PCM PRINCIPLES
1.0 INTRODUCTION
1.1 A long distance or local telephone conversation between two persons could be provided by using a pair of open wire lines or underground cable as early as early as mid of 19th century. However, due to fast industrial development and an increased telephone awareness, demand for trunk and local traffic went on increasing at a rapid rate. To cater to the increased demand of traffic between two stations or between two subscribers at the same station we resorted to the use of an increased number of pairs on either the open wire alignment, or in underground cable. This could solve the problem for some time only as there is a limit to the number of open wire pairs that can be installed on one alignment due to headway consideration and maintenance
problems. Similarly increasing the number of open wire pairs that can be installed on one alignment due to headway consideration and maintenance problems. Similarly increasing the number of pairs to the underground cable is uneconomical and leads to maintenance problems.
problems. Similarly increasing the number of open wire pairs that can be installed on one alignment due to headway consideration and maintenance problems. Similarly increasing the number of pairs to the underground cable is uneconomical and leads to maintenance problems.
1.2 It, therefore, became imperative to think of new technical innovations which could exploit the available bandwidth of transmission media such as open wire lines or underground cables to provide more number of circuits on one pair. The technique used to provide a number of circuits using a single transmission link is called Multiplexing.
2.0 MULTIPLEXING TECHNIQUES
2.1 There are basically two types of multiplexing techniques
i. Frequency Division Multiplexing (FDM)
ii Time Division Multiplexing (TDM)
2.2 Frequency Division Multiplexing Techniques (FDM)
The FDM techniques is the process of translating individual speech circuits (300-3400 Hz) into pre-assigned frequency slots within the bandwidth of the transmission medium. The frequency translation is done by amplitude modulation of the audio frequency with an appropriate carrier frequency. At the output of the modulator a filter network is connected to select either a lower or an upper side band. Since the intelligence is carried in either side band, single side band suppressed carrier mode of AM is used. This results in substantial saving of bandwidth mid also permits the use of low power amplifiers. Please refer Fig. 1.
FDM techniques usually find their application in analogue transmission systems. An analogue transmission system is one which is used for transmitting continuously varying signals.
2.3 Time Division Multiplexing
2.3.1 Basically, time division multiplexing involves nothing more than sharing
a transmission medium by a number of circuits in time domain by establishing a sequence of time slots during which individual channels (circuits) can be transmitted. Thus the entire bandwidth is periodically available to each channel. Normally all time slots1 are equal in length. Each channel is assigned a time slot with a specific common repetition period called a frame interval. This is illustrated in Fig. 2.
a transmission medium by a number of circuits in time domain by establishing a sequence of time slots during which individual channels (circuits) can be transmitted. Thus the entire bandwidth is periodically available to each channel. Normally all time slots1 are equal in length. Each channel is assigned a time slot with a specific common repetition period called a frame interval. This is illustrated in Fig. 2.
2.3.2 Each channel is sampled at a specified rate and transmitted for a fixed
duration. All channels are sampled one by, the cycle is repeated again
and again. The channels are connected to individual gates which are
opened one by one in a fixed sequence. At the receiving end also
similar gates are opened in unision with the gates at the transmitting
end.
duration. All channels are sampled one by, the cycle is repeated again
and again. The channels are connected to individual gates which are
opened one by one in a fixed sequence. At the receiving end also
similar gates are opened in unision with the gates at the transmitting
end.
2.3.3 The signal received at the receiving end will be in the form of discrete
samples and these are combined to reproduce the original signal. Thus, at a given instant of time, onty one channel is transmitted through the medium, and by sequential sampling a number of channels can be staggered in time as opposed to transmitting all the channel at the same time as in EDM systems. This staggering of channels in time sequence for transmission over a common medium is called Time Division Multiplexing (TDM).
samples and these are combined to reproduce the original signal. Thus, at a given instant of time, onty one channel is transmitted through the medium, and by sequential sampling a number of channels can be staggered in time as opposed to transmitting all the channel at the same time as in EDM systems. This staggering of channels in time sequence for transmission over a common medium is called Time Division Multiplexing (TDM).
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3.0 PULSE CODE MODULATION SYSTEM
3.1 It was only in 1938, Mr. A.M. Reaves (USA) developed a Pulse Code Modulation (PCM) system to transmit the spoken word in digital form. Since then digital speech transmission has become an alternative to the analogue systems.
