Abstract:
In a clock signal reproducing circuit in a pulse stuffed synchronizing system, a destuffing circuit removes stuff pulses and unnecessary bits from a higher order group signal to output a lower order group signal, and outputs stuff data indicating existence or non-existence of positive stuff or negative stuff in the higher order group signal. A storage circuit stores the lower order group signal outputted from the destuffing circuit. A stuff rate determining circuit determines a stuff rate from a difference between the number of positive stuffs and the number of negative stuffs to a stuffing possible period of the higher order group signal based on the stuff data outputted from the destuffing circuit. A variable frequency divider frequency-divides a clock signal of the higher order group signal based on the control signal outputted from the control circuit. A phase synchronization oscillation circuit reproduces a clock signal of the lower order group signal based on the frequency-divided clock signal outputted from the variable frequency divider.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a technique for reproducing a clock signal for a lower order group signal at a receiver side in a pulse stuffed synchronizing system. 
     2. Description of Related Art 
     In a conventional digital data transmission system, a transmitter converts digital signals into their high-speed digital signal form by time-division multiplexing and a receiver receives and demultiplexes the multiplexed signal to reproduce the original digital signals. The original digital signals to be multiplexed are however supplied from various devices and may not be matched in the clock rate without subjecting to a particular process. For matching or synchronizing the signals, a net synchronizing method or a stuffed synchronizing method may preferably be used. 
     The stuffed synchronizing method is not designed to directly synchronize the digital signals received from various devices. The stuffed synchronizing method stores the signals to be multiplexed in a memory and then reads out them by use of a common clock signal which is slightly faster than that of the digital signals to align the signals in the timing. A difference between the digital signal and the clock signal is compensated by inserting an extra number of pulses (referred to as stuffed pulses). It is thus needed at the receiver side to identify the position of stuffed pulses for removing the extra pulses. 
     More specifically, the pulse stuffed synchronizing system is depicted in “Simple Digital Data Transmission” by Makoto Yamashita et al, the Telecommunications Association in Japan, Ver. 4, Jun. 26, 1998. In this reference, there is a case where a clock signal for a lower order group signal and a clock signal for a higher order group signal are not synchronous with each other. At this time, extra pulses are inserted (stuffed) into the lower order group signal at the transmitter side to synchronize the clock signal for the lower order group signal and the clock signal for the higher order group signal. At the receiver side in the pulse stuffed synchronizing system, the extra or stuffed pulses are removed (de-stuffed) and then the clock signal for the lower order group signal is reproduced by a phase synchronization oscillating circuit. 
     Also, the pulse stuffed synchronizing system is described explicitly in “Waiting Time Jitter” by D. L. Duttweiler (The Bell System Technical Journal, Vol. 51, No. 1, January 1972). In this reference, it is described that the stuffed pulses can not fully be removed at the receiver side hence causing jitters. 
     Particularly, in a conventional pulse stuffed synchronizing method utilized with SONET (synchronous optical network) or SDH (synchronous digital hierarchy) in an advanced digital communication system, the extra pulses are inserted and removed on a byte-by-byte basis. As a result, a greater amplitude of jitter is generated. 
     A procedure of synchronously multiplexing existing DS3 signals under the SONET standard will now be described. FIGS. 17 to  19  are diagrams showing a frame structure of an STS-1 signal, a frame structure of an STS-1 SPE signal and a byte structure of data signal, respectively. 
     The SONET specifications are defined in ANSI T1.105-1995 (Synchronous optical network-Basic description including multiplex structure, rates, and formats) and ANSI T1.105.02-1995 (Synchronous optical network-Payload mappings) of the American National Standards Institute. In the standards, the DS3 signal having a nominal bit repetitive frequency of 44.736 Mb/s is accommodated in the STS-1 (synchronous transport signal level 1) signal having a nominal bit repetitive frequency of 51.84 Mb/s. The STS-1 signal is the higher order group signal while the DS3 signal is the lower order group signal. As shown in FIG. 17, the STS-1 signal has a capacity of 810 bytes, 90 bytes in horizontal by 9 rows in vertical and accommodates a single STS-1 SPE (synchronous payload envelope) signal. In the STS-1 signal, the STS-1 SPE is accommodated in the region of a frame other than the overhead region without considering the stuffed pulses and its region is 783 bytes per frame. 
     Also, the STS-1 signal frame and the STS-1 SPE frame are not always matched relative to each other. As shown in FIG. 17, one frame of the STS-1 SPE signal may be accommodated in two frames of the STS-1 signal. In other words, the head location of the STS-1 SPE signal may be varied in the frame of the STS-1 signal. The head location of the STS-1 SPE signal in the STS-1 signal frame is indicated with pointers H 1  and H 2  which are accommodated in the overhead region of the STS-1 signal frame. 
     The STS-1 signal and the STS-1 SPE signal are not always synchronized with each other. For this reason, the STS-1 signal includes positive/zero/negative stuff data in units of bytes. The existence or non-existence of the stuffed pulses is also indicated with the pointers H 1  and H 2 . More specifically, the existence or non-existence of the stuffed pulses is indicated by inverting of specific bits of the pointers H 1  and H 2 . 
     Also, there is a pointer operation H 3 . When the positive stuffing is made, one byte of stuffed pulses is inserted after the pointer operation H 3 . In case of the negative stuffing, STS-1 SPE data is accommodated in one byte of the pointer operation H 3 . The zero stuffing means that neither the positive stuffing nor negative stuffing is made. In case of the zero stuffing, the stuffed pulses are inserted in one byte of the pointer operation H 3  represents and STS-1 SPE data is accommodated in one byte after the pointer operation H 3 . 
     As shown in FIGS. 18 and 19, the frame of the STS-1 SPE signal is composed of 783 bytes, 87 bytes in horizontal by 9 rows in vertical, and accommodates a DS3 signal. Since the STS-1 SPE signal and the DS3 signal are not synchronous with each other, the positive stuffing is defined in units of bits. The region of the STS-1 SPE signal where the DS3 signal is accommodated is represented by a combination of stuffed bits s and data bits i regardless of the positive stuffing, and 622 bits per row. The bit s indicates the positive stuffing location where the data of the DS3 signal is usually stored while the stuffed pulses are stored only in a positive stuffing mode. The existence or non-existence of the positive stuffing is indicated by converting all the stuff control bits c to 1. It should be noted that in FIG. 19, o indicates an overhead bit and r indicates a fixed stuff bit which is a type of overhead bit. 
     When the DS3 signal is accommodated in the STS-1 signal, there are carried out two stages of the stuffing processes, i.e., the positive/zero/negative stuffing process in units of bytes in the STS-1 signal and the positive stuffing process in units of bits in the STS-1 SPE signal. As described previously, the positive/zero/negative stuffing process in units of bytes in the STS-1 signal may generate a greater amplitude of jitter. It is hence crucial to remove such jitter. 
     For the purpose, an apparatus and a method for mapping and removing jitter are disclosed in Japanese Patent Laid Open Patent Application (JP-A-Heisei 9-505705) as shown by a circuit arrangement of FIG.  1 . FIG. 1 is a block diagram showing the structure of a receiving unit (a de-synchronizer) for reproducing the inserted signals including asynchronous data from a high transmission rate synchronization signal in a predetermined clock rate. 
     Referring to FIG. 1, a first de-stuffing circuit  1  detects the positive/zero/negative stuffing in a received STS-1 signal and carries out the de-stuffing process to remove unnecessary bits such as of the overhead of the STS-1 signal. Thus, the first de-stuffing circuit  1  extract an STS-1 SPE signal  68 . Then, a second de-stuffing circuit  12  detects the positive stuffing in the STS-1 SPE signal and carries out the de-stuffing operation to remove unnecessary bits such as the overhead of the STS-1 SPE signal. Thus, the second de-stuffing circuit  12  extract a DS3 signal. 
     A stuff bit leak circuit  15  produces a data indicating that byte based stuff data  64  of the STS-1 signal detected by the first de-stuffing circuit and bit based stuff data  65  of the STS-1 SPE signal detected by the second de-stuffing circuit are dispersed into bits to remove the stuffed pulses. Then, the circuit  15  outputs the data as a stuff bits leak data  73 . Similarly, an overhead delete data generating circuit  16  produces a data indicating that data indicating the number of bytes of the overhead removed by the first and second de-stuffing circuits and data indicating the number of bytes of the unused bits are dispersed in unit of bits and removed. Then, the overhead delete data generating circuit  16  outputs the produced data as overhead delete data  74 . Only the DS3 signal extracted from the STS-1 SPE signal is stored in a storage circuit  2  which in turn detects a quantity of stored data and outputs data storage quantity data  75 . 
     First, second and third digital/analog converter circuits  17 ,  18  and  19  modulates into pulse modulated signals, the stuff bit leak data  73  from the stuff bits leak circuit  15 , the overhead delete data  74  from the overhead delete data generating circuit  16 , and the data storage quantity data  75  from the storage circuit  2 , respectively. An adder circuit  20  adds the three outputs of the first, second  18  and third digital/analog converter circuits  17 ,  18  and  19 . An output of the adder circuit  20  is passed through a low pass filter circuit  603  and fed to a voltage controlled oscillator circuit  604  to control the oscillation clock signal frequency. A clock output  58  outputted from the voltage controlled oscillator circuit  604  is synchronous with the clock signal of the extracted DS3 signal and can be used to read the DS3 signal from the storage circuit  2 . 
     In this manner, the circuit shown in FIG. 17 processes data such that the stuffed pulses are dispersed and removed in units of bits. Thus, variations in the controlled voltage from the voltage controlled oscillator circuit due to the removal of the stuffed pulses is restrained to reduce the generation of jitter. 
     Also, a stuff multiplexing receiver circuit shown in FIG. 12 is disclosed in Japanese Patent No. 2,697,371. This reference solves the problem that a difference in frequency between a write clock signal and the read clock signal becomes greater when a large number of bits having no data exist in a single frame. In this case, if the frequency difference is large, the drop of pulses from the clock signal which is to be supplied to a PLL circuit is increased so that the amplitude of jitter can be too large. As a result, the PLL circuit can not restrain the jitter. More particularly, the clock signal generated from a transmission line data is divided in frequency into units of frame periods. Also, the clock signal from the voltage controlled oscillator circuit in the PLL is variably divided in frequency into in units of frame periods depending on the existence or non-existence of the stuffed pulses. The two frame periods are then compared to each other in the phase by a phase comparator. The difference between the two frame periods is fed back. In this way, the effect of bits carrying no information in the frame may be avoided. 
     Next, the stuff multiplexing receiver circuit disclosed in the Japanese Patent No. 2,697,371 will now be described in more detail referring to FIG.  2 . The circuit shown in FIG. 2 includes a first and second de-stuffing circuit  1  and  12 , as shown in the circuit shown in FIG.  17  and extracts an STS-1 SPE signal  68  and a DS3 signal  52  respectively. The extracted DS3 signal  52  is then stored in a storage circuit  2 . 
