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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 40, NO. 1, JANUARY/FEBRUARY 2004 203

Voltage Sag Detection Technique for aDynamic Voltage Restorer

Chris Fitzer, Mike Barnes, Member, IEEE, and Peter Green

AbstractDynamic voltage restorers (DVRs) are used to protectsensitive loads from the effects of voltage sags on the distributionfeeder. This paper presents and verifies a novel voltage sag detec-tion technique for use in conjunction with the main control systemof a DVR. In all cases it is necessary for the DVR control systemto not only detect the start and end of a voltage sag but also to de-termine the sag depth and any associated phase shift. The DVR,which is placed in series with a sensitive load, must be able to re-spond quickly to a voltage sag if end users of sensitive equipmentare to experience no voltage sags. A problem arises when fast eval-uation of the sag depth and phase shift is required, as this informa-tion is normally embedded within the core of a main DVR controlscheme and is not readily available to either users monitoring thestate of the grid or parallel controllers. Previousresearch presentedan additionalcontroller, which required phase and sag depth infor-mation to manipulate the injection voltage vector returned by themain controller in order to prevent the DVRinjection transformersfrom saturating. Typical standard information tracking or detec-tion methods such as the Fourier transform or phase-locked loop(PLL) are too slow in returning this information, when either ap-plied to the injection voltage vector, or to the supply voltages di-rectly. As a result of this the voltage sag detection method in thispaper proposes a new matrix method, which is able to computethe phase shift and voltage reduction of the supply voltage muchquicker than the Fourier transform or a PLL. The paper also illus-trates that the matrix method returns results that can be directlyinterpreted, whereas other methods such as the wavelet transformreturn results that can be difficult to interpret.

Index TermsDynamic Voltage Restorer (DVR), voltage sag,voltage sag detection.

I. INTRODUCTION

VOLTAGE SAGS are one of many power quality relatedproblems the industrial process sector has to face [1], [2],though sags are one of the most severe.

Voltage sags are defined as short duration reductions in the

rms supply voltage that can last from a few milliseconds to a

few cycles, with typical dip depths ranging from 0.9 to 0.5 pu

of a 1-pu nominal. It has been shown that year on year voltage

Paper IPCSD 03101, presented at the 2002 Industry Applications SocietyAnnual Meeting, Pittsburgh, PA, October 1318, and approved for publicationintheIEEETRANSACTIONSON INDUSTRY APPLICATIONS by the IndustrialPowerConverter Committee of the IEEE Industry Applications Society. Manuscriptsubmitted for review October 15, 2002 and released for publication October 6,2003.

C. Fitzer and M. Barnes are with the Manchester Centre for ElectricalEnergy, Department of Electrical Engineering and Electronics, University ofManchester Institute of Science and Technology, Manchester M60 1QD, U.K.(e-mail: [email protected]; [email protected]).

P. Green is with the Digital Communications Research Group, Departmentof Electrical Engineering and Electronics, University of Manchester Institute ofScience and Technology, Manchester M60 1QD, U.K.

Digital Object Identifier 10.1109/TIA.2003.821801

sags cause extensive disruption to the industrial process sector in

terms of production loss [1], [3], which make them a particularly

important area.

There are various solutions to this problem, examples being:

Designing inverter drives for process equipment to be more tol-

erant of voltage fluctuations or the installation of voltage cor-

rection devices. For certain end users of sensitive equipment the

voltage correction device may be the only cost-effective option

available. It has already been shown [1] that for customers of

large loads, from the high kilowatt to the low megawatt range,

a good solution is the installation of a dynamic voltage restorer

(DVR); see Fig. 1.A DVR [4][10] is primarily for use at the distribution level,

where the basic principle is to inject a voltage in series with

the supply when an upstream fault is detected. Loads connected

downstream of the DVR are thus protected from any voltage

sags caused by faults elsewhere on the network.

The location of the DVR, in terms of the connection arrange-

ment of upstream transformers (typically ) and the type of

protection it is to offer to potentially sensitive loads, is a major

factor when determining the type of inverter control required.

