. 1 . That is, the waveform shaping circuit  130  may output the optical signal S 3  having an increased number of pulses through operation of the optical modulation circuit  133  and optical filter circuit  135 . 
     As described below with reference to  FIG. 9 , the number of the pulses included in the optical signal S 3  may be related to the bandwidth of the band of the signal S 4  output from the output circuit  140 . As the optical signal M 4  is combined with the optical signal M 2  by the combining circuit  140 , the bandwidth of the band of the signal S 4  may increase. An example operation of the combining circuit  136  will be described in more detail with reference to  FIG. 8 . 
     As described above with reference to  FIG. 1 , the waveform shaping circuit  130  may adjust the magnitudes and phases of the pulses included in the optical signal S 1  on the basis of the control signal C 2 . For example, the control signal C 2  may be generated in response to a user&#39;s command or a request of another device, and the waveform shaping circuit  130  may output the optical signal S 3  including pulses having magnitudes and phases adjusted in response to the user&#39;s command or the request of the other device. 
     Furthermore, the waveform shaping circuit  130  may adjust the intervals between the pulses included in the optical signal S 1  on the basis of the control signal C 2 . The control signal C 2  may be generated in response to a user&#39;s command or a request of another device, and the waveform shaping circuit  130  may output the optical signal S 3  having pulse intervals in response to the user&#39;s command or the request of the other device. 
     The waveform shaping circuit  130  may adjust the number of the pulses included in the optical signal S 1  on the basis of the control signal C 2 . The control signal C 2  may be generated in response to a user&#39;s command or a request of another device, and the waveform shaping circuit  130  may output the optical signal S 3  including an adjusted number of pulses. 
       FIG. 3  is a block diagram illustrating an example configuration of the output circuit of  FIG. 1 . 
     Referring to  FIG. 3 , the output circuit  140  may include an optical dispersive medium  141  and an optoelectric (OE) converting circuit  142 . 
     The optical dispersive medium  141  may receive the optical signal S 3  from the combining circuit  136  of the waveform shaping circuit  130 . The optical dispersive medium  141  may disperse the optical signal S 3  in a time domain on the basis of the frequencies of the pulses included in the optical signal S 3 . For example, the optical dispersive medium  141  may include an optical fiber or the like having a chromatic dispersion characteristic. 
     For example, the optical dispersive medium  141  may output pulses having a high frequency earlier than pulses having a lower frequency among signal components included in the optical signal S 3 . As the signal S 3  is dispersed in a time domain by the optical dispersive medium  141 , the optical dispersive medium  141  may output an optical signal FT. The optical signal FT may include optical signals dispersed in a time domain for each frequency. 
     The OE converting circuit  142  may receive the optical signal FT from the optical dispersive medium  141 . The OE converting circuit  142  may generate the signal S 4  by performing photoelectric conversion on the basis of the optical signal FT. For example, the OE converting circuit  142  may photomix dispersed pulses of the optical signal FT. Furthermore, the OE converting circuit  142  may generate the signal S 4  by photoelectrically converting the photomixed optical signal. 
     For example, the OE converting circuit  142  may perform an operation on dispersed optical signals included in the optical signal FT in order to perform photomixing. For example, the OE converting circuit  142  may perform a dot product operation on the pulses included in the optical signal FT. The OE converting circuit  142  may generate pulses having result values of the dot product operation as magnitudes. 
     The OE converting circuit  142  may include a photoelectric conversion element for photoelectrically converting the optical signal FT. For example, the OE converting circuit  142  may include a photoconductive sensor, a photodiode, a phototransistor, a solar cell, a photoconductive image sensor, a CCD image sensor, etc. using an internal photoelectric effect. Alternatively, the OE converting circuit  142  may include a photoelectric tube, a photomultiplier tube, a photoemissive image sensor, etc. using an external photoelectric effect. The OE converting circuit  142  may output the signal S 4  as an output signal of the waveform generator  100 . 
     The magnitude of the signal S 4  may be related to the magnitudes of the pulses included in the optical signal FT. Since the optical signal FT is generated on the basis of the optical signal S 3 , the magnitude of the signal S 4  may be related to the magnitudes of the pulses included in the optical signal S 3 . Since the optical signal FT is generated on the basis of the optical signal M 1  and the optical signal M 2 , the magnitude of the signal S 4  may be related to the magnitudes of the pulses included in the optical signal M 1  and optical signal M 2 . 
     The shape factor of the signal S 4  may be related to the phases of the pulses included in the optical signal FT. Since the optical signal FT is generated on the basis of the optical signal S 3 , the shape factor of the signal S 4  may be related to the phases of the pulses included in the optical signal S 3 . Since the optical signal FT is generated on the basis of the optical signal M 1  and the optical signal M 2 , the shape factor of the signal S 4  may be related to the phases of the pulses included in the optical signal M 1  and optical signal M 2 . 
     The signal S 4  may have at least one frequency band. The frequency bands of the signal S 4  may be related to the intervals between the pulses included in the optical signal FT. Since the optical signal FT is generated on the basis of the optical signal S 3 , the frequency bands of the signal S 4  may be related to the intervals between the pulses included in the optical signal S 3 . Since the optical signal FT is generated on the basis of the optical signal M 1  and the optical signal M 2 , the frequency bands of the signal S 4  may be related to the intervals between the pulses included in the optical signal M 1  and optical signal M 2 . 
