Fast frequency tracking
A method of periodical signal frequency tracking by the frequency-locked loops is proposed. Increasing of frequency adjustment accuracy is achieved by using of a new fast frequency discriminator, based on estimates of an instantaneous frequency. Reasonability of an input signal pre-filtering in case...
Збережено в:
| Дата: | 2013 |
|---|---|
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2013
|
| Назва видання: | Технология и конструирование в электронной аппаратуре |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/56394 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Fast frequency tracking / I.G. Prokopenko, I.P. Omelchuk, Yu.D. Chyrka, V.Yu. Vovk // Технология и конструирование в электронной аппаратуре. — 2013. — № 6. — С. 25-31. — Бібліогр.: 12 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-56394 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-563942014-02-18T03:15:35Z Fast frequency tracking Prokopenko, I.G. Omelchuk, I.P. Chyrka, Yu.D. Vovk, V.Yu. Системы передачи и обработки сигналов A method of periodical signal frequency tracking by the frequency-locked loops is proposed. Increasing of frequency adjustment accuracy is achieved by using of a new fast frequency discriminator, based on estimates of an instantaneous frequency. Reasonability of an input signal pre-filtering in case of nonlinear distortions, harmonics interferences and strong noise is proved. Предлагается метод отслеживания частоты периодического сигнала. Повышение точности подстройки частоты достигается благодаря использованию нового быстрого частотного дискриминатора на базе оценок мгновенной частоты. Также доказывается целесообразность предварительной фильтрации входного сигнала в случае нелинейных искажений, гармонических помех и сильного шума. Пропонується метод відслідковування частоти періодичного сигналу. Підвищення точності підлаштування частоти досягається завдяки використанню нового швидкого частотного дискримінатора на основі оцінок миттєвої частоти. Також доводиться доцільність попередньої фільтрації вхідного сигналу у випадку нелінійних спотворень, гармонічних завад та сильного шуму. 2013 Article Fast frequency tracking / I.G. Prokopenko, I.P. Omelchuk, Yu.D. Chyrka, V.Yu. Vovk // Технология и конструирование в электронной аппаратуре. — 2013. — № 6. — С. 25-31. — Бібліогр.: 12 назв. — англ. 2225-5818 http://dspace.nbuv.gov.ua/handle/123456789/56394 621.396.962.3/045 en Технология и конструирование в электронной аппаратуре Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Системы передачи и обработки сигналов Системы передачи и обработки сигналов |
| spellingShingle |
Системы передачи и обработки сигналов Системы передачи и обработки сигналов Prokopenko, I.G. Omelchuk, I.P. Chyrka, Yu.D. Vovk, V.Yu. Fast frequency tracking Технология и конструирование в электронной аппаратуре |
| description |
A method of periodical signal frequency tracking by the frequency-locked loops is proposed. Increasing of frequency adjustment accuracy is achieved by using of a new fast frequency discriminator, based on estimates of an instantaneous frequency. Reasonability of an input signal pre-filtering in case of nonlinear distortions, harmonics interferences and strong noise is proved. |
| format |
Article |
| author |
Prokopenko, I.G. Omelchuk, I.P. Chyrka, Yu.D. Vovk, V.Yu. |
| author_facet |
Prokopenko, I.G. Omelchuk, I.P. Chyrka, Yu.D. Vovk, V.Yu. |
| author_sort |
Prokopenko, I.G. |
| title |
Fast frequency tracking |
| title_short |
Fast frequency tracking |
| title_full |
Fast frequency tracking |
| title_fullStr |
Fast frequency tracking |
| title_full_unstemmed |
Fast frequency tracking |
| title_sort |
fast frequency tracking |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2013 |
| topic_facet |
Системы передачи и обработки сигналов |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/56394 |
| citation_txt |
Fast frequency tracking / I.G. Prokopenko, I.P. Omelchuk, Yu.D. Chyrka, V.Yu. Vovk // Технология и конструирование в электронной аппаратуре. — 2013. — № 6. — С. 25-31. — Бібліогр.: 12 назв. — англ. |
| series |