     A frame pulse generating circuit  21  divides in frequency the clock signal frequency of the STS-1 signal to produce pluses of each frame cycle of the STS-1 signal. A variable frequency dividing circuit  606  divides a clock output  652  outputted from a voltage controlled oscillator circuit  604  by L which is the number of bits of the DS3 signal accommodated in one frame of the STS-1 signal. It would be apparent that L is a natural number. The number of bits L of the DS3 signal may be varied from one frame to another. For this reason, a variable frequency dividing circuit controlling section  14  calculates L from the stuff data from the first de-stuffing circuit  1  and the second de-stuffing circuit  12  and controls the frequency division ratio of the variable frequency dividing circuit  606 . 
     A phase comparing circuit  601  compares the pulses of each frame cycle of the STS-1 signal received from the frame pulse generating circuit  21  with a clock signal  653  outputted from the variable frequency dividing circuit  606  in phase. The phase comparing circuit  601  transmits the comparing result to a voltage controlled oscillator circuit  604  via an amplifier circuit  602  and a low pass filter circuit  603  to control the oscillation clock signal frequency. The phase comparing circuit  601 , the amplifier circuit  602 , the low pass filter circuit  603 , the voltage controlled oscillator circuit  604 , and the variable frequency dividing circuit  606  constitute a phase synchronization oscillator circuit  9  with the frequency division ratio variable. The circuit of the Japanese Patent No. 2,697,371 shown in FIG. 2 carries out the phase comparison in each frame of the STS-1 signal independently of the removal of stuffed pulses, thereby to minimize the effect of jitter caused due to the stuffed pulses. 
     However, there are the following problems in the apparatus and method for mapping and removing jitter and shown in FIG.  17  and disclosed in the Japanese Laid Open Patent Application (JP-A-Heisei 9-505705). 
     That is, the oscillation frequency of the voltage controlled oscillator circuit  604  shown in FIG. 17 is determined based on the stuffed bits leak data  73 , the overhead delete data  74 , and the data storage quantity data  75 . For handling the three different types of the data, the circuit arrangement has to be bulky in the size. Also, because the overhead is not related directly to the stuffed pulses, the clock signal can be preferably reproduced without use of the overhead delete data  74 . In this respect, the circuit shown in FIG. 17 shall be modified for improvement. 
     There are the following problems in the stuff multiplex transmitter/receiver circuit of the patent No. 2,697.371 shown in FIG.  18 . The number of bits of the DS3 signal in one frame of the STS-1 signal is substantially 5592 in average. Accordingly, when the frequency division ratio L of the phase synchronization oscillator circuit  9  is as high as 5592, the voltage controlled oscillator circuit  604  will fail to restrain the effect of phase noise intrinsic to its circuit, resulting in deterioration of the quality of a reproduced clock signal. 
     It is desired that the frequency division ratio of the phase synchronization oscillator circuit is not higher than 100. Otherwise, the stuff multiplex transmitter/receiver circuit shown in FIG. 2 is disadvantageous in permitting the reproduced clock signal to have more phase noises. 
     In conjunction with the above description, a monitoring system of a PCM multiplexing apparatus is disclosed in Japanese Examined Patent Application (JP-B-Showa 63-9697). In this reference, the PCM multiplexing apparatus uses a stuff synchronization system. A stuff rate monitoring circuit is provided for each of channel sections which carries out a stuffing operation to a group of lower order signals to be multiplexed. The stuff rate monitoring circuit monitors whether the stuff rate of the lower order stuffed signals falls within a predetermined range. 
     Also, a destuffing circuit is disclosed in Japanese Laid Open Patent Application (JP-A-Heisei 5-153078). In this destuffing circuit, a signal from a transmission path is converted using a master clock signal provided in the apparatus such that a frame structure is realized of stuff bit inserting positions which are not continuous and are periodical in a constant interval. Moreover, the number of times of the insertion of the stuff bits is averaged. A signal after a re-stuffing operation is supplied to a conventional PLL circuit using a voltage controlled oscillator. Thus, a lower order group signal is smoothed so as to suppress output jitter. In this way, the output jitter of the lower order group signal can be restrained when the stuff bits exist continuously for a few to a few tens of bits in a digital stuff multiplex mode. 
     Also, a destuff synchronization circuit is disclosed in Japanese Laid Open Patent Application (JP-A-Heisei 8-181678). In this reference, a clock signal CK which is subjected to a destuff control is frequency-divided by first ½ frequency divider to 1/N frequency divider. Then, a signal WC is selected from the frequency-divided signals by a first selector ( 31 ) such that the signal WC does not have a relation of an integer ratio to an inserting bit period of an auxiliary signal which is inserted in a high order group signal S 1 . An output signal of a voltage controlled oscillator ( 7 ) which has the same frequency as the clock signal CK is frequency-divided by second frequency dividers ( 32  to  34 ). Then, a signal RC is selected from the frequency-divided signals by a second selector ( 35 ) such that the signal RC has the same frequency division ratio as the signal WC. A phase difference between the signal WC and the signal RC is detected by a phase comparator ( 5 ) and outputted to an oscillator ( 7 ) via a low pass filter ( 6 ). 
     SUMMARY OF THE INVENTION 
     Therefore, an object of the present invention is to provide a clock signal reproducing circuit of a lower order group signal in a pulse stuffed synchronizing system. 
     Another object of the present invention is to provide a clock signal reproducing circuit of a lower order group signal, in which the effect of jitter can be restrained, even when a large number of stuffed pulses have been inserted. 
     Still another object of the present invention is to provide a clock signal reproducing circuit of a lower order group signal, in which the phase synchronization oscillator circuit has a small frequency division ratio. 
     Yet still another object of the present invention is to provide a clock signal reproducing circuit of a lower order group signal, which has a relatively small circuit size. 
     In order to achieve an aspect of the present invention, a clock signal reproducing circuit in a pulse stuffed synchronizing system which reproduces a lower order group signal from a higher order group signal, includes a destuffing circuit, a storage circuit, a stuff rate determining circuit, a control circuit, a variable frequency divider and a phase synchronization oscillation circuit. The destuffing circuit removes stuff pulses and unnecessary bits from the higher order group signal to output the lower order group signal, and outputs stuff data indicating existence or non-existence of positive stuff or negative stuff in the higher order group signal. The lower order group signal is accommodated in the higher order group signal by inserting the stuff pulses in the lower order group signal. The storage circuit stores the lower order group signal outputted from the destuffing circuit. The stuff rate determining circuit determines a stuff rate from a difference between the number of positive stuffs and the number of negative stuffs to a stuffing possible period of the higher order group signal based on the stuff data outputted from the destuffing circuit. The control circuit outputs a control signal indicating a frequency division ratio based on the stuff rate. The variable frequency divider frequency-divides a clock signal of the higher order group signal based on the control signal outputted from the control circuit. The phase synchronization oscillation circuit reproduces a clock signal of the lower order group signal based on the frequency-divided clock signal outputted from the variable frequency divider. The lower order group signal is read out from the storage circuit in response to the reproduced clock signal of the lower order group signal. 
     The phase synchronization oscillation circuit multiplies a frequency of the frequency-divided clock signal outputted from the variable frequency divider by N (N is a predetermined positive integer) to reproduce the clock signal of the lower order group signal, when a frequency division ratio of the phase synchronization oscillation circuit is N. 
     Also, the clock signal reproducing circuit may further includes a separating circuit separates a specific lower order group signal accommodated in the higher order group signal; and an additional frequency divider frequency-divides the clock signal of the higher order group signal. The separated lower order group signal outputted from the separating circuit is supplied to the destuffing circuit, and the frequency-divided clock signal from the additional variable frequency divider is supplied to the variable frequency divider. 
     Also, the clock signal reproducing circuit may further includes a separating circuit separating a specific lower order group signal accommodated in the higher order group signal. The separated lower order group signal outputted from the separating circuit is supplied to the destuffing circuit. 
     Also, the control circuit includes a calculating circuit which carries out a calculation based on the stuff rate; a summing circuit summing an output of the calculating circuit for every frequency division period; and a determining circuit determining whether or not an output of the summing circuit is equal to or larger than a predetermined value. 
     Also, the stuff rate determining circuit includes: a shift register circuit which stores the stuff data in order; a summation calculating circuit which calculates a summation of input data and an output of the shift register circuit; and a multiplying circuit which multiplies an output of the summation calculating circuit by a predetermined value. 
     Also, the storage circuit includes a storage element, a write address counter, a read address counter and an address control circuit. The storage element stores a signal. The write address counter is driven in response to a write clock signal, and generates a write address to specify a position of the storage element in which an input signal is written. The read address counter is driven in response to a read clock signal and generates a read address to specify a position of the storage element from which an output signal is read out. The address control circuit prevents a writing operation and a reading operation to a same position of the storage element from being carried out at a same time. In this case, the address control circuit controls at least one of the write address counter and the read address counter such that the write address and the read address are apart from each other, when the write address and the read address becomes near to a limit. Also, the address control circuit controls at least one of the write address counter and the read address counter such that the write address and the read address are apart from each other at an initial setting. 
     In order to achieve another aspect of the present invention, a clock signal reproducing circuit in a pulse stuffed synchronizing system which reproduces a lower order group signal from a higher order group signal, includes a destuffing circuit, a storage circuit, a stuff rate determining circuit, a control circuit, a variable frequency divider and a phase synchronization oscillation circuit. The destuffing circuit removes stuff pulses and unnecessary bits from the higher order group signal to output the lower order group signal, and outputs stuff data indicating existence or non-existence of positive stuff or negative stuff in the higher order group signal. The lower order group signal is accommodated in the higher order group signal by inserting the stuff pulses in the lower order group signal. The storage circuit stores the lower order group signal outputted from the destuffing circuit. The stuff rate determining circuit determines a stuff rate from a difference between the number of positive stuffs and the number of negative stuffs to a stuffing possible period of the higher order group signal based on the stuff data outputted from the destuffing circuit. The control circuit outputs a control signal indicating a frequency division ratio based on the stuff rate. The frequency divider frequency-divides a clock signal of the higher order group signal in a predetermined frequency division ratio. The phase synchronization oscillation circuit frequency-divides the frequency-divided clock signal outputted from the variable frequency divider based on the control signal outputted from the control circuit, to reproduce a clock signal of the lower order group signal. The lower order group signal is read out from the storage circuit in response to the reproduced clock signal of the lower order group signal. 