3.2 PCM systems use TDM technique to provide a number of circuits on the same transmission medium viz open wire or underground cable pair or a channel provided by carrier, coaxial, microwave or satellite system.
3.3 Basic Requirements For PCM System
To develop a PCM signal from several analogue signals, the following processing steps are required
• Filtering
• Sampling
• Quantisation
• Encoding
• Line Coding
4.0 FILTERING
4.1 Filters are used to limit the speech signal to the frequency band 300-3400 Hz.
5.0 SAMPLING
5.1 It is the most basic requirement for TDM. Suppose we have an analogue signal Fig. 3 (b), which is applied across a resistor R through a switch S as shown in Fig. 3 (a) . Whenever switch S is closed, an output appears across R. The rate at which S is closed is called the sampling frequency because during the make periods of S, the samples of the analogue modulating signal appear across R. Fig. 3(d) is a stream of samples of the input signal which appear across R. The amplitude of the sample is depend upon the amplitude of the input signal at the instant of sampling. The duration of these sampled pulses is equal to the duration for which the switch S is closed. Minimum number of samples are to be sent for any band limited signal to get a good approximation of the original analogue signal and the same is defined by the sampling Theorem.
FIG. 3 : SAMPLING PROCESS
5.3 Sampling Theorem
5.3.1 A complex signal such as human speech has a wide range of frequency components with the amplitude of the signal being different at different frequencies. To put it in a different way, a complex signal will have certain amplitudes for all frequency components of which the signal is made. Let us say that these frequency components occupy a certain bandwidth B. If a signal does not have any value beyond this bandwidth B, then it is said to be band limited. The extent of B is determined by the highest frequency components of the signal.
5.3.2 Sampling Theorem States
"If a band limited signal is sampled at regular intervals of time and at a rate equal to or more than twice the highest signal frequency in the band, then the sample contains all the information of the original signal." Mathematically, if fH is the highest frequency in the signal to be sampled then the sampling frequency Fs needs to be greater than 2 fH.
i.e. Fs>2fH
5.3.3 Let us say our voice signals are band limited to 4 KHz and let sampling
frequency be 8 KHz.
frequency be 8 KHz.
Time period of sampling Ts = 1 sec
8000
or Ts = 125 micro seconds
If we have just one channel, then this can be sampled every 125 microseconds and the resultant samples will represent the original signal. But, if we are to sample N channels one by one at the rate specified by the sampling theorem, then the time available for sampling each channel would be equal to Ts/N microseconds.
5.3.4 Fig. .4 shows how a number of channels can be sampled and combined.
The channel gates (a, b ... n) correspond to the switch S in Fig. 3. These gates are opened by a series of pulses called "Clock pulses". These are called gates because, when closed these actually connect the channels to the transmission medium during the clock period and isolate them during the OFF periods of the clock pulses. The clock pulses are staggered so that only one pair of gates is open at any given instant and, therefore, only one channel is connected to the transmission medium. The time intervals during which the common transmission medium is allocated to a particular channel is called the Time Slot for that channel. The width of.this time slot will depend, as stated above, upon the number of channels to be combined and the clock pulse frequency i.e. the sampling frequency.
FIG. 4: SAMPLING & COMBINING CHANNELS
5.3 In a 30 channel PCM system. TS i.e. 125 microseconds are divided into
32 parts. That is 30 time slots are used for 30 speech signals, one time
slot for signalling of all the 30 chls, and one time slot for
synchronization between Transmitter & Receiver.
32 parts. That is 30 time slots are used for 30 speech signals, one time
slot for signalling of all the 30 chls, and one time slot for
synchronization between Transmitter & Receiver.
The time available per channel would be Ts/N = 125/32
= 3.9 microseconds
Thus in a 30 channel PCM system, time slot is 3.9 microseconds and time period of sampling i.e..the interval between 2 consecutive samples of a channel is 125 microseconds. This duration i.e. 125 microseconds is called Time Frame.