Технология и конструирование в электронной аппаратуре |
| work_keys_str_mv |
AT prokopenkoig fastfrequencytracking AT omelchukip fastfrequencytracking AT chyrkayud fastfrequencytracking AT vovkvyu fastfrequencytracking |
| first_indexed |
2025-07-05T07:39:43Z |
| last_indexed |
2025-07-05T07:39:43Z |
| _version_ |
1836791820961447936 |
| fulltext |
Òåõíîëîãèÿ è êîíñòðóèðîâàíèå â ýëåêòðîííîé àïïàðàòóðå, 2013, ¹ 6
25
SIGNALS TRANSFER AND PROCESSING SYSTEMS
ÓÄÊ 621.396.962.3/045
I. G. PROKOPENKO, Dr. Sci. (Techn), I. P. OMELCHUK, Yu. D. CHYRKA, V. Yu. VOVK
Ukraine, Kiev, National Aviation University
E-mail: prokop-igor@yandex.ru, omelip@ukr.net
FAST FREQUENCY TRACKING
Periodic signals processing is an important part
of electronic support measures (ESM) technologies
on which a variety of different modern technical
systems are based. Thus, the problem of frequency
synchronization in telecommunication systems is
still relevant [1]. The same applies to panoramic
receivers, the main feature of which is fast detec-
tion of signals with a priori unknown parameters
[2]. Coherent processing algorithms that are used
in the receiver require measurements of phase and
frequency of weak radio signals in the presence
of noise. Signals in Global Satellite Navigation
Systems besides have a large frequency (Doppler)
uncertainty at the receiver that is consequence of
the high relative satellite-to-receiver velocity [3].
The specificity of power systems of grid-connected
converter type is high-precision frequency tuning
to known nominal value and ensuring phase syn-
chronization [4—5].
In the most of above-mentioned systems, the
signal (x) can be considered as a single-tone (s)
with additive white Gaussian noise (η):
, , ,sinx s i j1i i i i
i
j
i0
0
η ρ ω τ ϕ η= + = + + =
=
e o/
The measurement of these parameters is consid-
ered in [6] the main point of which is an algorithm
of instantaneous frequency estimation. It was this
work which became the basis of the present study,
where we solve the problem of improving perform-
ance of harmonic signal synchronization systems.
We propose a new frequency tracking method
based on estimation of instantaneous frequencies
A method of periodical signal frequency tracking by the frequency-locked loops is proposed. Increasing
of frequency adjustment accuracy is achieved by using of a new fast frequency discriminator, based
on estimates of an instantaneous frequency. Reasonability of an input signal pre-filtering in case of
nonlinear distortions, harmonics interferences and strong noise is proved.
Keywords: FLL, speed, frequency estimation, interference, adaptive filter, open loop.
and fast frequency-locked loop (FLL) system with
a new fast frequency discriminator (FD) and an
open loop to enhance the frequency tracking with
nonlinear element in the closed loop. We also
propose to implement the input signal pre-filtering
using an adaptive low-pass filter (ALPF).
At first we consider general principles of
frequency tracking with the use of phase-locked
loops (PLL) and frequency-locked loops. Then we
provide detailed description of the proposed system
and its structural elements. System effectiveness is
researched by computer simulations and analysis
of frequency tracking transient processes for dif-
ferent versions of the FLL. Finally, we prove it
necessary to use an adaptive filter for reduction of
noise, interferences and higher harmonics.
Basic methodology
The conventional synchronization technique
is based on the application of PLL which also
provides phase synchronization of reference and
generated signals. These systems generally in-
clude the three typical structural blocks: phase
discriminator, control unit (CU) and controlled
oscillator (CO).
The typical examples of such systems are three-
phase PLL-systems [4]. Although these systems
are fast and accurate under balanced conditions,
they become inapplicable when the utility voltage
is unbalanced. This circumstance leads to system
decomposition onto three independent channels
with individual parameters tracking [4]. The usage
of the single-phase PLL is typical for the above-
mentioned ESM-systems.