     That is, the frequency bands of the signal S 4  may correspond to differences between the frequencies of the pulses included in the optical signal S 3 . The frequency bands of the signal S 4  may correspond to differences between the frequencies of the pulses included in the optical signal M 1  and optical signal M 2 . As described above with reference to  FIG. 2 , the waveform shaping circuit  132  may attenuate the magnitudes of pulses corresponding to specific frequencies among the pulses included in the optical signal S 1  so as to adjust the intervals between the pulses. As the magnitudes of the pulses included in the optical signal S 1  is attenuated, the frequency bands of the signal S 4  corresponding to attenuated pulses may be adjusted. 
     The number of the frequency bands of the signal S 4  may be related to the intervals between the pulses included in the optical signal FT. In detail, the number of the frequency bands may be related to the number of values that the intervals between the pulses have. 
     The bandwidths of the frequency bands may be related to the number of the pulses included in the optical signal FT. Since the optical signal FT is generated on the basis of the optical signal S 3  combined by the combining circuit  136 , the bandwidth may be related to the number of the pulses included in the optical signal S 3 . Since the optical signal S 3  is generated on the basis of the optical signal M 3  and the optical signal M 4 , the bandwidth may be related to the number of the pulses included in the optical signal M 3  and optical signal M 4 . 
     As described above with reference to  FIG. 1 , a user may adjust characteristics of the optical signal S 3  generated by the waveform shaping circuit  130  on the basis of the control signal C 2  generated by the controlling circuit  150 . As described below with reference to  FIG. 3 , the characteristics of the signal S 4  may correspond to the characteristics of the signal S 3 . Therefore, the user may adjust the characteristics of the signal S 4  on the basis of the control signal C 2  generated by the controlling circuit  150 . 
       FIG. 4  is a graph illustrating an example optical signal generated by the optical signal generating circuit of  FIG. 1 . In the example of  FIG. 4 , the x-axis may represent a frequency in hertz [Hz]. The y-axis may represent the magnitude of the pulses included in the optical signal S 1 . 
     As described above with reference to  FIGS. 1 and 2 , the optical signal S 1  may include the optical comb signal. Referring to  FIG. 4 , the optical signal S 1  may include n number of pulses in a frequency domain (where n is a natural number). The magnitudes of the pulses may be “P1”. The intervals between the pulses may be “Δf1”. Although not illustrated in  FIG. 4 , the phases of the pulses may be “0”. Although  FIG. 4  illustrates that the all of the intervals between the pulses are “Δf1”, all of the magnitudes of the pulses are “P1”, and all of the phases of the pulses are “0” for better description, the inventive concept may include any example of the optical signal S 1  having different intervals, different magnitudes, and different phases. 
       FIG. 5  is a graph illustrating an example optical signal generated by the AGC amplifying circuit of  FIG. 2 . In the example of  FIG. 5 , the x-axis may represent a frequency in hertz [Hz]. The y-axis may represent the magnitude of the pulses included in the optical signal M 1 . 
     Referring to  FIG. 5 , the optical signal M 1  may include n number of pulses in a frequency domain. The magnitudes of the pulses may be “P2”. For better description, an example in which “P2” is smaller than “P1” (i.e., an example in which the AGC amplifying circuit  131  attenuates the magnitude of the optical signal S 1 ) will be described, but it should be understood that “P2” may be equal to or larger than “P1”. 
     Although not illustrated in  FIG. 5 , the phases of the pulses included in the optical signal M 1  may be substantially the same as the phases of the pulses included in the optical signal S 1 . In the example of  FIG. 5 , the phases of the pulses included in the optical signal M 1  may be “0”. The intervals between the pulses included in the optical signal M 1  may be substantially the same as the intervals between the pulses included in the optical signal S 1 . In the example of  FIG. 5 , the intervals between the pulses included in the optical signal M 1  may be “Δf1”. 
     As described above with reference to  FIG. 2 , the pulse shaping circuit  132  may operate normally on the basis of pulses having a magnitude within the reference range. The AGC amplifying circuit  131  may adjust the magnitudes of the pulses included in the optical signal S 1  within the reference range. In  FIG. 5 , the dotted lines may represent the pulses included in the optical signal S 1 , and the solid lines may represent the pulses included in the optical signal M 1 . The AGC amplifying circuit  131  may decrease the magnitude of the pulses included in the optical signal S 1  from “P1” to “P2” to generate the optical signal M 1 . “P2” may be a value which falls within the reference range of the pulse shaping circuit  132 . 
       FIG. 6  is a graph illustrating an example optical signal generated by the pulse shaping circuit of  FIG. 2 . In the example of  FIG. 6 , the x-axis may represent a frequency in hertz [Hz]. The y-axis may represent the magnitude of the pulses included in the optical signal M 2 . The z-axis may represent a phase in degree [°]. 
     Referring to  FIG. 6 , the optical signal M 2  may include pulses in a region R 1 , a region R 2 , and a region R 3  in a frequency domain. The optical signal M 2  may include k number of pulses in the region R 1 . The optical signal M 2  may include m number of pulses in the region R 2 . The optical signal M 2  may include i number of pulses in the region R 3 . 