The main DVR control used in conjunction with the sag detec-

tion techniques presented in this paper utilizes a type a vector

control that only considers the positive and negative sequence

information in the supply. The DVR is located downstream of adelta-star distribution transformer (Fig. 1), thus eliminating the

need to control the zero sequence.

A DVR utilizing vector control can also protect downstream

loads from any phase shift that may occur, which results in a

DVR system that can protect downstream loads from all types

of sags, provided the sag depth is not beyond the capacity of the

DVR. The vector control topology is illustrated in Fig. 2.

The core of this controller is the phase-locked loop (PLL) [4],

[11], [12], which locks a synchronous reference frame to

the positive-sequence component of the supply. The angle theta

that is used by the synchronous reference frame is also used

to generate a reference vector . The difference between the

supply and the reference vector produces an injected voltagevector that can be used by the final part of the DVR controller

to produce the pulse patterns that are used to control the in-

verter. This type of control is commonly known as space-vector

control and the inverter pulse pattern strategy as space-vector

pulsewidth modulation (SVPWM) [4], [5], [7], [13].

Although this and countless other control schemes inherently

detect thestartand end of any voltage disturbances, such as sags,

they cannot directly return information regarding phase shift

and voltage drop. The DVR control, Figs. 2 and 3, computes

an injection vector at any instant in time, without the need for

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204 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 40, NO. 1, JANUARY/FEBRUARY 2004

Fig. 1. Typical location of a DVR in a power network.

Fig. 2. Main control system topology.

decoupling (separating) information such as, sag depth, phase

shift, start, and end times. The same is true for other control

schemes, vector or otherwise, that track the difference between

two values.When implementing a DVR system, such as the one il-

lustrated in Fig. 1, it may be necessary to switch the DVR

offline when little or no injected voltage is required, Fig. 4,

then a controlled switch-on otherwise. If a controlled DVR

switch-on is required, where injection transformer inrush is

to be minimized, then both the magnitude and the phase of

each injected voltage are required [14]. In order to obtain these

parameters further analysis is required, where the magnitude

and phase are required to be available/updated as quickly/regu-

larly as possible. There have been numerous papers published

in this area, mainly focusing on the application of the wavelet

transform (WT) [15]. This paper investigates the use of a

numerical method to detect voltage sags, their depth and any

associated phase shift. The paper highlights the problems with

existing techniques such as the Fourier transform and the PLL.

The real-time constraints of the WT are also illustrated.

II. CURRENT METHODS TO DETECT VOLTAGE SAGS

There tends to be no one particular preferred method to de-

tect sags, especially if sag depth and phase shift information are

required along with start and end times. There are, however, a

selection of standard signal processing techniques that can be

used to detect the start and end of a voltage sag and/or the as-

sociated dip depth and phase shift. Current methods in use are

[4], [11], [15][17] the following:

monitoring the peak values of the supply;

monitoring of in a vector controller;

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FITZER et al.: VOLTAGE SAG DETECTION TECHNIQUE FOR A DVR 205

Fig. 3. DVR vector control principle.

Fig. 4. Typical ideal control response to a balanced dip with shift.

locking a narrow bandpass filter or PLL to each phase;

applying the Fourier transform to each phase;

appling the WT to each phase.

Apart from for the vector control, the sag detection methods

tend to be applied to each of the three supply phases separately.

In the following sections, unless otherwise stated, a transform

applied to a sinusoidal waveform can be interpreted as a trans-

form as applied to each supply phase.

A. Monitoring the Peak Values of the Supply

The simplest conceptual method of monitoring the supplyis to monitor the peak, or amplitude. This can be achieved by

simply finding the point at which the gradient of each of the

supply phases is zero, then comparing the supply value at that

instant with a reference. A controller could be set to recognize if

there is a difference greater than 5% and switch in a DVR or ap-

propriate corrective device. The gradient is found, for example,

from (1)

Gradient (1)

where is the voltage value at the time instant , and is

the voltage value at the time instant .

This method returns the sag depth, start, and end times, al-though to extract phase shift information is difficult since a ref-

erence waveform is required. The drawback of this method is

that it can take up to half a cycle for the sag depth information

to become available and the possibility of noise affecting the

differential function. The lack of readily available phase shift

information is also less than desirable.