     The phase synchronization oscillation circuit multiplies a frequency of the frequency-divided clock signal outputted from the variable frequency divider by N (N is a predetermined positive integer) to reproduce the clock signal of the lower order group signal, when a frequency division ratio of the phase synchronization oscillation circuit is N. 
     Also, the clock signal reproducing circuit may further includes a separating circuit separates a specific lower order group signal accommodated in the higher order group signal; and an additional frequency divider frequency-divides the clock signal of the higher order group signal. The separated lower order group signal outputted from the separating circuit is supplied to the destuffing circuit, and the frequency-divided clock signal from the additional variable frequency divider is supplied to the variable frequency divider. 
     Also, the clock signal reproducing circuit may further includes a separating circuit separating a specific lower order group signal accommodated in the higher order group signal. The separated lower order group signal outputted from the separating circuit is supplied to the destuffing circuit. 
     Also, the control circuit includes a calculating circuit which carries out a calculation based on the stuff rate; a summing circuit summing an output of the calculating circuit for every frequency division period; and a determining circuit determining whether or not an output of the summing circuit is equal to or larger than a predetermined value. 
     Also, the stuff rate determining circuit includes: a shift register circuit which stores the stuff data in order; a summation calculating circuit which calculates a summation of input data and an output of the shift register circuit; and a multiplying circuit which multiplies an output of the summation calculating circuit by a predetermined value. 
     Also, the storage circuit includes a storage element, a write address counter, a read address counter and an address control circuit. The storage element stores a signal. The write address counter is driven in response to a write clock signal, and generates a write address to specify a position of the storage element in which an input signal is written. The read address counter is driven in response to a read clock signal and generates a read address to specify a position of the storage element from which an output signal is read out. The address control circuit prevents a writing operation and a reading operation to a same position of the storage element from being carried out at a same time. In this case, the address control circuit controls at least one of the write address counter and the read address counter such that the write address and the read address are apart from each other, when the write address and the read address becomes near to a limit. Also, the address control circuit controls at least one of the write address counter and the read address counter such that the write address and the read address are apart from each other at an initial setting. 
     In order to achieve still another aspect of the present invention, a clock signal reproducing circuit in a pulse stuffed synchronizing system which reproduces a lower order group signal from a higher order group signal, includes a destuffing circuit, a storage circuit, a stuff rate determining circuit, a first control circuit, a second control circuit, a variable frequency divider and a phase synchronization oscillation circuit. The destuffing circuit removes stuff pulses and unnecessary bits from the higher order group signal to output the lower order group signal, and outputs stuff data indicating existence or non-existence of positive stuff or negative stuff in the higher order group signal. The lower order group signal is accommodated in the higher order group signal by inserting the stuff pulses in the lower order group signal. The storage circuit stores the lower order group signal outputted from the destuffing circuit. The stuff rate determining circuit determines a stuff rate from a difference between the number of positive stuffs and the number of negative stuffs to a stuffing possible period of the higher order group signal based on the stuff data outputted from the destuffing circuit. The first control circuit outputs a first control signal indicating a first frequency division ratio based on the stuff rate. The second control circuit outputs a second control signal indicating a predetermined second frequency division ratio. The variable frequency divider frequency-dividing a clock signal of the higher order group signal based on the first control signal from the first control circuit. The phase synchronization oscillation circuit frequency-divides the frequency-divided clock signal outputted from the variable frequency divider based on the second control signal outputted from the second control circuit, to reproduce a clock signal of the lower order group signal. The lower order group signal is read out from the storage circuit in response to the reproduced clock signal of the lower order group signal. 
     The phase synchronization oscillation circuit multiplies a frequency of the frequency-divided clock signal outputted from the variable frequency divider by N (N is a predetermined positive integer) to reproduce the clock signal of the lower order group signal, when a frequency division ratio of the phase synchronization oscillation circuit is N. 
     Also, the clock signal reproducing circuit may further includes a separating circuit separates a specific lower order group signal accommodated in the higher order group signal; and an additional frequency divider frequency-divides the clock signal of the higher order group signal. The separated lower order group signal outputted from the separating circuit is supplied to the destuffing circuit, and the frequency-divided clock signal from the additional variable frequency divider is supplied to the variable frequency divider. 
     Also, the clock signal reproducing circuit may further includes a separating circuit separating a specific lower order group signal accommodated in the higher order group signal. The separated lower order group signal outputted from the separating circuit is supplied to the destuffing circuit. 
     Also, the control circuit includes a calculating circuit which carries out a calculation based on the stuff rate; a summing circuit summing an output of the calculating circuit for every frequency division period; and a determining circuit determining whether or not an output of the summing circuit is equal to or larger than a predetermined value. 
     Also, the stuff rate determining circuit includes: a shift register circuit which stores the stuff data in order; a summation calculating circuit which calculates a summation of input data and an output of the shift register circuit; and a multiplying circuit which multiplies an output of the summation calculating circuit by a predetermined value. 
     Also, the storage circuit includes a storage element, a write address counter, a read address counter and an address control circuit. The storage element stores a signal. The write address counter is driven in response to a write clock signal, and generates a write address to specify a position of the storage element in which an input signal is written. The read address counter is driven in response to a read clock signal and generates a read address to specify a position of the storage element from which an output signal is read out. The address control circuit prevents a writing operation and a reading operation to a same position of the storage element from being carried out at a same time. In this case, the address control circuit controls at least one of the write address counter and the read address counter such that the write address and the read address are apart from each other, when the write address and the read address becomes near to a limit. Also, the address control circuit controls at least one of the write address counter and the read address counter such that the write address and the read address are apart from each other at an initial setting. 
     In order to achieve yet still another aspect of the present invention, a clock signal reproducing circuit in a pulse stuffed synchronizing system which reproduces a lower order group signal from a higher order group signal, includes a destuffing circuit, a storage circuit, a stuff rate determining circuit, a first control circuit, a second control circuit, a variable frequency divider and a phase synchronization oscillation circuit. The destuffing circuit removes stuff pulses and unnecessary bits from the higher order group signal to output the lower order group signal, and outputs stuff data indicating existence or non-existence of positive stuff or negative stuff in the higher order group signal. The lower order group signal is accommodated in the higher order group signal by inserting the stuff pulses in the lower order group signal. The storage circuit stores the lower order group signal outputted from the destuffing circuit. The stuff rate determining circuit determines a stuff rate from a difference between the number of positive stuffs and the number of negative stuffs to a stuffing possible period of the higher order group signal based on the stuff data outputted from the destuffing circuit. The first control circuit outputs a first control signal indicating a predetermined first frequency division ratio. The second control circuit outputs a second control signal indicating a second frequency division ratio based on the stuff rate. The variable frequency divider frequency-divides a clock signal of the higher order group signal based on the first control signal from the first control circuit. The phase synchronization oscillation circuit frequency-divides the frequency-divided clock signal outputted from the variable frequency divider based on the second control signal outputted from the second control circuit, to reproduce a clock signal of the lower order group signal. The lower order group signal is read out from the storage circuit in response to the reproduced clock signal of the lower order group signal. 
     The phase synchronization oscillation circuit multiplies a frequency of the frequency-divided clock signal outputted from the variable frequency divider by N (N is a predetermined positive integer) to reproduce the clock signal of the lower order group signal, when a frequency division ratio of the phase synchronization oscillation circuit is N. 
     Also, the clock signal reproducing circuit may further includes a separating circuit separates a specific lower order group signal accommodated in the higher order group signal; and an additional frequency divider frequency-divides the clock signal of the higher order group signal. The separated lower order group signal outputted from the separating circuit is supplied to the destuffing circuit, and the frequency-divided clock signal from the additional variable frequency divider is supplied to the variable frequency divider. 
     Also, the clock signal reproducing circuit may further includes a separating circuit separating a specific lower order group signal accommodated in the higher order group signal. The separated lower order group signal outputted from the separating circuit is supplied to the destuffing circuit. 
     Also, the control circuit includes a calculating circuit which carries out a calculation based on the stuff rate; a summing circuit summing an output of the calculating circuit for every frequency division period; and a determining circuit determining whether or not an output of the summing circuit is equal to or larger than a predetermined value. 
     Also, the stuff rate determining circuit includes: a shift register circuit which stores the stuff data in order; a summation calculating circuit which calculates a summation of input data and an output of the shift register circuit; and a multiplying circuit which multiplies an output of the summation calculating circuit by a predetermined value. 
     Also, the storage circuit includes a storage element, a write address counter, a read address counter and an address control circuit. The storage element stores a signal. The write address counter is driven in response to a write clock signal, and generates a write address to specify a position of the storage element in which an input signal is written. The read address counter is driven in response to a read clock signal and generates a read address to specify a position of the storage element from which an output signal is read out. The address control circuit prevents a writing operation and a reading operation to a same position of the storage element from being carried out at a same time. In this case, the address control circuit controls at least one of the write address counter and the read address counter such that the write address and the read address are apart from each other, when the write address and the read address becomes near to a limit. Also, the address control circuit controls at least one of the write address counter and the read address counter such that the write address and the read address are apart from each other at an initial setting. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a block diagram showing the structure of a first conventional a clock signal reproducing circuit; 