     The magnitudes of the pulses in the region R 1  may be “P3” and the phases may be “0”. The intervals between the pulses in the region R 1  may be “Δf1”. The magnitudes of the pulses in the region R 2  may be “P2” and the phases may be “α”. The intervals between the pulses in the region R 2  may be “Δf2”. The magnitudes of the pulses in the region R 3  may be “P2” and the phases may be “0”. The intervals between the pulses in the region R 3  may be “Δf3”. 
     As described above with reference to  FIG. 2 , the pulse shaping circuit  132  may adjust the magnitudes of the pulses included in the optical signal M 1 . The pulse shaping circuit  132  may adjust the magnitudes of k number of pulses in the region R 1  among n number of pulses included in the optical signal M 1 . For example, the pulse shaping circuit  132  may decrease the magnitudes of the pulses included in the region R 1  from “P2” to “P3”. 
     The pulse shaping circuit  132  may adjust the phases of the pulses included in the optical signal M 1 . The pulse shaping circuit  132  may adjust the phases of m number of pulses in the region R 1  among n number of pulses included in the optical signal M 1 . For example, the pulse shaping circuit  132  may adjust the phases of the pulses included in the region R 2  from “0” to “α”. 
     As described above with reference to  FIG. 2 , the pulse shaping circuit  132  may adjust the intervals between the pulses included in the optical signal M 1 . Furthermore, the pulse shaping circuit  132  may adjust the number of the pulses included in the optical signal M 1 . 
     The pulse shaping circuit  132  may adjust the intervals between the pulses included in the region R 2  to generate m number of pulses. For example, the pulse shaping circuit  132  may decrease the magnitudes of some pulses among the pulses included in the region R 2  from “P2” to “0”. For example, the pulse shaping circuit  132  may attenuate pulses between two pulses so as to adjust the interval between the two pulses. Therefore, the intervals between the pulses in the region R 2  may increase from “Δf1” to “Δf2”. 
     The pulse shaping circuit  132  may adjust the intervals between the pulses included in the region R 3  to generate i number of pulses. For example, the pulse shaping circuit  132  may decrease the magnitudes of some pulses among the pulses included in the region R 3  from “P2” to “0”. For example, the pulse shaping circuit  132  may attenuate pulses between two specific pulses so as to adjust the interval between the two pulses. Therefore, the intervals between the pulses in the region R 3  may increase from “Δf1” to “Δf3”. 
     Since the magnitudes of some pulses among the pulses included in the region R 3  are attenuated, the number of the pulses included in the region R 3  may decrease. Therefore, the number “k+m+i” of the pulses included in the optical signal M 2  may be smaller than the number “n” of the pulses included in the optical signal M 1 . 
       FIG. 7  is a graph illustrating an example optical signal generated by the optical modulation circuit of  FIG. 2 . In the example of  FIG. 7 , the x-axis may represent a frequency in hertz [Hz]. The y-axis may represent the magnitude of the pulses included in the optical signal M 3 . 
     In  FIG. 7 , the dotted lines represent noise corresponding to the pulses (i.e., the pulses illustrated in  FIG. 4 ) included in the optical signal S 1 . The solid lines represent the pulses included in the optical signal M 3 . Referring to  FIG. 7 , the optical signal M 3  may include n number of pulses. The magnitudes of the pulses may be “P1”, and the intervals between the pulses may be “Δf1”. Although not illustrated in  FIG. 7 , the phases of the pulses may be “0”. 
     As described above with reference to  FIG. 2 , the optical modulation circuit  133  may adjust the frequencies of the pulses. The optical modulation circuit  133  may receive a signal having a reference frequency “fs” from the oscillator  134 . The optical modulation circuit  133  may adjust the frequencies of the pulses included in the optical signal M 3  on the basis of the signal received from the oscillator  134 . In the example of  FIG. 7 , the optical modulation circuit  133  may adjust the frequencies of the pulses by as much as “fs”. 
     The optical modulation circuit  133  may modulate the frequencies of the pulses included in the optical signal S 1  to generate the optical signal M 3 . A noise may be generated while the optical signal M 3  is generated from the optical signal S 1  by the optical modulation circuit  133 . The optical modulation circuit  133  may modulate a frequency “fa” of a pulse PS 1  to generate a pulse PS 2  having a frequency “fb”. During modulation of the frequency of the pulse PS 1 , some components of the pulse PS 1  may cause generation of a noise. Therefore, the optical signal M 3  may include a noise (residual components after modulation) having a frequency “fa”. 
     The optical filter circuit  135  may receive the optical signal M 3  of  FIG. 7  from the optical modulation circuit  133 . The optical filter circuit  135  may filter the noise included in the optical signal M 3 . For example, the optical filter circuit  135  may include a notch filter configured to block the noise included in the optical signal M 3 . The notch filter may be implemented as one of a periodic optical filter, an arrayed grating filter, and the like. The notch filter may be configured to attenuate the magnitudes of signals having frequencies included in a stop band. 
     For example, a designer may design the notch filter so that the stop band of the notch filter includes frequency bands of a noise. The optical filter circuit  135  may pass the optical signal M 3  through the notch filter so as to block noise corresponding to the signals illustrated in dotted lines. Therefore, the optical signal M 4  may correspond to the solid lines in  FIG. 7 . 
       FIG. 8  is a graph illustrating an example optical signal generated by the coupling circuit of  FIG. 2 . In the example of  FIG. 8 , the x-axis may represent a frequency in hertz [Hz]. The y-axis may represent the magnitude of the pulses included in the optical signal S 3 . The z-axis may represent a phase in degree [°]. 