As it is said in [5], PLLs synchronize with the
phase of the input signal, and hence, the accuracy
and dynamical response of its estimation under
transient conditions are highly influenced by phase
jumps. An FLL, on the other hand, estimates the
frequency of the input signal, which does not
the current sample index;
the amplitude;
the initial phase;
the unknown frequency that can vary in time;
the sampling period.
where j —
ρ —
ϕ0 —
ω —
τ —
Òåõíîëîãèÿ è êîíñòðóèðîâàíèå â ýëåêòðîííîé àïïàðàòóðå, 2013, ¹ 6
26
SIGNALS TRANSFER AND PROCESSING SYSTEMS
experience such sudden changes and can acquire
and track signals which are at higher frequency
offsets than a PLL can. A significant improvement
of measurement ability in FLL is achieved by re-
ducing the parametric dimension of the problem.
The general approach to designing the FLL is
to adjust the output signal frequency to the refer-
ence signal frequency, which may be constant or
changed by an unknown law. It is similar to the
PLL, but a phase discriminator is replaced by FD
(see Fig. 1).
There is also an open loop of an instantaneous
frequency ω*x estimation of the reference signal
besides the closed loop and the ALPF of the ref-
erence signal. The digital harmonic output signal
(u) with the desired frequency is generated by
the CO, which is schematically shown in Fig. 2.
In order to approximate this model to real tech-
nical systems, it is considered that the dependence
of CO on the control signal adjusting characteristic
∆ϕj is nonlinear and generally can be represented
by functional transformation
( ),G
j jϕ ϕ∆ ∆=I
where
j
ϕ∆I is an actual generator phase growth
at j-th step.
The instantaneous frequency of the output
signal equals
/ .,u j j
ω ϕ τ∆= I
The current phase
j
ϕI of the output signal
sinuj j
ϕ= I is formed in the block Ф (see Fig. 2)
as the sum of all phase growths between the ad-
jacent samples
.
j i
i
j
1
ϕ ϕ∆=
=
I I/
The CU considered in the paper (Fig. 3) is the
simplest first order unit, which provides astatism
by frequency. The corresponding mathematical
model of the CU can be written as
,K K ,j l i x j
i
j
1
ϕ ω ω∆ ∆= + )
ω
=
/
Fast frequency discriminator
Frequency tracking speed in the FLL system
is largely determined by the inertia of the FD.
Usually the FD includes a mixer (multiplier) of
two signals connected in series with a low pass
filter [7] without direct frequency estimation.
The fundamental need for a filter to isolate low-
frequency component leads to considerable inertia
of a closed loop control. A transient process may
exceed approximately ten cycles of the harmonic
signal. Construction of the FD by zero-crossing
digital method also reduces adjustment time be-
cause data appearance tempo is only half of the
signal period.
The problem of FLL performance improve-
ment is solved in this study by using a new FD,
the block diagram of which is shown in Fig. 4.
Instantaneous frequency estimates of reference and
output signal are obtained independently in fast
frequency estimation (f_FE) blocks. It also allows
us to use the value of the instantaneous frequency
estimation of the reference signal in the open loop
control. Another considerable feature is absence of
a filter in opposite to the classical FD.
Digital instantaneous frequency measurement
receivers have been used for wideband monitor-
ing of radar environments in naval, airborne and
gains of close and open control loops,
respectively; Δ
the difference between instantaneous
frequency estimates of the reference
ω*
x,j and output ω*
u,j signals.
where Kl, Kω —
∆ωj —
Fig. 1. Proposed fast FLL structure
Fig. 2. Controlled oscillator block diagram
Fig. 3. Control unit structure
Fig. 4. The structure of the proposed fast frequency
discriminator
Òåõíîëîãèÿ è êîíñòðóèðîâàíèå â ýëåêòðîííîé àïïàðàòóðå, 2013, ¹ 6
27
SIGNALS TRANSFER AND PROCESSING SYSTEMS
ground-based ESM-systems all over the world for
over 50 years [8]. There are a lot of researches on
algorithms improvement at present time, but they
usually provide sufficient noise immunity only on
condition of significant observation interval and
can be based, for example, on Fourier and Hilbert
transforms. It is necessary to use algorithms that
can work with a short sample of signal, in par-
ticular, the one developed by authors of [6, 9].