5.4The signals on the common medium (also called the common highway)
of a TDM system will consist of a series of pulses, the amplitudes of
which are proportional to the amplitudes of the individual channels at
their respective sampling instants. This is illustrated in Fig. 5
of a TDM system will consist of a series of pulses, the amplitudes of
which are proportional to the amplitudes of the individual channels at
their respective sampling instants. This is illustrated in Fig. 5
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FIG 5 : PAM OUTPUT SIGNALS
5.5 The original signal for each channel can be recovered at the receive end by applying gate pulses at appropriate instants and passing the signals through low pass filters. (Refer Fig. 6)
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Fig. 6 : RECONSTRUCTION OF ORIGINAL SIGNAL
6.0 QUANTISATION
6.1 In FDM systems we convey the speech signals in their analogue electrical form. But in PCM, we convey the speech in discrete form. The sampler selects a number of points on the analogue speech signal (by sampling process) and measures their instant values. The output of the sampler is a PAM signal as shown in Fig. 3; The transmission of PAM signal will require linear amplifiers at trans and receive ends to recover distortion less signals. This type of transmission is succeptible to all the disadvantages of AM signal transmission. Therefore, in PCM systems, PAM signals are converted into digital form by using Quantization Principles. The discrete level of each sampled signal is quantified with reference to a certain specified level on an amplitude scale.
6.2 The process of measuring the numerical values of the samples and giving them a table value in a suitable scale is called "Quantising". Of course, the scales and the number of points should be so chosen that the signal could be effectively reconstructed after demodulation.
6.3 Quantising, in other words, can be defined as a process of breaking down a continuous amplitude range into a finite number of amplitude values or steps.
6.4 A sampled signal exists only at discrete times but its amplitude is drawn from a continuous range of amplitudes of an analogue signal. On this basis, an infinite number of amplitude values is possible. A suitable finite number of discrete values can be used to get an. approximation of the infinite set. The discreate value of a sample is measured by comparing it with a scale having a finite number of intervals and identifying the interval in which the sample falls. The finite number of amplitude intervals is called the "quantizing interval". Thus, quantizing means to divide the analogue signal's total amplitude range into a number of quantizing intervals and assigning a level to each intervals.
For example, a 1 volt signal can be divided into 10mV ranges like 10-20mV, 30-40mV and.so on. The interval 10-20 mV, may be designated as level 1, 20-30 mV as level 2 etc. For the purpose of transmission, these levels are given a binary code. This is called encoding. In practial systems-quantizing and encoding are a combined process. For the sake of understanding, these are treated separately.
For example, a 1 volt signal can be divided into 10mV ranges like 10-20mV, 30-40mV and.so on. The interval 10-20 mV, may be designated as level 1, 20-30 mV as level 2 etc. For the purpose of transmission, these levels are given a binary code. This is called encoding. In practial systems-quantizing and encoding are a combined process. For the sake of understanding, these are treated separately.
6.5 Quantizing Process
6.5.1 Suppose we have a signal as shown in Fig. 7 which is sampled at instants a, b, c, d and e. For the sake of explanation, let us suppose that the signal has maximum amplitude of 7 volts.
In order to quantize these five samples taken of the signal, let us say the total amplitude is divided into eight ranges or intervals as shown in Fig. 7. Sample (a) lies in the 5th range. Accordingly, the quantizing process will assign a binary code corresponding to this i.e. 101, Similarly, codes are assigned for other samples also. Here the quantizing intervals are of the same size. This is called Linear Quantizing.
FIG. 7 : QUANTIZING-POSITIVE SIGNAL
6.5.2 Assigning an interval of 5 for sample 1, 7 for 2 etc. is the quantizing
process. Giving, the assigned levels of samples, the binary code is
called coding of the quantized samples.
process. Giving, the assigned levels of samples, the binary code is
called coding of the quantized samples.
6.5.3 Quantizing is done for both positive and negative swings. As shown in
Fig. 6, eight quantizing levels are used for each direction of the
analogue signal. To indicate whether a sample is negative with
reference to zero or is positive with reference zero, an extra digit is
added to the binary code. This extra digit is called the "sign bit". In Fig.
8. positive values have a sign bit of '1' and negative values have sign
bit of'0'.
Fig. 6, eight quantizing levels are used for each direction of the
analogue signal. To indicate whether a sample is negative with
reference to zero or is positive with reference zero, an extra digit is
added to the binary code. This extra digit is called the "sign bit". In Fig.
8. positive values have a sign bit of '1' and negative values have sign
bit of'0'.