     FIG. 2 is a block diagram showing the structure of a second conventional a clock signal reproducing circuit; 
     FIG. 3 is a block diagram showing the structure of a clock signal reproducing circuit according to a first embodiment of the present invention; 
     FIG. 4 is a block diagram showing the structure of the clock signal reproducing circuit according to a second embodiment of the present invention; 
     FIG. 5 is a block diagram showing the structure of the clock signal reproducing circuit according to a third embodiment of the present invention; 
     FIG. 6 is a block diagram showing the structure of a clock signal reproducing circuit according to a fourth embodiment of the present invention; 
     FIG. 7 is a block diagram showing the structure of a clock signal reproducing circuit according to a fifth embodiment of the present invention; 
     FIG. 8 is a block diagram showing the structure of an example of a stuff rate measuring circuit of the clock signal reproducing circuit in the first embodiment; 
     FIG. 9 is a block diagram showing the structure of an example of a variable frequency dividing circuit controlling section of the clock signal reproducing circuit in the first embodiment; 
     FIG. 10 is a block diagram showing the structure of an example of a phase synchronization oscillator circuit of the clock signal reproducing circuit in the first embodiment; 
     FIG. 11 is a block diagram showing the structure of an example of a storage circuit of the clock signal reproducing circuit in the first embodiment; 
     FIG. 12 is a block diagram showing the structure of a variable frequency dividing circuit of the clock signal reproducing circuit in the fifth embodiment; 
     FIG. 13 is a block diagram showing an example of a phase synchronization oscillator circuit in the second embodiment; 
     FIG. 14 is a block diagram showing an example of a control circuit for a variable frequency dividing circuit of the clock signal reproducing circuit in the third embodiment; 
     FIG. 15 is a block diagram showing the structure of the clock signal reproducing circuit according to the sixth embodiment of the present invention; 
     FIG. 16 is a block diagram showing the structure of the clock signal reproducing circuit according to the seventh embodiment of the present invention; 
     FIG. 17 is a diagram showing a frame structure of STS-1 signal; and 
     FIGS. 18 and 19 are diagrams showing a frame structure of STS-1 SPE signal and a bit format. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Hereinafter, the clock signal reproducing circuit for a lower order group signal of the present invention will be described with reference to the attached drawings. 
     FIG. 3 is a block diagram showing the structure of the clock signal reproducing circuit according to the first embodiment of the present invention. Referring to FIG. 3, the clock signal reproducing circuit is composed of a destuffing circuit  1 , a storage circuit  2 , a stuff rate measuring circuit  3 , a control circuit  4 , a variable frequency dividing circuit  5 , and a phase locked loop circuit  6 . 
     The de-stuffing circuit  1  carries out a de-stuffing operation to a higher order group signal  51  to delete unwanted bits and extracts a lower order group signal  52  which is then stored in a storage circuit  2 . Also, the de-stuffing circuit  1  detects a stuff data  53  through the stuffing operation and supplies the detected stuff data  53  to a stuff rate measuring circuit  3 . The stuff rate measuring circuit  3  calculates a stuff rate  54  from the stuff data  53  received from the de-stuffing circuit  1 . The stuff rate data  54  calculated by the stuffing rate measuring circuit  3  is transmitted to a control circuit  4 . The control circuit  4  generates the variable frequency division control signal  55  based on the stuff rate data  54 . A variable frequency dividing circuit  5  carries out a frequency division of M 1  or M 2  to a clock signal  56  of the higher order group signal in accordance with a variable frequency division control signal  55 . A phase synchronization oscillator circuit  6  generates or reproduces a clock signal  58  from a clock signal  57  outputted from the variable frequency dividing circuit  5 . The reproduced clock signal  58  has the frequency N (N is a natural number) times greater than the frequency of the clock signal  57 . The clock signal  58  reproduced from the phase synchronization oscillator circuit  6  is the reproduced clock signal for the lower order group signal and is used as a read clock to the storage circuit  2 . 
     FIG. 8 is a block diagram of an example of the stuff rate measuring circuit  3  shown in FIG.  3 . As shown in FIG. 8, an input signal  351  is the stuff data  53  outputted from the de-stuffing circuit  1 . The input signal  351  is +1, when the positive stuffing is made, is 0 when the zero stuffing is made, i.e., no stuffing is made, and −1 when the negative stuffing is made. 
     A series of storage elements  301  form an (X−1)-stage shift register  302  where the storage content is shifted up at each of stuffing enable periods of the higher order group signal. The stuffing enable period means a period between positions in which the stuffing operation is carried out. For example, if a single position where the stuffing operation is carried out is present in one frame of the higher order group signal, the stuffing enable period is equal to one period of the higher order group signal frame. A summing circuit  303  calculates a sum of outputs of the storage elements  301 . A multiplier circuit  304  multiplies an output  352  of the summing circuit  303  by 1/X, where X is the number of input signals to the summing circuit  303 . Thus, an output  353  of the multiplier circuit  304  is the stuffing rate data  54  shown in FIG.  3 . The circuit shown in FIG. 8 is a known finite impulse response type digital filter and may be replaced by another appropriate circuit whose characteristics are alike. Also, an infinite impulse response type digital filter whose characteristics are similar to those of the circuit shown in FIG. 8 may be used with same success. 
     FIG. 9 is a block diagram of an example of the control circuit  4  for variable frequency dividing circuit  5  shown in FIG.  3 . As shown in FIG. 9, a calculating circuit  401  calculates the output  452  which is to be supplied to the summing circuit  404  based on the stuff rate data  451 . An adder circuit  402  and a storage circuit  403  form a summing circuit  404  where an output  452  of a calculating circuit  401  is repeatedly added at each of the frequency division periods in the variable frequency dividing circuit  5 . A determining circuit  405  determines whether a summation result  453  of the summing circuit  404  is not lower than “1”. When the summation result is not lower than “1”, the determining circuit  405  outputs “1”. If the summation result is lower than “1”, the determining circuit  405  outputs “0” An output  454  of the determining circuit  405  is the variable frequency division control signal  55  shown in FIG.  3 . 
     FIG. 10 is a block diagram showing an example of the phase synchronization oscillator (phase locked loop) circuit  6 . As shown in FIG. 10, the output of a voltage controlled oscillator circuit  604  is divided in frequency by N by a frequency dividing circuit  605  and then compared in phase with a clock signal  651  by a phase comparing circuit  601 . An output of the phase comparing circuit  601  is passed through an amplifier circuit  602  and a low pass filter circuit  603 , and then is fed to the voltage controlled oscillator circuit  604  for controlling the oscillation frequency. In the phase synchronization oscillator circuit  6  shown in FIG. 10, the voltage controlled oscillator circuit  604  produces a clock signal whose frequency is N times greater than the frequency of the clock signal  651  and outputs as a clock signal  652 . The phase synchronization oscillator circuit is known by those skilled in the art. In the present invention, it is sufficient that the frequency of the outputted clock signal is N times greater than that of the inputted clock signal, N being a natural number. The phase synchronization oscillator circuit may have any structure. Therefore, it will be described in no more detail. 
     FIG. 11 is a block diagram of an example of the storage circuit  2  shown in FIG.  3 . An input data signal  251  is stored in a location of a storage element  201  which is specified by a write address signal  253 . The write address signal  253  is generated by a write address counter or write address generating circuit  202  which is controlled in accordance with a write clock signal  252 . A read address counter or read address generating circuit  203  is controlled in accordance with a read clock signal  255  to generate a read address signal  256 . The data signal  251  is read out from a location of the storage element  201  which is specified by the read address signal  256  and then is outputted as an output signal  254 . An address control circuit  204  prevents an event known as slipping operation, in which a particular location of the storage element  201  is accessed for the writing operation and the reading operation simultaneously. When the write address  253  and the read address  256  come too close to each other to leave a smaller distance, the address control circuit  204  controls the write address counter  202  and/or the read address counter  203  to properly space the write address  253  and the read address  256  from each other. Also, the address control circuit  204  controls the write address counter  202  and/or the read address counter  203  at the initial setting such as the connection to power supply or the input of a first signal. As a result, the write address  253  and the read address  256  are properly spaced from each other. The arrangement of such a storage element is known by those skilled in the art. Therefore, it will be described in no more detail. 
     Next, the operation of the clock signal reproducing circuit in the first embodiment of the present invention shown in FIG. 3 will now be described in more detail. 
     The de-stuffing circuit  1  carries out the de-stuffing operation to the higher order group signal  51  to delete or remove unwanted bits and then to extract the lower order group signal  52 . The lower order group signal  52  is stored in the storage circuit  2  while the stuff data  53  detected by the de-stuffing circuit  1  is transmitted to the stuff rate measuring circuit  3 . 
     The operation of the stuff rate measuring circuit  3  having the arrangement shown in FIG. 8 will be described. It is supposed that the stuff rate is p/q. In this case, pp−pn=p is met, where q is the number of stuffing enable periods, pp is the number of times of the positive stuffing operations, and pn is the number of times of the negative stuffing operations. Also, the stuffed pulse detected in each stuffing enable period is “1” in case of the positive stuffing operation, 0 in case of the zero stuffing or no stuffing operation, and −1 in case of the negative stuffing operation. Then, the output  352  of the summing circuit  303  shown in FIG. 8 is p, when q=X at the stuff rate of p/q. Accordingly, the stuff rate can be obtained by multiplying the output  352  of the summing circuit  303  by 1/X by the multiplier circuit  304 . X is the length of the shift register and also the divisor for determining the stuff rate. Hence, the accuracy of the calculation depends on X. When X is greater, the accuracy increases, but the circuitry arrangement becomes greater in the size. When X is smaller, the circuitry arrangement becomes smaller in the size but the accuracy will be decreased. 
     According to the present invention, the clock signal frequency for the lower order group signal is calculated from the stuff rate. Thus, the accuracy of the stuff rate largely governs the accuracy of the clock signal frequency for the lower order group signal. It is essential to selection an optimum value of X for obtaining the stuff rate of a higher accuracy in the stuff rate measuring circuit  3  shown in FIG.  8 . Particularly, when the nominal stuff rate is 0, a higher level of the accuracy is required and X has to be as greater as possible. 
     It is supposed that the lower order group signal is accommodated in the high order signal through a single stage of the stuffing process. In this case, the stuff rate S is expressed as follows: 
     