     Referring to  FIG. 8 , the optical signal S 3  may include “n+k+m+i” number of pulses. The optical signal S 3  of  FIG. 8  may include the pulses illustrated in  FIG. 6  (the pulses of the optical signal M 2 ) and the pulses illustrated in solid lines in  FIG. 7  (the pulses of the optical signal M 4 ). 
     The combining circuit  136  may combine the optical signal M 2  and the optical signal M 4 . An example in which the frequencies of the pulses included in the optical signal M 2  are different from the frequencies of the pulses included in the optical signal M 4  will be described with reference to  FIG. 8 . However, as described above with reference to  FIG. 2 , at least two of the frequencies included in the optical signal M 2  and optical signal M 4  may be the same. 
     When the frequency of the pulse included in the optical signal M 2  is different from the frequency of the pulses included in the optical signal M 4 , the combining circuit  136  may generate the optical signal S 3  including both the pulses. Therefore, the number of the pulses included in the optical signal S 3  may be “n+k+m+i” obtained by adding the number “k+m+i” of the pulses included in the optical signal M 2  and the number “n” of the pulses included in the optical signal M 4 . However, an embodiment of the inventive concept is not limited to the example of  FIG. 8 , and thus may include any example of the combining circuit  136  configured to combine at least two pulses of the same frequency on the basis of an operation of vector summation. In this case, the number of the pulses included in the optical signal S 3  may be smaller than “n+k+m+i”. 
       FIG. 9  is a graph illustrating an example signal generated by the OE converting circuit of  FIG. 3 . In the example of  FIG. 9 , the x-axis may represent a frequency in hertz [Hz]. The y-axis may represent the magnitude of the signal S 4 . 
     Referring to  FIG. 9 , the signal S 4  may include a signal ER 1  of a first band. The magnitude of the signal ER 1  may be “Q1”. The signal S 4  may include a signal ER 2  of a second band. The magnitude of the signal ER 2  may be “Q1”. The signal ER 2  may include a component represented as a graph having a gradient of “SL”. The signal S 4  may include a signal ER 3  of a third band. The magnitude of the signal ER 3  may be “Q2”. The first to third bands may not overlap each other. The bandwidth of the third band may be larger than the bandwidth of the second band. The bandwidth of the second band may be larger than the bandwidth of the first band. 
       FIG. 9  illustrates the signals ER 1 , ER 2 , and ER 3  having a flat magnitude according to a frequency. However, an embodiment of the inventive concept is not limited thereto, and it could be understood that the magnitudes of the signals ER 1 , ER 2 , and ER 3  may vary with a frequency. 
     As described above with reference to  FIG. 3 , the output circuit  140  may photoelectrically convert the optical signal S 3  to generate the signal S 4 . As described above with reference to  FIG. 3 , since the OE converting circuit generates the signal S 4  by converting the optical signal FT, and the optical dispersive medium  141  generates the optical signal FT on the basis of the optical signal S 3 , the characteristics of the signal S 4  may be related to the characteristics of the optical signal S 3 . 
     For better description, an example in which pulses of a specific region included in the optical signal S 3  of  FIG. 3  one-to-one correspond to the signal of a specific band of  FIG. 9  will be described. However, an embodiment of the inventive concept is not limited thereto, and thus may include any example in which arbitrary pulses included in the optical signal S 3  correspond to the signal of a specific band included in the signal S 4 . 
     Referring to  FIGS. 6, 8, and 9 , the magnitudes of the pulses of  FIG. 8  may be related to the magnitudes (e.g., “Q1” and “Q2”) of the signals ER 1  to ER 3  of  FIG. 9 . For example, the magnitude of the signal ER 3  of the third band may be related to the magnitudes of the pulses of the region R 1 . For example, the magnitude of the signal ER 3  of the third band and the magnitudes of the pulses of the region R 1  may have a positive correlation. 
     The phases of the pulses of  FIG. 8  may be related to the shape factors of the signals ER 1  to ER 3  of  FIG. 9 . The shape factors of the signals ER 1  to ER 3  may be related to change rates (e.g., “SL”) of the magnitudes relative to the frequencies of the signals ER 1  to ER 3 . 
     For example, the waveform shaping circuit  130  may adjust the phases of the pulses included in the optical signal S 1 . The optical signal M 3  may include pulses having a phase “α” in the region R 2 . The output circuit  140  may output the signal ER 2  having a shape factor corresponding to the value of “SL”, in response to the pulses having the phase “α”. The shape factor of the signal ER may be adjusted according to the phase “α” adjusted by the waveform shaping circuit  130 . 
     The number of the pulses of  FIG. 8  may be related to the bandwidths of the first to third bands. For example, the number of the pulses included in the region R 1  may be larger than the number of the pulses included in the region R 3 . The bandwidth of the band of the signal ER 3  corresponding to the region R 1  may be larger than the bandwidth of the band of the signal ER 1  corresponding to the region R 3 . 