FIG. 8 : QUANTIZING - SIGNAL WITH + Ve & - Ve VALUES
6.6 Relation between Binary Codes and Number of levels.
6.1 Because the quantized samples are coded in binary form, the quantization intervals will be in powers of 2. If we have a 4 bit code, then we can have 2" = 16 levels. Practical PCM systems use an eight bit code with the first bit as sign bit. It means we can have 2" = 256 (128 levels in the positive direction and 128 levels in the negative direction) intervals for quantizing.
6.7 Quantization Distortion
Practically in quantization we assign lower value of each interval to a sample falling in any particular interval and this value is given an
Table-1 : Illustration of Quantization Distortion
Analogue Signal Amplitude Range | Quantizing Interval (mid value) | Quantizing Level | Binary Code |
0-10 mv | 5 mv | 0 | 1000 |
10-20mv | 15mv | 1 | 1001 |
20-30 mv | 25 mv | 2 | 1010 |
30-40 mv | 35 mv | 3 | 1011 |
40-50 mv | 45 mv | 4 | 1100 |
If a sample has an amplitude of say 23 mv or 28 mv, in either case it will be assigned \he \eve\ "2". This Is represented in binary code 1010. When this is decoded at the receiving end, the decoder circuit on receiving a 1010 code will convert this into an analogue signal of amplitude 25 mv only. Thus the process' of quantization leads to an approximation of the input signal with the detected signal having some deviations in amplitude from the actual values. This deviation between the amplitude of samples at the transmitter and receiving ends (i.e. the difference between the actual value & the reconstructed value) gives rise to quantization distortion.
6.7.2 If V represent the step size and 'e' represents the difference in amplitude fe' must exists between - V/2 & + V/2) between the actual signal level and its quantized equivalent then it can be proved that mean square quantizing error is equal to (V2). Thus, we see that the error depends upon the size of the step. 12
6.7.3 In linear quantization, equal step means equal degree of error for all input amplitudes. In other words, the signal to noise ratio for weaker signals will be poorer.
6.7.4 To reduce error, we, therefore, need to reduce step size or in other words, increase th,e number of steps in the given amplitude range. This would however, increase the transmission bandwidth because bandwidth B = fm log L. where L is the number of quantum steps and fm is the highest signal frequency. But as we knows from speech statistics that the probability of occurrence of a small amplitude is much greater than large one, it seems appropriate to provide more quantum levels (V = low value) in the small amplitude region and only a few (V = high value) in the region of higher amplitudes. In this case, provided the total number of specified levels remains unchanged, no increase in transmission bandwidth will be required. This will also try to bring about uniformity in signal to noise ratio at all levels of input signal. This type of
quantization is called non-uniform quantization.
quantization is called non-uniform quantization.
6.7.5 In practice, non-uniform quantization is achieved using segmented quantization (also called companding). This is shown in Fig. 9 (a). In fact, there are equal number of segments for both positive and negative excursions. In order to specify the location of a sample value it is necessary to know the following :
1. The sign of the sample (positive or negative excursion)
2. The segment number
3. The quantum level within the segment
As seen in Fig. 9 (b), the first two segment in each polarity are collinear, (i.e. the slope is the same in the central region) they are considered as one segment. Thus the total number of segment appear to be 13. However, for purpose of analysis all the 16 segments will be taken into account.
7.0 ENCODING
7.1 Conversion of quantised analogue levels to binary signal is called encoding. To represent 256 steps, 8 level code is required. The eight bit code is also called an eight bit "word".
The 8 bit word appears in the form
P ABC WXYZ
Polarity bit ‘1’ Segment Code Linear encoding
for + ve 'O' for - ve. in the segment
The first bit gives the sign of the voltage to be coded. Next 3 bits gives the segment number. There are 8 segments for the positive voltages and 8 for negative voltages. Last 4 bits give the position in the segment. Each segment contains 16 positions.
Referring to Fig. 9(b), voltage Vc will be encoded as 1 111 0101.
FIG. 9 (b) : ENCODING CURVE WITH COMPRESSION 8 BIT CODE
7.2 The quantization and encoding are done by a circuit called coder. The coder converts PAM signals (i.e. after sampling) into a 8 bit binary signal. The coding is done as per Fig. 9 which shows a relationship between voltage V to be coded and equivalent binary number N. The function N = f(v) is not linear.
The curve has the following characteristics.