       
           S =( Bl−Bh*Fl/Fh )/ Bs   
       
     
     where Bh is the number of bits in one frame of the higher order group signal, Bl is the number of bits in the lower order group signal accommodated in one frame of the higher order group signal with no stuffing involved, Bs is the unit of bits when the stuffing operation is carried out, Fh is the clock signal frequency for the higher order group signal, and Fl is the clock signal frequency for the lower order group signal. Therefore, when the stuff rate S is given, the relation between the clock signal frequency for the higher order group signal and the clock signal frequency for the lower order group signal is expressed by the following equation (1): 
     
       
           Fl=Fh/{Bh /( Bl−S*Bs )}  (1) 
       
     
     The equation (1) shows that the clock signal frequency Fh for the higher order group signal and the clock signal frequency Fl for the lower order group signal are proportional to each other and its constant of proportion k is Bh/(Bl−S*Bs). When both sides of the equation (1) is divided by N, the following equation (2) is given: 
     
       
           Fl/N=Fh/{Bh*N /( Bl−S*Bs )}  (2) 
       
     
     Therefore, when the clock signal frequency for the lower order group signal is divided by N, a resultant quotient is equal to the clock signal frequency for the higher order group signal divided by Bh*N/(Bl−S*Bs). Because Bh, Bl, and Bs are known, Bh*N/(Bl−S*Bs) can be calculated using the stuff rate S. That is, if the clock signal frequency for the higher order group signal can be divided in frequency by Bh*N/(Bl−S*Bs), the clock signal for the lower order group signal can be reproduced by multiplying the frequency division resultant frequency by N by the phase synchronization oscillator circuit. 
     A usual frequency dividing circuit allows the frequency division by only a natural number. Because Bh*N/(Bl−S*Bs) is typically a real number, the usual frequency dividing circuit can not be used. However, when a variable frequency dividing circuit having a variable frequency division ratio is used, a frequency division ratio of a real number can be realized through averaging. For example, it is supposed that the variable frequency dividing circuit have the two different frequency division ratios of M 1  and M 2 . Also, it is supposed that the ratio of frequency division ratio of M 1  is R 1  and the ratio of frequency division ratio of M 2  is R 2 =1−R 1 . In this case, the average of the frequency division ratio is equal to R 1 *M 1 +R 2 *M 2 . Therefore, the clock signal frequency for the higher order group signal can equivalently be divided in frequency by Bh*N/(Bl−S*Bs), when R 1  and R 2  are determined so that the following equation (3) is met: 
     
       
           R   1 * M   1 + R   2 * M   2 = Bh*N /( Bl−S*Bs )  (3) 
       
     
     The control circuit  4  of FIG. 3 shown in FIG. 9 operates as follows. That is, using R 1 =1−R 2 , the equation (3) is transformed to: 
     
       
           R   2 ={ Bh*N /( Bl−S*Bs )− M   1 }/( M   2 − M   1 )  (4) 
       
     
     Since Bh, Bl, and Bs are known and M 1 , M 2 , and N are predetermined, R 2  can be calculated from the stuff rate S using the equation (4). The calculating circuit  401  shown in FIG. 9 calculates R 2  from the stuff rate S using the equation 4 to output as the output  451 . 
     The summing circuit  404  composed of the adder circuit  402  and the storage circuit  403  repeats to add the output  451  of the calculating circuit  401  at every period of the frequency division in the variable frequency dividing circuit  5 . The determining circuit  405  determines whether the resultant output  453  of the summing circuit  404  is not lower than “1”. When the resultant output  453  is equal to or higher than “1”, the output of the determining circuit  405  is “1”. When the resultant output  453  is lower than “1”, the output of the determining circuit  405  is “0”. The rate when the output  454  of the determining circuit  401  is “1” is R 2 . Accordingly, the output  454  of the determining circuit  405  shown in FIG. 9 is utilized as the variable frequency division control signal  55 . That is, the variable frequency dividing circuit  5  uses the frequency division ratio of M 1  in response to “0” of the variable frequency division control signal  55  and the frequency division ratio of M 2  in response to “1” of the same. 
     Returning to FIG. 3, in the above case, the frequency of the clock signal  57  outputted from the variable frequency dividing circuit  5  becomes equal to 1/N the clock signal frequency for the lower order group signal. The phase synchronization oscillator circuit  6  generates a clock signal whose frequency is N times greater than the frequency of the clock signal  57  outputted from the variable frequency dividing circuit  5 . Hence, the frequency of the clock signal  58  outputted from the phase synchronization oscillator circuit  6  is matched to that for the lower order group signal, allowing the reproduction of the clock signal for the lower order group signal. The reproduced clock signal for the lower order group signal is then used for reading out the lower order group signal  59  from the storage circuit  2 . 
     The equations (1) to (4) are applicable when the lower order group signal is accommodated in the higher order group signal through a single state of the stuffing operation. The equations (1) to (4) are properly be modified when the lower order group signal is accommodated in the higher order group signal through two or more stages of the stuffing operation. 
     For this purpose, the clock signal reproducing circuit according to the second embodiment of the present invention with reference to FIG.  4 . In the second embodiment, the lower order group signal is accommodated in the higher order group signal through two stages of the stuffing operation. 
     FIG. 4 is a block diagram of the structure of the clock signal reproducing circuit according to the second embodiment of the present invention in which a DS3 signal is accommodated in the frames of an STS-1 signal in accordance with the frame arrangement shown in FIGS. 17 to  19 . 
     When the DS3 signal is accommodated in the STS-1 signal, two stages of the stuffing operation are carried out in which the positive/zero/negative stuffing in the STS-1 signal and the positive stuffing in the STS-1 SPE are used. As shown in FIG. 4, a first de-stuffing circuit  1  detects the positive/zero/negative stuffing in the STS-1 signal  51  and outputs a stuff rate date  64  to the stuff rat measuring circuit  3 . Then, the first de-stuffing circuit  1  carries out the de-stuffing operation to delete unwanted bits in the overhead of the STS-1 signal, and extracts the STS-1 SPE signal  68  to supply to a second de-stuffing circuit  12 . The second de-stuffing circuit  12  detects the positive stuffing in the STS-1 SPE signal  68  and outputs a second stuff data  65  to a second stuff rate measuring circuit  13 . Then, the second de-stuffing circuit  12  carries out the de-stuffing operation to delete unwanted bits in the overhead of the STS-1 SPE signal, and extracts the DS3 signal  52  to supply to the storage circuit  2  in which the extracted DS3 signal is stored in the storage circuit  2 . 
     A first stuff rate measuring circuit  3  measures a stuff rate of the positive/zero/negative stuffing in the STS-1 signal  51  from the stuff data  64  of the STS-1 signal  51  and outputs the rate as a first stuff rate data  66 . Similarly, a second stuff rate measuring circuit  13  measures a stuff rate of the positive stuffing in the STS-1 SPE signal  68  from a stuff data  65  of the STS-1 SPE signal  68  and outputs the rate as a second stuff rate data  67 . 
     A variable frequency dividing circuit  5  divides the frequency of the clock signal  56  of the STS-1 signal in accordance with the frequency division ratios M 1  or M 2 . On the other hand, a control circuit  14  for the variable frequency dividing circuit  5  determines the frequency. division ratios for the variable frequency dividing circuit  5  based on the two stuff rate data  66  and  67  supplied from the first stuff rate measuring circuit  3  and the second stuff rate measuring circuit  13 , respectively. 
     FIG. 12 is a block diagram of an example of the control circuit  14  shown in FIG.  4 . As shown in FIG. 12, a calculating circuit  406  determines an input  452  to a summing circuit  404  from the first stuff rate data  451  and the second stuff rate data  455 . The other components and their operations in FIG. 12 are identical to those of the control circuit  4  shown in FIG.  9 . 
     It is supposed that the repetitive frequency of the STS-1 signal is Fh and the stuff rate for the positive/zero/negative stuffing in the STS-1 signal is S 1 . In this case, Bh=6480, Bl=6264, and Bs=8 for the STS-1 signal, and the bit repetitive frequency Fi of the STS-1 SPE signal is calculated from the following equation (5) using the equation (1). 
     