     For example, the waveform shaping circuit  130  may adjust the number of pulses by attenuating the magnitudes of the pulses included in the optical signal S 1  (e.g., by attenuating the magnitudes of the pulses to “0”). The waveform shaping circuit  130  may generate the optical signal S 3  including an adjusted number of pulses (in the example of  FIG. 6 , m number of pulses of the region R 2 , and i number of pulses of the region R 3 ). The output circuit  140  may generate the signals ER 2  and ER 3  of bands having bandwidths corresponding to the number of the pulses included in the optical signal S 3 . Therefore, the output circuit  140  may output the signals ER 2  and ER 3  of bands having bandwidths adjusted as the magnitudes of the pulses included in the optical signal S 1  is attenuated. 
     The intervals between the pulses included in the optical signal of  FIG. 8  may be related to the bands (e.g., first to third bands) of the signals ER 1  to ER 3  included in the signal S 4  of  FIG. 9 . 
     The pulses included in the region R 1  of  FIG. 8  may include the pulses included in the region R 1  of  FIG. 6 . The intervals between the pulses included in the region R 1  of  FIG. 6  are “Δf1”. The pulses included in the region R 3  of  FIG. 8  may include the pulses included in the region R 3  of  FIG. 6 . The intervals between the pulses included in the region R 3  of  FIG. 6  are “Δf3”. “Δf3” may be larger than “Δf1”. Therefore, the intervals between the pulses included in the region R 3  may be larger than the intervals between the pulses included in the region R 1  in  FIG. 8 . 
     Likewise, the intervals between the pulses included in the region R 3  may be larger than the intervals between the pulses included in the region R 2 . The intervals between the pulses included in the region R 2  may be larger than the intervals between the pulses included in the region R 1 . 
     As the intervals between pulses increase, the OE converting circuit  142  may output a signal of a higher band. For example, the pulses included in the region R 1  of  FIG. 8  may be converted into the signal ER 1  of the first band of  FIG. 9 . The pulses included in the region R 2  of  FIG. 8  may be converted into the signal ER 2  of the second band of  FIG. 9 . The pulses included in the region R 3  of  FIG. 8  may be converted into the signal ER 3  of the third band of  FIG. 9 . 
     For example, the waveform shaping circuit  130  may adjust the intervals between the pulses included in the optical signal S 3  by attenuating the pulses included in the optical signal S 1  (e.g., by attenuating the magnitudes of the pulses to “0”). The waveform shaping circuit  130  may generate the optical signal S 3  including pulses having adjusted intervals (in the example of  FIG. 6 , the pulses having the intervals of “Δf2” of the region R 2 , and the pulses having the intervals of “Δf3” of the region R 3 ). The output circuit  140  may generate the signals ER 2  and ER 3  of bands corresponding to the intervals between the pulses included in the optical signal S 3 . Therefore, the output circuit  140  may output the signals ER 2  and ER 3  of bands adjusted as the magnitudes of the pulses included in the optical signal S 1  is attenuated. 
     The intervals between the pulses included in the optical signal S 3  of  FIG. 8  may be related to the number of the bands (e.g., first to third bands) of the signals ER 1  to ER 3  included in the signal S 4  of  FIG. 9 . 
     For example, the intervals between the pulses included in the optical signal M 2  may have one of at least three values “Δf1”, “Δf2”, and “Δf3”. Since the optical signal S 3  of  FIG. 8  is generated on the basis of the optical signal M 2  of  FIG. 6 , the intervals between the pulses included in the optical signal S 3  may have at least three different values. Therefore, the signal S 4  of  FIG. 9  may include at least three bands (first to third bands). 
     As described above with reference to  FIG. 1 , an external user (or another device) of the waveform generator  100  may adjust the characteristics of the optical signal S 3  by means of the controlling circuit  100 . For example, the user may adjust the magnitudes, phases, intervals, and number of the pulses included in the optical signal S 3 . 
     Since the signal S 4  is generated on the basis of the optical signal S 3 , the user may adjust the characteristics of the signal S 4 . For example, the user signal S 4  may adjust the magnitude and shape factor of the signal S 4 . The user may determine or select frequency bands of the signal S 4 . The user may adjust the number of the frequency bands of the signal S 4 . Therefore, the waveform generator  100  may output the signal S 4  having a waveform generated according to an intention of the user. 
       FIG. 10  is a flowchart illustrating an example operation of the waveform generator of  FIG. 1 . 
     In operation S 110 , the AGC amplifying circuit  131  may adjust the magnitudes of the pulses included in the optical signal S 1  on the basis of the control signal C 2  received from the controlling circuit  150 . The AGC amplifying circuit  131  may adjust the magnitudes of the pulses within a required reference range by means of the pulse shaping circuit  132 . The AGC amplifying circuit  131  may generate the optical signal M 1  including pulses having adjusted magnitudes. 
     In operation S 120 , the waveform shaping circuit  130  may adjust the characteristics (magnitude, phase, number, and intervals between pulses) of the pulses included in the optical signal M 1  on the basis of the control signal C 2 . The waveform shaping circuit  130  may generate the optical signal M 2  including pulses having adjusted characteristics. 
     In operation S 130 , the optical modulation circuit  133  may adjust the frequencies of the pulses included in the optical signal S 1 . For example, the optical modulation circuit  133  may generate the optical signal M 3  by modulating the frequencies of the pulses. The optical modulation circuit  133  may increase or decrease the frequencies of the pulses by as much as a reference frequency 
     In operation S 140 , the optical filter circuit  135  may block noise of the optical signal M 3  generated in operation S 130  so as to generate the optical signal M 4 . 