It is symmetrical about the origins. Zero level corresponds to zero voltage to be encoded.
It is logarithmatic function approximated by 13 straight segments numbered 0 to 7 in positive direction and 'O' to 7 in the negative direction. However 4 segments 0, 1, 0, 1 lying between levels + vm/64 -vm/64 being colinear are taken as one segment.
The voltage to be encoded corresponding to 2 ends of successive segments are in the ratio of 2. That is vm, vm/2, vm/4, vm/8, vm/16, vm/32, vm/64, vm/128 (vm being the maximum voltage).
There are 128 quantification levels in the positive part of the curve and 128 in the negative part of the curve.
7.3 In a PCM system the channels are sampled one by one by applying the sampling pulsqs to the sampling gates. Refer Fig. 10. The gates open only when a pulse is applied to them and pass the analogue signals through them for the duration for which the gates remain open. Since only one gate will be activated at a given instant, a common encoding circuit is used for all channels. Here the samples are quantized and encoded. The encoded samples of all the channels and signals etc are combined in the digital combiner and transmitted.
7.4 The reverse process is carried out at the receiving end to retreive the original analogue signals. The digital combiner combines the encoded samples in the form of "frames". The digital separator decombines the incoming digital streams into individual frames. These frames are decoded to give the PAM (Pulse Amplitude Modulated) samples. The samples corresponding to individual channels are separated byoperating the receive sample gates in the same sequence i.e. in synchronism with the transmit sample gates.
8.0 CONCEPT OF FRAME
8.1 In Fig. 10, the sampling pulse has a repetition rate of Ts sees and a pulse width of "St". When a sampling pulse arrives, the sampling gate remains opened during the time "St" and remains closed till the next pulse arrives. It means that a channel is activated for the duration "St". This duration, which is the width of the sampling puse, is called the "time slot" for a given channel.
8.2. Since Ts is much larger as compared to St. a number of channels can be sampled each for a duration of St within the time Ts. With reference to Fig. 10, the first sample of the first channel is taken by pulse 'a', encoded and is passed on the combiner. Then the first sample of the second channel is taken by pulse 'b' which is also encoded and passed on to the combiner, Likewise the remaining channels are also sampled sequentially and are encoded before being fed to the combiner. After the first sample of the Nth channel is taken and processed, the second sample of the first channel is taken, this process is repeated for all channels. One full set of samples for all channel taken within the duration Ts is called a "frame". Thus the set of all first samples of all channels is one frame; the set of all second samples is another frame and so on.
8.3 As already said in para 5.3.5, Ts in a 30 channel PCM system is 125 microseconds and the signalling information of all the channels is transmitted through a separate time slot. To maintain synchronization between transmit and receive ends, the synchronization data is transmitted through another time slot. Thus for a 30 chl PCM system, we have 32 time slots.
Thus the time available per channel would be 3.9 microsecs.
Thus for a 30 chl PCM system,
Frame = 125 microseconds
Time slot per chl = 3.9 microseconds.
8.4 Structure of Frame
8.4.1 A frame of 125 microseconds duration has 32 time slots. These slots are numbered Ts 0 to Ts 31.
Information for providing synchronization between trans and receive ends is passed through a separate time slot. Usually the slot Ts 0 caries the synchronizsation signals. This slot is also called Frame alignment word (FAW).
The signalling informatiori is transmitted through time slot Ts 16.
Ts 1 to Ts 15 are utilized for voltage signal of channels 1 to 15 respectively.
Ts 17 to Ts 31 are utilized for voltage signal of channels 16 to 30 respectively.
9.0 SYNCHRONIZATION
9.1 The output of a PCM terminal will be a continuous stream of bits. At the receiving end, the receiver has to receive the incoming stream of bits and discriminate between frames and separate channels from these. That is, the receiver has to recognise the start of each frame correctly. This operation is called frame alignment or Synchronization and is achieved by inserting a fixed digital pattern called a "Frame Alignment Word (FAW)" into the transmitted bit stream at regular intervals. The receiver looks for FAW and once it is detected, it knows that in next time slot, information for channel one will be there and so on.
9.2 The digits or bits of FAW occupy seven out of eight bits of Ts 0 in the following pattern.
Bit position of Ts 0 B1 B2 B3 B4 B5 B6 B7 B8
FAW digit value X 0 0 1 1 0 1 1
FAW digit value X 0 0 1 1 0 1 1
9.3 The bit position B1 can be either '1' or '0'. However, when the PCM system is to be linked to an international network, the B1 position is fixed at '1'.