B. Monitoring of or in a Vector Controller

This is an obvious method as it utilizes the space vector con-

trol method described in Section I, which is part of the core DVR

control system. The three supply phases are converted into one

phasor which itself is comprised of two orthogonal compo-

nents and . A synchronous reference frame is locked

to via a PLL, Fig. 5, which produces a vector when

locked and , otherwise. The vectors are generated by the

following formulas: (2):

(2)

Fig. 5 illustrates the effect of a balanced sag on the vectors in

the rotating frame.

If the sag is not accompanied by any phase shift then the fol-lowing expression is true:

i.e., (3)

where

(4)

This is simplest type of voltage sag in terms of detection and

control, where monitoring either or (3), (4)

will return the state of the supply at any instant in time and,

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Fig. 5. Sag detection using the d q frame with a balanced fault with no phase jump.

hence, detect whether or not a sag has occurred. If the balanced

sag is accompanied by a balanced phase jump then (3) is no

longer valid, because the PLL has to first track the new angle.

Hence, initially,

(5)

where

(6)

(7)

Monitoring will return the sag depth while monitoring

and manipulation of will return the initial phase jump in-

formation.If an unbalanced sag occurs the ability for this method to re-

turn information regarding the individual supply phases is com-

promised.

When an unbalanced voltage sag occurs as in Fig. 7, the

supply as seen in both the fixed and the synchronous

frames may at any instant in time appear similar to the

vector plot in Fig. 6. The unbalanced supply now contains both

negative and positive sequence information (all zero-sequence

information is assumed to be removed by upstream delta-star

distribution transformers, Fig. 1). The space vector now

contains an oscillation with a base frequency of 100 Hz, which

when viewed in a synchronous frame locked onto fixed

Fig. 6. Sag detection using the d q frame.

velocity vector (positive sequence) appears as a pure 100-Hz os-

cillation in the and components, Figs. 711.

Figs. 711 illustrate the difficulty in determining the supply

magnitude (or sag depth) and phase information of the supply

phases. The Synchronous frame components and os-

cillate with a frequency of 100 Hz due to the unbalanced fault,

or negative sequence, which means it can take up to half a cycle

before a minimum value is reached. Unlike for the case

of a balanced fault there is no direct relationship between the

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Fig. 7. Supply voltage as seen by the DVR during an upstream fault.

Fig. 8. Trajectory of the supply vector V .

Fig. 9. Phase of the supply vector V .

values of , at any instant and the magnitudes of the in-

dividual supply phases: many different values of supply voltage

can give the same and values. An advantage though

is the relative ease at which it can be implemented within a prac-tical real-time control system [4], [5], [17].

C. Locking a Narrow Bandpass Filter or PLL to Each Phase

This sag detection method is similar to the previous method,

except that the PLL is applied to each supply phase indepen-

dently and is tuned to respond to phase jumps in the supply

quickly.

Although this method can track changes in supply phase it

cannot directly return information regarding sag depth. As with

the previous PLL method it can be easily be implemented in

real time and can be used if only phase jump information is

required. It may be possible to use this method as part of a larger

Fig. 10. Magnitude of the supply vector V .

Fig. 11. The d and q of the supply vector.

control scheme to detect both magnitude and phase but there are

no current publications in this method.

D. Appling the Fourier Transform to Each Phase

A technique that can return information regarding the state of

a system supply is the Fourier transform to each supply phase.

The advantage of this method is that it can return magnitude and

phase of each frequency component within the supply, which is

particularly important if there are harmonics present, such as

the fifth or seventh. In order to prevent errors occurring with

the information returned regarding the fundamental (50 Hz) the

previous methods effectively filter out harmonics other than the

fundamental. The effect of doing so can be to introduce transient

delays in detecting changes in the phase of the fundamental. The

Fourier transform or the practical digital implementation of it,

the windowed fast Fourier transform (WFFT) automatically

accounts for all frequencies (bearing in mind the Nyquist Cri-

terion). Depending on the type of controller the information re-

garding frequencies other than the fundamental can either beused or ignored.