     In operation S 150 , the combining circuit  136  may generate the signal S 3  by combining the optical signal S 2  generated in operation S 120  and the optical signal M 4  generated in operation S 140 . 
     In operation S 160 , the output circuit  140  may photoelectrically convert the optical signal S 3  generated in operation S 150  to output the signal S 4 . For example, the signal S 4  may be an electric signal. 
     Although  FIG. 10  illustrates an embodiment in which operations S 110  and S 120  are performed prior to operations S 130  and S 140 , the inventive concept may include all embodiments in which operations S 110 , S 120 , S 130 , and S 140  are performed in an arbitrary order or simultaneously. 
       FIG. 11  is a block diagram illustrating a waveform generator according to an embodiment of the inventive concept. 
     Referring to  FIG. 11 , a waveform generator  200  may include an optical signal generating circuit  210 , frequency interval adjusting circuits  220 _ 1  and  220 _ 2 , waveform shaping circuits  230 _ 1  and  230 _ 2 , and an output circuit  240 . 
     Since a specific configuration and operation of the optical signal generating circuit  210  of  FIG. 11  are similar to those of the optical signal generating circuit  110  of  FIG. 1 , detailed descriptions thereof are not provided below. Since specific configurations and operations of the waveform shaping circuits  230 _ 1  and  230 _ 2  of  FIG. 11  are similar to those of the waveform shaping circuit of  FIG. 1 , detailed descriptions thereof are not provided below. Since a specific configuration and operation of the output circuit  240  of  FIG. 11  are similar to those of the output circuit  140  of  FIG. 1 , detailed descriptions thereof are not provided below. Since a specific configuration and operation of the controlling circuit  250  of  FIG. 11  are similar to those of the controlling circuit  150  of  FIG. 1 , detailed descriptions thereof are not provided below. 
     However, the output circuit  240  of  FIG. 11  may further include a combining circuit configured to combine an optical signal S 3 _ 1  and an optical signal S 3 _ 2 . Alternatively, a separate combining circuit may be connected between the waveform shaping circuits  230 _ 1  and  230 _ 2 , or the waveform shaping circuits  230 _ 1  and  230 _ 2  may include a combining circuit. Since a configuration and operation of the combining circuit are similar to those of the combining circuit  136  of  FIG. 2 , detailed descriptions thereof are not provided below. 
     The optical signal generating circuit  210  may output the optical signal S 1  to the frequency interval adjusting circuits  220 _ 1  and  220 _ 2 . The frequency interval adjusting circuits  220 _ 1  and  220 _ 2  may receive the optical signal S 1  from the optical signal generating circuit  210 . For example, the frequency interval adjusting circuits  220 _ 1  and  220 _ 2  may receive the optical comb signal included in the optical signal S 1 . The frequency interval adjusting circuits  220 _ 1  and  220 _ 2  may respectively receive control signals C 1 _ 1  and C 1 _ 2  from the controlling circuit  250 . 
     The frequency interval adjusting circuit  220 _ 1  may generate an optical signal S 2 _ 1  on the basis of the control signal C 1 _ 1  and the optical signal S 1 . The frequency interval adjusting circuit  220 _ 2  may generate an optical signal S 2 _ 2  on the basis of the control signal C 1 _ 2  and the optical signal S 1 . For example, the frequency interval adjusting circuits  220 _ 1  and  220 _ 2  may adjust the intervals between the pulses included in the optical signal S 1 . 
     For example, the control signal C 1 _ 2  may indicate a first group of pulses determined to be attenuated among the pulses included in the optical signal S 1 . The control signal C 1 _ 2  may indicate a second group of pulses determined to be attenuated among the pulses included in the optical signal S 1 . The frequency interval adjusting circuit  220 _ 1  may attenuate the first group of pulses to adjust the intervals between pulses. The frequency interval adjusting circuit  220 _ 2  may attenuate the second group of pulses to adjust the intervals between pulses. An example operation of the frequency interval adjusting circuits  220 _ 1  and  220 _ 2  will be described in more detail with reference to  FIG. 12 . 
     The output circuit  240  may combine optical signals S 3 _ 1  and S 3 _ 2 . For example, the output circuit  240  may include an element similar to the combining circuit  136  of  FIG. 2  to combine the optical signals S 3 _ 1  and S 3 _ 2 . The output circuit  240  may photoelectrically convert an optical signal generated by combining the optical signals S 3 _ 1  and S 3 _ 2 . 
     The output circuit  240  may generate a signal on the basis of the optical signal S 3 _ 1  received from the waveform shaping circuit  230 _ 1 . The output circuit  240  may generate a signal on the basis of the optical signal S 3 _ 2  received from the waveform shaping circuit  230 _ 2 . The frequency band of the signal generated on the basis of the optical signal S 3 _ 1  may be different from the frequency band of the signal generated on the basis of the optical signal S 3 _ 2 . 
     The frequency interval adjusting circuit  220 _ 1  and the waveform shaping circuit  230 _ 1  may be cascode-connected to the frequency interval adjusting circuit  220 _ 2  and the waveform shaping circuit  230 _ 2 . Since the frequency interval adjusting circuits  220 _ 1  and  220 _ 2  and the waveform shaping circuits  230 _ 1  and  230 _ 2  are provided as a cascode structure, a plurality of processes for a single optical signal may be performed in parallel. For example, the waveform generator  200  may perform in parallel a process of generating the optical signal S 3 _ 1  on the basis of the optical signal S 1  and a process of generating the optical signal S 3 _ 2  on the basis of the optical signal S 1 . 