The FAW is transmitted in the Ts O of every alternate frame.
Frame which do not contain the FAW, are used for transmitting supervisory and alarm signals.
To distinguish the Ts 0 of frame carrying supervisory/alarm signals from those carrying the FAW, the B2 bit position of the former are fixed at T. The FAW and alarm signals are transmitted alternatively as shown in Table - 2.
TABLE-2
Frame | Remark | ||||||||
Numbers | B1 | B2 | B3 | B4 | B5 | B6 | B7 | B8 | |
FO | X | 0 | 0 | 1 | 1 | 0 | 1 | 1 | FAW |
F1 | X | 1 | Y | Y | Y | 1 | 1 | 1 | ALARM |
F2 | X | 0 | 0 | 1 | 1 | 0 | 1 | 1 | FAW |
F3 etc | X | 1 | Y | Y | Y | 1 | 1 | 1 | ALARM |
In frames 1, 3, 5, etc, the bits B3, B4, B5 denote various types of alarms. For example, in B3 position, if Y = 1, it indicate Frame synchronisation alarm. If Y = 1 in B4, it indicates high error density alarm. When there is no alarm condition, bits B3 B4 B5 are set 0. An urgent alarm is indicated by transmitting "all ones". The code word for an urgent alarm would be of the form.
X 111 1111
10.0 SIGNALLING IN PGM SYSTEMS
10.1 In a telephone network,-the signalling information is used for proper routing of a call between two subscribers, for providing certain status information like dial tone, busy tone, ring back. NU tone, metering pulses, trunk offering signal etc. All these functions are grouped under the general terms "signalling" in PCM systems. The signaling information can be transmitted in the form of DC pulses (as in step by step exchange) or multifrequency pulses (as in cross bar systems) etc.
10.2 The signalling pulses retain their amplitude for a much longer period than the pulses carrying speech information. It means that the signalling information is a slow varying signal in time compared to the speech signal which is fast changing in the time domain. Therefore, a signalling channel can be digitized with less number of bits than a voice channel.
10.3 In a 30 chl PCM system, time slot Ts 16 in each frame is allocated for carrying signalling information.
10.4 The time slot 16 of each frame carries the signalling data corresponding to two VF channels only. Therefore, to cater for 30 channels, we must transmit 15 frames, each having 125 microseconds duration. For carrying synchronization data for all frames, one additional frame is used. Thus a group of 16 frames (each of 125 microseconds) is formed to make a "multiframe". The duration of a multiframe is 2 milliseconds. The multiframe has 16 major time slots of 125 microseconds duration. Each of these (slots) frames has 32 time slots carrying, the encoded samples of all channels plus the signaling and synchronization data. Each sample has eight bits of duration 0.400 microseconds (3.9/8 = 0.488) each. The relationship between the bit duration frame and multiframe is illustrated in Fig. 11 (a) & 11 (b).
FIG. 11 (B) 2.048 Mb/s PCM MULTIFRAME
10.4 We have 32 time slots in a frame, each slot carries an 8 bit word.
The total number of bits per frame = 32 x 8 = 256
The total number of frames per seconds is 8000
The total number of bits per second are 256 x 8000 = 2048 K/bits.
Thus, a 30 chP PCM system has 2048 K bits.
10.6 Multiframe Structure
10.6.1 In the time slot 16 of FO, the first four bits (positions 1 to 4) contain the multiframe alignment signal which enables the receiver to identify a multiframe.
The other four bits (no. 5 to 8) are spare. These may be used for carrying alarm signals.
Time slots 16 of frames F1 to FT5 are used for carrying the signalling information. Each frame carries signalling, data for two VF channels. For instance, time slot Ts 16 of frame F1 carries the signal data for VF channel 1 in the first four bits. The next four bits are used for carrying signalling information
for channel 16. Similarly, time slot Ts16 of F2 carries signalling data of chls 2 .and 17.
Thus in multiframe structure, four signalling bits are provided for each VF channels.
As each multiframe includes 16 frames, each with a sacnqtoq -
per sec.,.the.signalling of each channel will occur at a rate of 500 persec.