Although the WFFT can return accurate steady-state infor-

mation about the supply phases, the WFFT kernel is itself an

averaging function. Thus, it can take up to one cycle of the fun-

damental when a sag has commenced before information re-

garding the magnitude and phase can be assumed accurate. As

with the previous detection methods the WFFT can easily be

implemented within a real-time control system.

E. Applying the WT to Each Phase

The application of the WT to detect faults within electrical

power systems is becoming increasingly popular [15], as it can

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Fig. 12. Supply phase sampled at regular intervals.

detect changes in the state of the supply phases quickly. The

main differences between the WT and WFFT is the former

operates in the time as opposed to the frequency domain and

uses variable window sizes (multiresolution analysis) to capture

changes. In theory it is possible to use this method to detect

and sudden changes in the supply state, which could be usedto determine sag start and end times, depth, and phase shift

information. The WT returns different signatures depending

on the type of sag that occurs and training a neural network to

respond to these could for example be used to detect voltage

sags.

The difficulties with using this method are as follows. The

signatures returned can be difficult to directly interpret and

the use of large neural networks is difficult to implement in

real time. There is also a delay associated with many mother

wavelets as data either side of a time instant may be required in

the convolution process.

III. NUMERICAL MATRIX SAG DETECTION METHOD

A numerical sag detection method has been developed that,

unlike the previous methods, has a small time latency when

implemented and returns results that are directly interpretable.

The method is applied to each supply phase independently and

as such can monitor the start or end of a sag, sag depth, and

any phase jump. The method involves sampling the supply and

storing the data in a matrix format, Fig. 12.

Provided bands of dominant supply frequency components

are known, a set of (8)(11) can be developed

(8)

(9)

(10)

(11)

where

magnitude of the fundamental (50 Hz);

magnitude of the fifth harmonic (250

Hz);

phase of the fundamental with respect to

a cosine wave;

phase of the fifth harmonic with respect

to a cosine wave;

angular frequency of the fundamental;

angular frequency of the fifth harmonic;

time;

sampling period;current sample of the supply voltage;

previous samples of the supply voltage.

In order to allow for a unique solution, the number of

equations to be solved increases or decreases depending upon

the harmonics detected in the supply. For illustration simplicity

(8)(11) have been developed assuming that 5th is the only

dominant harmonic. The two frequencies (50 and 250 Hz)

generate four unknowns, magnitude and phase, hence, four

simultaneous equations are required if a unique numerical

solution is to be found (12)

No. of Simultaneous Equations Required

Total No. of Frequencies (12)

If dominant harmonics are not included in the equations the

solution can contain errors, with the size of the errors referred to

as the sensitivity of the matrix to unknown harmonics. Typi-

cally, the sensitivity of the matrix increases for a given sampling

rate with the order of the unknown harmonics, for example, a

small amount of 20th may give the same errors as a large amount

of fifth. The matrix method does however allow harmonics close

together in the frequency spectrum to be grouped into bands and

included as oneharmonicentry in the matrixwithout anyserious

performance degradation in the sag detection results. It has also

been found that the sensitivity increases with increasing num-

bers of harmonics included in the matrix and a smaller sampling

period .

It is assumed that the matrix method would be used with

an additional controller that determines, which harmonics are

present on a cycle-by-cycle basis, using an FFT or similar. The

simultaneous equations would then be updated accordingly.

However, this controller explanation is not relevant in this paper

and is therefore not included. Instead, the only the common

dominant harmonics are included in the matrix, such as fifth

or seventh [1]. Any zero-sequence harmonics need not be in-

cluded in the equations as the DVR is assumed to be connected

downstream of the delta-star distribution transformer.

Expanding and rearranging (8)(11) into a standard matrixformat (13) and (14), as shown at the bottom of the next page,

manipulates the frequency components into pairs of solvable

simultaneous equations, which effectively converts the original

equations into a more readily analyzable state.

As the sampling period and the angular frequencies ,

are known the inverse of matrix and the variables , , ,

can be evaluated. The magnitude and phase of each harmonic

component included in the matrix can now be found. To equate

and ,

(15)

(16)

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Fig. 13. Supply voltage (50 and 250 Hz).