     Although  FIG. 11  illustrates a configuration including the frequency interval adjusting circuit  220 _ 1  and the frequency interval adjusting circuit  220 _ 2 , the inventive concept may include any embodiment which includes either the frequency interval adjusting circuit  220 _ 1  or the frequency interval adjusting circuit  220 _ 2 . For example, the waveform generator  200  may include only the frequency interval adjusting circuit  220 _ 2 . In this example, the optical signal generating circuit  210  may directly output the optical signal S 1  to the waveform shaping circuit  230 _ 1 . The waveform shaping circuit  230 _ 1  may operate on the basis of the optical signal S 1 . 
       FIG. 12  is a graph illustrating an example optical signal generated by the frequency interval adjusting circuits of  FIG. 11 . In the example of  FIG. 12 , the x-axis may represent a frequency in hertz [Hz]. The y-axis may represent the magnitude of the pulses included in the optical signal S 3 _ 1  or S 3 _ 2 . 
     An example operation of the frequency interval adjusting circuit  220 _ 1  of  FIG. 11  will be described with reference to  FIG. 12 . The operation of the frequency interval adjusting circuit  220 _ 2  is similar to the operation of the frequency interval adjusting circuit  220 _ 1 , and is thus not described below. Referring to  FIG. 12 , the optical signal S 2 _ 1  may include a “2/n” number of pulses. The intervals between the pulses may be “2×Δf1”. The magnitudes of the pulses may be “P4”. 
     The frequency interval adjusting circuit  220 _ 1  may adjust the intervals between the pulses included in the optical signal S 1  in a frequency domain on the basis of the control signal C 1 _ 1 . 
     The frequency interval adjusting circuit  220 _ 1  may obtain information related to the intervals between pulses from the control signal C 1 _ 1 . The frequency interval adjusting circuit  220 _ 1  may adjust the intervals between pulses. A method of adjusting the intervals between pulses by the frequency interval adjusting circuit  220 _ 1  is similar to a method of adjusting the intervals between pulses by the pulse shaping circuit  132  of  FIG. 2 , and is thus not described below. For example, the frequency interval adjusting circuit  220 _ 1  may include at least one of a waveform shaping device, a periodic optical filter, or an arrayed grating filter to adjust the intervals between pulses. 
     The frequency interval adjusting circuit  220 _ 1  may attenuate the magnitudes of pulses included in a specific group among the pulses included in the optical signal S 1 . For example, when comparing  FIG. 4  and  FIG. 12 , the frequency interval adjusting circuit  220 _ 1  may attenuate pulses located at jth positions (where j is an even number) based on a pulse corresponding to a lowest frequency among the pulses included in the optical signal S 1 . The fact that a pulse is located at a specific position represents that a graph of the pulse is displayed in correspondence to a specific point on an x-axis. Therefore, the intervals between the pulses included in the optical signal S 2 _ 1  may be two times the intervals between the pulses included in the optical signal S 1 . The number of the pulses included in the optical signal S 2 _ 1  may be half the number of the pulses included in the optical signal S 1 . 
     However, the operation of the frequency interval adjusting circuit  220 _ 1  described above with reference to  FIG. 12  is merely an example, and thus the inventive concept may include all embodiments of the frequency interval adjusting circuit  220 _ 1  configured to adjust the intervals between pulses by attenuating pulses having arbitrary frequencies in response to a control of the controlling circuit  250 . 
       FIG. 13  is a graph illustrating an example signal generated by the output circuit of  FIG. 11 . In the example of  FIG. 13 , the x-axis may represent a frequency in hertz [Hz]. The y-axis may represent the magnitude of the signal S 4 . 
     Referring to  FIG. 13 , the signal S 4  may include a signal ER 4  of a fourth band. The magnitude of the signal ER 4  may be “Q3”. The signal S 4  may include a signal ER 5  of a fifth band. The magnitude of the signal S 4  may be “Q4”. The fourth and fifth bands may not overlap each other. Each of the signal ER 4  and the signal ER 5  may have a specific shape factor. The bandwidth of the fourth band may be larger than the bandwidth of the fifth band. 
       FIG. 13  illustrates the signals ER 4  and ER 5  having a flat magnitude. However, an embodiment of the inventive concept is not limited thereto, and it could be understood that the magnitudes of the signals ER 4  and ER 5  may vary with a frequency. 
     The output circuit  240  may photoelectrically convert the optical signal S 3 _ 1  to generate the signal ER 4  of the fourth band. The output circuit  240  may photoelectrically convert the optical signal S 4 _ 1  to generate the signal ER 5  of the fifth band. The frequency interval adjusting circuit  220 _ 1  and the waveform shaping circuit  230 _ 1  may process the optical signal S 1  in response to a control of the controlling circuit  250  to generate the optical signal S 3 _ 1  corresponding to the signal ER 4  of the fourth band. The frequency interval adjusting circuit  220 _ 2  and the waveform shaping circuit  230 _ 2  may process the optical signal S 1  in response to a control of the controlling circuit  250  to generate the optical signal S 3 _ 2  corresponding to the signal ER 5  of the fifth band. 