       
           Fi=Fh /{6480/(6264−8 *S   1 )}= Fh /{810/(783 −S   1 )}  (5) 
       
     
     Also, it is supposed that the stuff rate for the positive stuffing in the STS-1 SPE signal is S 2 . In this case, when the DS3 signal is accommodated in the STS-1 SPE signal, one row of the STS-1 SPE signal is considered as one frame. With Bh=696 and Bl=622, the bit repetitive frequency Fl of the DS4 signal is calculated by the following equation (6) using the equation (1). 
     
       
           Fl=Fi /{696/(622 −S   2 )}  (6) 
       
     
     From the equations (5) and (6), Fh is expressed by the following equation (7). 
     
       
           Fl=Fh /[810*696/{(783 −S   1 )* (622 −S   2 )}]  (7) 
       
     
     The equation 7 shows that the higher order group signal and the lower order group signal are proportional in the clock signal frequency to each other and its constant of proportion k is 810*696/{(783−S 1 )*(622−S 2 )}. This corresponds to the equation (1) when the lower order group signal is accommodated in the higher order group signal through the single stage of the stuffing operation. When both sides of the equation 7 are divided by N, the equation (8) is given as follows. 
     
       
           Fl/N=Fh /[810*696 *N /{(783 −S   1 )* (622 −S   2 )}]  (8) 
       
     
     The equation 8 shows that the clock signal frequency for the lower order group signal divided by N is equal to the clock freluency for the higher order group signal divided by 810*696*N/{(783−S 1 )*(622−S 2 )}. This corresponds to the equation 2 when the lower order group signal is accommodated in the higher order group signal through the single stage of the stuffing operation. It is supposed that the variable frequency dividing circuit  5  shown in FIG. 4 can have the two different frequency division ratios of M 1  and M 2 . Also, it is supposed that the ratio of utility of the frequency division ratio of M 1  to the frequency division ratio of M 2  is R 1 :R 2 =1−R 1 . In this case, the clock signal for the higher order group signal can be divided in frequency by 810*696*N/{(783−S 1 )*(622−S 2 )} when R 1  and R 2  are determined in such a manner that the equation (9) is met. 
     
       
           R   1 * M   1 + R   2 * M   2 =810*696 *N /{(783 −S   1 )*(622 −S   2 )}  (9) 
       
     
     The equation (9) corresponds to the equation (3) when the lower order group signal is accommodated in the higher order group signal through the single stage of the stuffing operation. Using R 1 =1−R 2 , the equation (10) is transformed to the equation (10). 
     
       
           R   2 =[810*696 *N /{(783 −S   1 )* (622 −S   2 )}− M   1 ]/( M   2 − M   1 )  (10) 
       
     
     The equation 10 corresponds to the equation (4) when the lower order group signal is accommodated in the higher order group signal through the single stage of the stuffing operation. Because M 1 , M 2 , and N are predetermined, R 2  can be calculated from the stuff rate S 1  for the positive/zero/negative stuffing in the STS-1 signal and the stuff rate S 2  for the positive stuffing in the STS-1 SPE signal, using the equation (10). 
     The control circuit  14  shown in FIG. 4 is constituted by the circuit shown in FIG. 12, and R 2  is calculated by the calculating circuit  406  using the equation  10 . At this time, R 2  represents a rate that the output of the determining circuit  405  is “1”. The variable frequency dividing circuit  5  shown in FIG. 4 carries out the frequency division by M 1  in response to “0” of the variable frequency division control signal  55  and the frequency division by M 2  in response to “1” of the same. Thus, the output  454  of the determining circuit  405  shown in FIG. 12 can be used as the variable frequency division control signal  55  of FIG.  4 . 
     Returning to FIG. 4, the variable frequency dividing circuit  5  carries out the frequency division based on the frequency division ratios of M 1  and by M 2 , when the variable frequency division control signal  55  is “0” and “1”, respectively. Then, the frequency of the clock signal  57  outputted from the variable frequency dividing circuit  5  is equal to 1/N the clock signal frequency for the lower order group signal. The phase synchronization oscillator (phase locked loop) circuit  6  generates a clock signal whose frequency is N times greater than the frequency of the clock signal  57  outputted from the variable frequency dividing circuit  5 . Hence, the frequency of the clock signal  58  outputted from the phase synchronization oscillator circuit  6  is equal to that for the lower order group signal, allowing the reproduction of the clock signal for the lower order group signal. The reproduced clock signal  58  for the lower order group signal is then used for reading out the lower order group signal  59  from the storage circuit  2 . 
     More particularly, M 1 , M 2 , and N are now considered in practice. Supposing that M 1 =16 and M 2 =17 for a first example, N is determined as follows. The nominal clock signal frequency for the higher order group signal is 51.84 MHz. At this time, 51.84 MHz/16=3.24 MHz or 51.84 MHz/17=3.09 MHz. Thus, the frequency of the clock signal outputted from the variable frequency dividing circuit  5  ranges from 3.09 MHz to 3.24 MHz. When N=14, the nominal clock signal frequency for the lower order group signal, 44.736 MHz divided by N falls in the range. 
     For a second example, M 1  and M 2  can be determined when N=16 is given. Because 44.736 MHz/16=2.796 MHz, the range of the frequencies of the clock signals outputted from the variable frequency dividing circuit  5  has to include 2.796 MHz. This is satisfied when M 1 ≦18 and M 2 ≧19 because 51.84 MHz/2.796 MHz=18.84 is met. As described previously, the difference between the frequency division ratios of M 1  and M 2  is preferably “1” for minimizing the effect of jitter in the clock signal outputted from the variable frequency dividing circuit  5 . Hence, M 1 =18 and M 2 =19 are desired. There would be a case where N can not be set to a natural number due to the values of frequency division ratios of M 1  and M 2 . Also, there would be a case where the difference between frequency division ratios of M 1  and M 2  is not “1” due to the value of N. In such cases, the other conditions may properly be modified for the equal effect. 
     The second embodiment of the present invention shown in FIG. 4 will now be compared with the conventional technique. In the conventional technique shown in FIG. 1, the overhead delete data  74  is used which is unrelated to the stuffed pulses. The second embodiment of the present invention shown in FIG. 4 does not use overhead delete data but only the stuff data. Hence, the circuit arrangement is smaller in the size than that of the conventional technique shown in FIG.  1 . Also, the phase synchronization oscillator circuit  9  in the circuitry arrangement of the prior art shown in FIG. 18 has a frequency division ratio of as a large value as 5592. In the second embodiment of the present invention shown in FIG. 4, the frequency division ratio of the phase synchronization oscillator circuit is favorably not higher than 100. Accordingly, the reproduced clock signal hardly suffers from phase noises which are inevitable in the conventional technique and will thus be improved in the quality. 
     Other embodiments of the present invention will be described in more detail referring to the relevant drawings. FIG. 5 is a block diagram showing the structure of the clock signal reproducing circuit according to the third embodiment of the present invention. The circuit structure shown in FIG. 5 is different from that shown in FIG. 3 in the following points. That is, the clock signal  56  for the higher order group signal is divided in frequency by a variable in the variable frequency dividing circuit  5  shown in FIG.  3 . However, the same is fixedly divided in frequency based on a constant frequency division ratio M in the frequency dividing circuit  8 . Also, the frequency division ratio of the phase synchronization oscillator  6  shown in FIG. 3 is a fixed number, while the same shown in FIG. 5 is a variable. The variable factor is determined by the control circuit  7 . 
     The de-stuffing circuit  1 , the storage circuit  2 , and the stuff rate measuring circuit  3  of the structure shown in FIG. 3 are identical in their structure and operation to those shown in FIG.  5 . The stuff rate measuring circuit  3  and the control circuit  7  shown in FIG. 5 may be realized by the circuits shown in FIGS. 8 and 9. FIG. 13 is a block diagram of an example of the phase synchronization oscillator circuit shown in FIG.  5 . As shown in FIG. 5, the output of a voltage controlled oscillator circuit  604  is averagely divided in frequency by a variable frequency dividing circuit  606 , since N is not always a natural number. Then, the frequency-divided signal is subjected to phase comparison with a clock input  651  by a phase comparing circuit  601 . An output of the phase comparing circuit  601  is passed through an amplifier circuit  602  and a low pass filter  603  and fed to the voltage controlled oscillator circuit  604  for controlling the oscillation frequency. 
     In the phase synchronization circuit shown in FIG. 13, the voltage controlled oscillator circuit  604  generates a clock signal whose frequency is N times greater than the frequency of the clock input and outputs as clock output  652 . The structure of the phase synchronization circuit is well known by those skilled in the art. The frequency division ratio is a variable and the clock signal is produced of which the frequency is N times greater than that of the clock signal inputted thereto, when N is not always a natural number. 
     The operation of the clock signal reproduced circuit according to the third embodiment of the present invention shown in FIG. 5 will be now described. When the lower order group signal is accommodated in the higher order group signal through a single stage of the stuffing operation, the equation (1) is met. As both sides of the equation 1 are divided by M, the equation (1) is transformed into the following equation (11). 
     