Fig. 14. Magnitude of the 50-Hz component of the supply (spike in the resultsdue to transient settling time).

Equating (15) and (16) gives

(17)

(18)

(19)

The ability of this method to decouple the individual frequency

components in the supply is a key feature when the strong

voltage harmonics are present.

Figs. 1316 illustrate the ability of the numerical matrix

method to extract information regarding the fundamental. The

supply in Fig. 13 contains two dominant frequency compo-

nents, 50 and 250 Hz (fifth).

Fig. 15. Phase of the 50-Hz component of the supply.

Fig. 16. Filtered supply (250 Hz removed).

Figs. 14 and 15 highlight the accuracy to which informa-

tion regarding the fundamental magnitude and phase can be ex-

tracted and the response time to which changes can be tracked.

A byproduct of the numerical calculations is a filtered supply

Fig. 16, with the unwanted frequency component fifth removed.The response time to detect changes in magnitude and phase

of the fundamental 50-Hz component depends on the sampling

rate and the number of dominant harmonic components present

in the supply, assuming they are included in the matrix (20)

Response Time Sampling Rate

No. of Frequency Components. (20)

In order to improve response time a smaller sampling rate

can be used, although as explained previously, this will increase

the sensitivity of the matrix, which may lead to previously neg-

ligible harmonics producing errors.

(13)

(14)

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Fig. 17. The 3-kW medium-power hardware rig.

It is also important to note that the ability of the DVR to cor-

rect for voltage sags is not directly dependent on the perfor-mance of the matrix method. The main space-vector controller

is primarily responsible for this. The main purpose of the matrix

method is to extract information from the main controller, thus,

the spike seen in the results would either be ignored by addi-

tional numerical controllers using the data or rejected visually

by a user monitoring the data.

IV. EXPERIMENTAL RESULTS

In order to test the ability of the matrix method with real data,

a real-time algorithm has been developed and implemented in

the control systemof a 3-kW DVR laboratory prototype, Fig. 17.

To introduce a fault, Fig. 17, a variable impedance is placed in

series in between the source and the delta-wye transformer. This

configuration gives fault types that are comparable with those

experienced in a real power system at distribution level, Fig. 1.

The DVR system is connected to a nominal 415-V rms three-

phase supply with the load rated at 3 kW, which is sufficient to

test the DVR dynamic response.

In a practical DVR installation at the distribution level, the

magnitudes of any voltage harmonics are usually small, with

the lower order harmonics normally dominant [1]. In the case of

the laboratory prototype the source impedance of the laboratory

power supply is unusually high, which results in a significant

fifth harmonic created by a nearby computer cluster. To avoidlarge errors in the results returned from the sag detection algo-

rithm the fifth-order harmonic is accounted for in the sag detec-

tion matrix. The switching harmonics created by the three-phase

inverter, are also found to create significant voltage harmonics

across the source impedance and the digital phase shifters used

to correct for the time delay of the fundamental (50 Hz) through

the digital control system unavoidably causing amplification of

them. As explained previously it is possible to group harmonics

into bands, however due to the number of distinct frequency

bands and the sampling rate it is not possible to include them

all in the matrix without introducing a significant latency in the

detection time (12) and (20). As the sampling frequency is fixed

Fig. 18. Phase-a supply voltage.

Fig. 19. Magnitude of phase-a

supply voltage.

at 1200 Hz due to the detection algorithm being part of a larger

DVR control topology and the property that makes the matrix

method more sensitive to the neglected harmonics if only one

of the higher order frequencies is included, all the high order

switching related harmonics have been left out. Although this

does generate some degradation in the quality of the results ob-

tained, it is the optimum solution given the constraints of the

laboratory DVR system.

The following experimental results, Figs. 1823, illustrate the

response of the sag detection algorithm when presented with a

three-phase balanced fault.

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Fig. 20. Phase-a supply voltage.

Fig. 21. Angle of phase-a supply voltage.