     The controlling circuit  250  may generate the control signals C 1 _ 1 , C 1 _ 2 , C 2 _ 1 , and C 2 _ 2  in response to a user&#39;s command or a request of another device. The user may control the frequency interval adjusting circuit  220 _ 1  and the waveform shaping circuit  230 _ 1  by means of the controlling circuit  250  to adjust the characteristics of the signal ER 4 . The user may control the frequency interval adjusting circuit  220 _ 2  and the waveform shaping circuit  230 _ 2  by means of the controlling circuit  250  to adjust the characteristics of the signal ER 5 . For example, the waveform generator  200  may generate the signal S 4  having frequency bands, bandwidths of the frequency bands, the number of the frequency bands, shaping factors, and magnitudes determined according to a user&#39;s command or a request of another device. 
       FIG. 14  is a flowchart illustrating an example operation of the waveform generator of  FIG. 11 . 
     Operations S 220  to S 250  of  FIG. 14  are similar to operations S 110  to S 140  of  FIG. 10 , are thus not described below. 
     In operation S 210 , the frequency interval adjusting circuits  220 _ 1  and  220 _ 2  may adjust the magnitudes of the pulses included in the optical signal S 1  to generate the optical signals S 2 _ 1  and S 2 _ 2 . The frequency interval adjusting circuits  220 _ 1  and  220 _ 2  may adjust the magnitudes of the pulses included in the optical signal S 1  on the basis of the control signals C 2 _ 1  and C 2 _ 2  to adjust the intervals between the pulses. 
     In operation S 260 , the waveform shaping circuit  230 _ 1  or a separate combining circuit may generate the optical signal S 3 _ 1  by combining the optical signal generated in operations S 220  and S 230  on the basis of the optical signal S 2 _ 1  and the optical signal generated in operations S 240  and S 250  on the basis of the optical signal S 2 _ 1 . The waveform shaping circuit  230 _ 2  or the separate combining circuit may generate the optical signal S 3 _ 2  by combining the optical signal generated in operations S 220  and S 230  on the basis of the optical signal S 2 _ 2  and the optical signal generated in operations S 240  and S 250  on the basis of the optical signal S 2 _ 2 . 
     In operation S 270 , the output circuit  240  may generate a new optical signal by combining the optical signal S 3 _ 1  and the optical signal S 3 _ 2 . The output circuit  240  may photoelectrically convert the combined signal to output the signal S 4 . The signal S 4  may be an electric signal. The signal S 4  may include a signal of a frequency band corresponding to the optical signal S 3 _ 1  and a signal of a frequency band corresponding to the optical signal S 3 _ 2 . Since the optical signal S 3 _ 1  is generated on the basis of the optical signal S 2 _ 1  and the optical signal S 3 _ 2  is generated on the basis of the optical signal S 2 _ 2 , the signal S 4  may include a signal of a frequency band corresponding to the optical signal S 2 _ 1  and a signal of a frequency band corresponding to the optical signal S 2 _ 2 . 
       FIG. 15  is a block diagram illustrating a waveform generator according to an embodiment of the inventive concept. 
     Referring to  FIG. 15 , a waveform generator  1000  may include an optical signal processing block  1100  and an electric signal processing block  1200 . An optical signal generating circuit  1110 , a frequency interval adjusting circuit  1120 , a waveform shaping circuit  1130 , and an output circuit  1140  may be arranged in the optical signal processing block  1100 . Ta controlling circuit  1210  and a bias circuit  1220  may be arranged in the electric signal processing block  1200 . 
     The waveform generator  1000  may be implemented as at least one semiconductor chip. For example, the waveform generator  1000  may be implemented as an indium arsenide/indium phosphide (InAs/InP) compound semiconductor chip based on a silicon photonics technology. The waveform generator  1000  may be implemented in a form of an opto-electronic integrated circuit including the optical signal generating block  1110  which operates on the basis of optical signals and the electric signal processing block  1200  which operates on the basis of electric signals. 
     Configurations and operations of the optical signal generating circuit  1110 , the waveform shaping circuit  1130 , the output circuit  1140 , and the controlling circuit  1210  of  FIG. 15  are similar to those of the optical signal generating circuit  110 , the waveform shaping circuit  130 , the output circuit  140 , and the controlling circuit  150  of  FIG. 1 , and are thus not described below. A configuration and operation of the frequency interval adjusting circuit  1120  of  FIG. 15  are similar to those of the frequency interval adjusting circuits  220 _ 1  and  220 _ 2  of  FIG. 11 , and are thus not described below. 
     The bias circuit  1220  of  FIG. 15  may supply a bias voltage to the controlling circuit  1210 . For example, the bias circuit  1220  may be supplied with a voltage from a power supply or the like outside the waveform generator  1000 . The bias circuit  1220  may include a regulator or the like for supplying the bias voltage. The bias circuit  1220  may convert a voltage supplied through the regulator or the like. The bias circuit  1220  may supply the converted voltage to the controlling circuit  1210  as the bias voltage. 
     According to an embodiment of the inventive concept, signals having characteristics determined according to a user&#39;s command may be generated. 
     Although the example embodiments of the present invention have been described, it is understood that the present invention should not be limited to these example embodiments but various changes and modifications can be made by one ordinary skilled in the art within the spirit and scope of the present invention as hereinafter claimed.