       
           Fh/M=Fl/{M *( Bl−S*Bs )/ Bh}   (11) 
       
     
     The equation (11) corresponds to the equation (2) of the first embodiment of the present invention. The equation (11) shows that the frequency of the clock signal for the higher order group signal divided by M is equal to the frequency of the clock signal for the lower order group signal divided by M*(Bl−S*Bs)/Bh. Because Bh, Bl and Bs are predetermined, M*(Bl−S*Bs)/Bh can practically be calculated from the stuff rate S. Here, it is supposed that the frequency division ratios of the variable frequency dividing circuit  606  shown in FIG. 13 are N 1  and N 2 . Also, it is supposed that the ratio of utility of N 1  to N 2  is R 1 :R 2 =1−R 1 . In this case, the frequency for the lower order group signal can be divided by M*(Bl−S*Bs)/Bh when the values R 1  and R 2  are controlled so that the equation (12) is satisfied. 
     
       
           R   1 * N   1 + R   2 * N   2 = M *( Bl−S*Bs )/ Bh   (12) 
       
     
     The equation (12) corresponds to the equation (3) in the first embodiment of the present invention. Using R 1 =1−R 2 , the equation (12) is transformed into the following equation (13). 
     
       
           R   2 ={ M *( Bl−S*Bs )/ Bh−N   1 }/( N   2 − N   1 )  (13) 
       
     
     The equation (13) corresponds to the equation (4) in the first embodiment of the present invention. As Bh, Bl and Bs are known and N 1 , N 2 , and M are predetermined, R 2  can be calculated from the stuff rate S using the equation 13. When the control circuit  7  shown in FIG. 5 is realized by the circuit structure shown in FIG. 9, R 2  is calculated by the calculating circuit  401  shown in FIG. 9 using the equation (13). The value R 2  represents a rate that the output of the determining circuit  405  is “1”. Therefore, the frequency division ratio of the phase synchronization oscillator circuit  9  is set to N 1  based on “0” of the variable frequency division control signal  60  and to N 2  based on “1” of the same. In this way, the output  454  of the determining circuit  405  shown in FIG. 9 can be used as the variable frequency division control signal  60  of FIG.  5 . 
     Returning to FIG. 5, the frequency division ratios of the phase synchronization oscillator circuit  9  are N 1  and N 2 , when the variable frequency division control signal  60  has the values of “0” and “1”, respectively. The frequency of the clock signal outputted from the phase synchronization oscillator circuit  9  is equal to Bh/(M*(Bl−S*Bs)) times greater than the clock signal frequency of the frequency dividing circuit  8 . The frequency dividing circuit  8  divides the frequency of the clock signal  56  for the higher order group signal by M. Hence, the phase synchronization oscillator circuit  9  generates a clock signal whose frequency is Bh/{M*(Bl−S*Bs)} times greater than the frequency of the clock signal for the higher order group signal. As shown in the equation (1), the frequency of the clock signal  58  outputted from the phase synchronization oscillator circuit  9  is equal to the frequency of the clock signal for the lower order group signal. Thus, the clock signal for the lower order group signal can be reproduced. The reproduced clock signal  58  for the lower order group signal is used for reading out the lower order group signal  59  from the storage circuit  2 . 
     The equations (11) to (13) are applicable when the lower order group signal is accommodated in the higher order group signal through a single stage of the stuffing operation. However, the equations (11) to (13) need be properly modified when the lower order group signal is accommodated in the higher order group signal through two or more stages of the stuffing operation. Also, the second embodiment is applicable to the third embodiment. 
     Specific examples of N 1 , N 2 , and M will be described referring to FIGS. 17 to  19  in which the higher order group signal is STS-1 signal and the lower order group signal is DS3 signal. 
     First, consider a case that M is determined, when N 1 =16 and N 2 =17 are given. Because 44.736 MHz/16=2.796 MHz and 44.736 MHz/17=2.632 MHz, the frequency of the clock output  653  of the variable frequency dividing circuit  606  shown in FIG. 13 needs to range from 2.632 MHz to 2.796 MHz. When M=19, the frequency of the clock signal  61  outputted from the frequency dividing circuit  8  where the clock signal frequency  56  for the higher order group signal is divided by M falls in the range. 
     Next, consider a case that N 1  and N 2  are determined when M=16 is given. Because 51.84 MHz/16=3.24 MHz, the range of the frequencies of the clock signal  653  outputted from the variable frequency dividing circuit  606  has to include 3.24 MHz. This is satisfied when N 1 ≦13 and N 2 ≧14, because 44.736 MHz/3.24 MHz=13.8 is established. The difference between N 1  and N 2  is preferably “1” for minimizing the effect of jitter in the clock signal outputted from the variable frequency dividing circuit. Hence, N 1 =18 and N 2 =19 are determined. 
     As described above, in the third embodiment of the present invention shown in FIG. 5, the stuff rate measuring circuit  3  is used. This allows the frequency division ratio of the phase synchronization oscillator circuit to be set to favorably not higher than 100 which is impossible in the conventional technique shown in FIG.  1 . 
     In the first embodiment of the present invention, the clock signal for the higher order group signal is divided in frequency by the variable frequency dividing circuit. On the other hand, in the third embodiment of the present invention, the frequency division ratio of the phase synchronization oscillator circuit is variable. In the fourth embodiment of the present invention, the clock signal for the higher order group signal is divided in frequency by a variable frequency dividing circuit, and the frequency division ratio of a phase synchronization oscillator (phase locked loop) circuit is a variable. Also, an average value of the frequency division ratios is controlled. At this time, the average value is not necessarily a natural number. 
     FIG. 6 is a block diagram showing the structure of the clock signal reproduced circuit according to the fourth embodiment of the present invention. The structure of the fourth embodiment shown in FIG. 6 is different from that of the first embodiment shown in FIG. 3 in the following point. That is, the frequency division ratio of a phase synchronization oscillator circuit  9  shown in FIG. 6 is a variable while the frequency division ratio of the phase synchronization oscillator circuit  6  shown in FIG. 3 is fixed. The frequency division ratio of the phase synchronization oscillator circuit  9  is determined by a control circuit  10 . The phase synchronization oscillator circuit  9  shown in FIG. 6 may be realized to have the circuit structure of FIG.  13 . The frequency division ratio of a variable frequency circuit  5  shown in FIG. 6 is determined by a control circuit  4  for a variable frequency dividing circuit  5 . The control circuit  4  shown in FIG. 6 is identical in the operation to the control circuit  3  shown in FIG.  3 . Also, the control circuit  10  shown in FIG. 6 controls the phase synchronization oscillator circuit  9  such that the frequency division ratio of the phase synchronization oscillator circuit  9  has a predetermined average value. 
     FIG. 14 is a block diagram of an example of the control circuit  10  shown in FIG.  6 . As shown in FIG. 14, a calculating circuit  407  determines an input  452  to an summing circuit  404  based on a predetermined data without using external data. The other components and their operations shown in FIG. 14 are identical to those of the control circuit shown in FIG.  9 . Also, the other components and their operations shown in FIG. 6 are identical to those shown in FIG.  3 . Further, the second embodiment is applicable to the fourth embodiment. 
     An average frequency division ratio N of the phase synchronization oscillator circuit  9  shown in FIG. 6 can be expressed by Q 1 *N 1 +Q 2 *N 2 , where the rate for dividing in frequency by N 1  is Q 1  and the rate for dividing in frequency by N 2  is Q 2 =1−Q 1 . When N 1 , N 2 , and N are given, Q 2  can be calculated using the following equation (14). However, N is not necessarily a natural number. 
     
       
           Q   2 =( N−N   1 )/( N   2 − N   1 )  (14) 
       