The sag detection algorithm operates on each supply phase

independently, with the results obtained from one phase being

comparable with the other two. Fig. 18 is a snapshot of thesupply at the point when a voltage sag commences. The figure

illustrates the fifth harmonic component present and the level of

the higher order switching harmonics. There is a small transient

time before the supply settles down to its steady-state value,

which appears to be due to the impedance of the laboratory pro-

totype.

Fig. 19. Illustrates the time taken for the matrix algorithm

to detect the change in supply voltage. The apparent noise on

the waveform is due to the switching frequency harmonics not

included in the matrix.

The large spike around 0.01 s highlights the settling time

or time latency of the algorithm in returning correct results

when presented with a transient change. Any sudden transientchange can be represented as high-order harmonics for which

the matrix method is already known to be sensitive to, which

accounts for the magnitude of the error spike. The transient

decay experienced between 0.010.02 s is an effect due to

two factors. Firstly, the system supply voltage experiences a

disturbance when the voltage sag occurs, Fig. 18. Secondly

the digital phase shifters which are used to correct for the

steady-state time latency of the main DVR control system

require a significant time to settle, thus producing a transient

time latency.

As stated earlier, the performance of the matrix method does

not directly relate to the performance of the DVR system as a

Fig. 22. Phase-a injected voltage.

Fig. 23. Phase-a load voltage.

whole. The transient settling time of the matrix method there-

fore should not be taken to reflect the transient response of the

main DVR control. The transient response of the matrix method

along with its sensitivity to unknown harmonics is an importantarea that does require further discussion. However the authors

feel that a detailed discussion of this topic is not necessary in

order to verify the fundamental concept of the matrix method

and may also obscure some of the important steady-state results

presented.

Figs. 20 and 21 illustrate the ability of the detection algorithm

to return the phase of the supply during the steady-state period

of a sag.

Fig. 22 shows the DVRs response to a sag, i.e., the voltage

it injects in order to compensate the sag. Fig. 23 illustrates the

DVRs ability to maintain the load voltage constant. The error

between 0.010.017 s is due to the transient time latency of the

digital phase shifters, which are part of the DVR control.

Figs. 22 and 23 have been included for completeness to

show that the matrix method has been implemented as part of a

working real-time DVR control scheme. Space-vector control

is used to control the overall DVR, which has already been

presented in [5].

V. CONCLUSION

A novel sag detection algorithm has been proposed and com-

pared to other sag detection algorithms. Results from an exper-

imental prototype DVR have been presented and the algorithm

is shown to work well.

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The transient response of the matrix method along with its

sensitivity to unknown harmonics is an important area that will

require further future research.

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Chris Fitzer received the B.Sc. (Hons.) degreein electronics from the University of CentralLancashire, Preston, U.K., in 1999, and the Ph.D.degree from the University of Manchester Instituteof Science and Technology (UMIST), Manchester,U.K., in 2003.

Since 2003, he has been a Research Engineerat UMIST. His research interests include dynamicvoltage restorers for voltage sag mitigation, flywheelenergy storage systems and power electronicsfor microgrid applications, power electronics and

control systems for rail power delivery applications, transformer saturationprevention, digital signal processing, digital control of power quality devices,and hybrid filters.

Mike Barnes (M96) received the B.Eng. and Ph.D.degrees from the University of Warwick, Coventry,U.K., in 1993 and 1998, respectively.

He was a Research Associate on a DTI/LINKproject on low-cost switched reluctance drives anda Lecturer at the University of Warwick. For the lastthree years, he has been a Lecturer at the Universityof Manchester Institute of Science and Technology,Manchester, U.K., where his research interests havecovered power electronics applied to power systems,machine drives, and photovoltaics.

Peter Green received the M.A. degree from Cam-bridge University, Cambridge, U.K., in 1988, and the

M.Sc. degree from the University of Manchester In-stitute of Science and Technology (UMIST), Man-chester, U.K., in 1990.

In 1991, he joined the Communication Engi-neering Group, Departmentof ElectricalEngineeringand Electronics, UMIST, where he is currently aSenior Lecturer. His research interests include HFspectral occupancy, high-rate data waveforms forHF communication systems, communication system

applications of DSPs, and the analysis of the binary and polyphase sequences.

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