     
     The control circuit  10  shown in FIG. 6 is realized to have the circuit structure shown in FIG.  14  and the phase synchronization oscillator circuit  9  shown in FIG. 6 is realized to have the circuit structure shown in FIG.  13 . The variable frequency dividing circuit  606  shown in FIG. 13 carries out the frequency division by N 1  based on “0” of the variable frequency division control signal  654  and the frequency division by N 2  based on “1” of the same. In this case, the phase synchronization oscillator circuit  9  shown in FIG. 6 carries out the frequency division by averagely N. When M 1 , M 2 , N 1 , N 2 , and N are properly selected and determined, the frequency of a clock signal  58  outputted from the phase synchronization oscillator circuit  9  can be equal to the frequency of the clock signal for the lower order group signal. Thus, the clock signal can be reproduced. 
     The structure shown in FIG. 6 may be utilized in case that the structure of in FIG. 3 or  4  can not be used for any natural number of N. For example, when M 1 =8 and M 2 =9 in the structure of the first or second embodiment of the present invention, 51.84 MHz/7=7.406 MHz and 51.84 MHz/8=6.48 MHz are established. The frequency of the clock signal  57  outputted from the variable frequency dividing circuit  5  shown in FIG. 4 falls within a range from 6.48 MHz to 7.406 MHz. In this case, when N is a natural number, the frequency of 44.736 MHz divided by N is not within the range. 
     In the fourth embodiment of the present invention, the average frequency division ratio of the phase synchronization oscillator circuit  9  is controlled to be 6.4. In this case, the frequency of the clock signal can be included within the frequency range of the clock signal outputted from the variable frequency dividing circuit  5 . Now, it is supposed that N 1 =6, N 2 =7, and N=6.4. In this case, Q 2 =0.4 is determined from the equation (14). Thus, the control circuit  10  shown in FIG. 6 is realized to have the circuit structure shown in FIG. 14, and the summing circuit carries out the repetitive adding operation for 0.4. Thus, the average frequency division ratio of the phase synchronization oscillator circuit  9  can be 6.4, permitting the frequency of 44.736 MHz divided by N to fall within a range from 6.48 MHz to 7.406 MHz. 
     In the third embodiment of the present invention, the frequency of the clock signal for the higher order group signal is divided by the frequency division ratio of a natural number by the typical common frequency dividing circuit. However, similar to the above, it could be considered that the frequency of the clock signal for the higher order group signal is divided by a predetermined average frequency division ratio, which is not necessarily a natural number, by the variable frequency dividing circuit. Therefore, in the clock signal reproducing circuit according to the fifth embodiment of the present invention, the frequency of the clock signal for the higher order group signal is divided in frequency using a variable frequency dividing circuit whose frequency division ratio is a variable. At the same time, the frequency division ratio of the phase synchronization oscillation circuit is set to be variable. The average frequency division ratio of the variable frequency dividing circuit is controlled to be a predetermined value which is not necessarily a natural number. 
     FIG. 7 is a block diagram showing a structure of the clock signal reproducing circuit according to the fifth embodiment of the present invention. In the fourth embodiment shown in FIG. 5, the clock signal  56  for the higher order group signal is divided in frequency by the frequency dividing circuit  8 . However, in the clock signal reproducing circuit of the fifth embodiment shown in FIG. 7, the clock signal  56  for the higher order group signal is divided in frequency by a variable frequency dividing circuit  5  of which the frequency division ratio is determined by a control circuit  11 . A phase synchronization oscillator (phase locked loop) circuit shown in FIG. 7 may be realized to have the structure shown in FIG.  13  and its frequency division ratio is determined and controlled by a control circuit  7  shown in FIG.  7 . The control circuit  7  shown in FIG. 7 carries out the same operation as the control circuit shown in FIG. 5, and the control circuit  11  shown in FIG. 7 controls the frequency division ratio of the variable frequency dividing circuit  5  to have an predetermined average value. The other components and their operations shown in FIG. 7 are identical to those shown in FIG. 5 as denoted like numerals. 
     When the rate of the frequency division ratio of M 1  is R 1  and the rate the frequency division ratio of M 2  is R 2 =1−R 1 , the average frequency division ratio of M in the variable frequency dividing circuit  5  shown in FIG. 7 can be expressed by R 1 *M 1 +R 2 *M 2 . When M 1 , M 2 , and M are given, R 2  can be calculated using the following equation (15). However, M is not necessarily a natural number. 
     
       
           R   2 =( M−M   1 )/( M   2 − M   1 )  (15) 
       
     
     The control circuit  11  shown in FIG. 7 is realized to have the circuit structure shown in FIG.  14  and the summing circuit carries out the repetitive adding operation for the value of R 2 . The variable frequency dividing circuit  5  shown in FIG. 7 carries out the frequency division by M 1  based on “0” of a first variable frequency division control signal  63  and the frequency division by M 2  based on “1” of the same. Thus, the frequency division by M can be made averagely. When M 1 , M 2 , N 1 , N 2 , and M are properly determined, the frequency of a clock signal  58  outputted from the phase synchronization oscillator circuit  9  shown in FIG. 7 becomes equal to the frequency of the clock signal for the lower order group signal. Thus, the clock signal for the lower order group signal can be reproduced. 
     As compared with the fourth embodiment of the present invention, the fifth embodiment may be applicable when M can not be determined to a natural number in the third embodiment of the present invention. In common, the frequency of the clock signal for the higher order group signal is definitely higher than that for the lower order group signal. Therefore, M can generally be a natural number in the third embodiment of the present invention. In the second embodiment of the present invention, there may be a case that the frequency division ratio of the frequency dividing circuit  8  shown in FIG. 5 is not found in natural numbers favorably. 
     In the third embodiment shown in FIG. 5, for example, it is assumed that the higher order group signal is STS-1 and the lower order group signal is DS3, and N 1 =6 and N 2 =7 are given. In this case, because 44.736 MHz/6=7.456 MHz and 44.736 MHZ/7=6.391 MHz, the frequency of the clock signal  58  outputted from the phase synchronization oscillator circuit  9  shown in FIG. 5 falls within a range from 6.391 MHz to 7.456 MHz. When M=7 or M=8, M being a natural number, the frequency of the clock signal  61  outputted from the frequency dividing circuit  8  resulted from the frequency division of the clock signal  56  for the higher order group signal by M can be within the range. In this case, when either M=7 or M=8, 51.84 MHZ/7=7.406 MHz and 51.84 MHz/8=6.48 MHz are given. The frequencies of the clock signals  61  outputted from the frequency dividing circuit  8  shown in FIG. 5 are close to the end portions of the range permitted for frequencies of the clock signal  58  outputted from the phase synchronization oscillator circuit  9 . On considering the effect of fluctuation on the clock signal frequency for the higher order group signal or the lower order group signal, it is highly desired that the frequency of the clock signal  61  outputted from the frequency dividing circuit  8  stays near the center of the range of frequencies of the clock signal  58  outputted from the phase synchronization oscillator circuit  9 . In the fifth embodiment of the present invention, M=7.5 is permitted, as it is not necessarily required that M is a natural number. The frequency of 51.84 MHz/7.5=6.912 MHz falls approximately in the center of the range of frequencies of the clock signal  58  outputted from the phase synchronization oscillator circuit  9 . 
     In the first embodiment of the present invention, the clock signal for the higher order group signal is frequency divided by the variable frequency dividing circuit. However, in case that a number of lower order group signals are multiplexed on the higher order group signal, the frequency of the clock signal for the higher order group signal may be not directly divided by the variable frequency dividing circuit but divided by a frequency dividing circuit having a fixed frequency division ratio and then by the variable frequency dividing circuit having a variable frequency division ratio. For example, an STS-3 (synchronous transport signal level 3) signal is defined which is produced by multiplexing three STS-1 signals as depicted in ANSI T1.105-1995. In this case, there may be a case that the DS3 lower order group signal is accommodated in at least one of the three STS-1 signals of the STS-3 higher order group signal. 
     For the above case, as shown in FIG. 13, in the clock signal reproducing circuit according to the sixth embodiment of the present invention, the higher order group signal  51  is separated by a separating circuit  14  and a resultant separated signal containing one lower order group signal is fed to the de-stuffing circuit  1 . Also, the clock signal  56  for the higher order group signal is divided in frequency by n (n is a natural number) by a frequency dividing circuit  15  and then transmitted to the variable frequency dividing circuit  5 . When the multiplexing degree of the higher order group signal is equal to the frequency division ratio n of the frequency dividing circuit  15 , the succeeding procedure can be identical to that of the structure shown in FIG.  3 . It is not always necessary that the multiplexing degree is equal to the frequency division ratio n. In this case, the same effect could be given by selecting and determining M 1 , M 2 , and N. Also, n=1 is possible. In this case, the frequency dividing circuit  15  shown in FIG. 15 can be omitted. 
     A practical example will be described in which the higher order group signal is an STS-3 signal having a nominal repetitive frequency of 155.52 Mb/s and three STS-1 signals are multiplexed therein. At least one of the three STS-1 signals accommodates a DS3 signal. When N=16, 44.736 MHz/16=2,796 MHz and 155.53 MHz/2.796=55.62. Therefore, M 1 ≦55 and M 2 ≧56 are calculated. If the multiplexing degree on the higher order group signal is n, n=3. The largest of multiples of 3 not greater than 55 is 54=3*18. The smallest of the multiples of 3 not smaller than 56 is 57=3*19. Accordingly, as M 1 =54 and M 2 =57, the variable frequency dividing circuit  5  shown in FIG. 15 can carry out the frequency division by 18 and by 19. 
     In case that n=2, the largest of multiples of 2 not greater than 55 is 54=2*27 and the smallest of the multiples of 2 not smaller than 56 is 56=2*28. Accordingly, as M 1 =54 and M 2 =56, the variable frequency dividing circuit  5  shown in FIG. 15 can carry out the frequency division by 27 and by 28. If n=1 or the frequency dividing circuit  15  shown in FIG. 15 is unused, M 1 =55 and M 2 =56 are selected and the variable frequency dividing circuit  5  shown in FIG. 15 can carry out the frequency division by 55 and by 56. Assuming that the frequency division ratios of the variable frequency dividing circuit  5  shown in FIG. 15 are 16 and 17 at n=3, 155.52 MHz/(3*16)=3.24 MHz and 155.52 MHz/(3*17)=3.09 MHz are calculated. Accordingly, the frequency of the clock signal  57  outputted from the variable frequency dividing circuit  5  shown in FIG. 15 falls within a range from 3.09 MHz to 3.24 MHz. Hence, when N=14 is given, the frequency of the divided-by-N clock signal for the lower order group signal stays within the range. 
     If M 1 =55 and M 2 =56, a natural number N can not be selected for n=2 or N=1. In that case, the fourth embodiment of the present invention may be applicable. Similarly, when a plurality of lower order group signals are multiplexed in the higher frequency of the clock signal for the lower order group signal. Thus, the clock signal having the determined frequency can be directly reproduced. In particular, as the measurement of the stuff rate is improved, the accuracy of the clock signal can be increased. 
     Also, according to the present invention, the reproduced clock signal is prevented from having phase noises intrinsic to the voltage controlled oscillator circuit. This is because the frequency division ratio of the phase synchronization oscillator circuit can relatively be smaller. The reason is that the frequency division ratios of a frequency dividing circuit or a phase synchronization oscillator circuit can be equivalently set to any value other than natural numerals 
     Further, according to the present invention, the clock signal reproducing circuit is comparatively reduced in the circuit structure. 
     The reason is that the overhead delete data employed commonly in any conventional technique is not used but the stuff rate is measured and used for reproducing the clock signal for the lower order group signal. 
     It would be apparent that the present invention is not limited to the foregoing embodiments but various changes and modifications may be made without departing from the scope of the present invention.