These algorithms are based on an auto regres-
sion model of sine wave:
sn = asn–1– sn–2, , ,n M3= a = 2cos(g),
where g is a phase shift between adjacent samples
of the signal. This phase shift is named normal-
ized frequency.
Auto regression model allows building the phase
shift estimate:
( ) / ,arccos B x B x 2 2( )1 2
2!γ = +) ^`` h j j
where B x^ h is calculated in M-size running win-
dow as
0.5
( )
( ) –
.B x
x x x
x x x2
–
–
–
–
k k k
k j M
j
k k k
k j M
j
1 1
1
1 1
2 2
1
=
+
+
+
= +
+
= +^ h
6
6
@
@
/
/
The next step is to select the value of g* located
in the zone of the method unambiguity (0, p/2).
And finally, the real frequency is calculated as
f *
s = g*/(2pτ).
The single instantaneous frequency value at
a certain point j of discrete time is calculated
by f_FE algorithm on the basis of several (M in
number) previous consecutive signal samples (the
so-called “window”). The size of this window must
be at least 4 samples. Larger window sizes in real
systems increase stability in noise conditions.
For the current time j window models of ref-
erence and output signals, which are processed
parallel in two f_FE blocks, can be written in a
vector form:
Xj = {xj–M+1, xj–M+2, …, xj},
Uj = {uj–M+1, uj–M+2, …, uj}.
A model of the fast harmonic signal frequency
discriminator can be written as
– , , .EE X U, , , ,j x j u j x j j u j jω ω ω ω ω∆ = = =) ) ) ) )
ω ω^ ^h h
Thus, sequential evaluation of the input proc-
ess instantaneous frequencies is performed by the
f_FE in running window mode step by step for
each point in discrete time.
The appearance of the proposed fast FD leads
to a necessity of carrying out a specific research on
the influence of open loop and adaptive filtration
on effectiveness of frequency adjustment. Quality
of the frequency adjustment is determined by the
stability and duration of the transition process and
steady-state error.
Because the fast FD is a nonlinear element,
the behavior of the frequency closed loop control
cannot be accurately described in the framework of
classical control theory. Therefore, initial research
of the f_FLL, as the new system, is implemented
by computer simulation.
Open loop
First of all, it is necessary to point out
that in case of linear adjusting characteristic
(Kω ⋅ G(∆ϕj) ≡ 1), only the open loop is enough
to carry out the frequency adjustment in an FLL-
system. Thus, close loop becomes unnecessary.
So from now on we shall consider the nonlinear
adjusting characteristic. As an example, we have
chosen the following expression:
( ) ,/
j j
3 4ϕ ϕ∆ ∆=I
and the following general conditions for computer
simulations: the reference signal frequency range
is 25—400% of the nominal value of 1 MHz;
sampling frequency 50 MHz (τ = 20 μs); running
window size M=50, which corresponds to 1 cycle
of the nominal signal.
Fig. 5 demonstrates acceleration of the tran-
sient process by the open loop when the closed
loop gain is invariable Kl = 0.012. It should be
noted, that this coefficient is almost proportional
to the τ value.
The maximum value of the open loop gain
Kw=0.9, with which the best result was obtained,
is close to the stability boundary for the given
frequency range (16-fold frequency variation). In
different situations, the duration of the aperiodic
transient process (up to 5% deviation level) is 3 to
5 signal cycles. There is a possibility to shorten this
time by simultaneously decreasing the frequency
range by means of increasing Kw coefficient. It was
found that nonlinearity of quadratic and square
root functions leads to considerable dynamic range
narrowing from the point of view of its stability.
Fig. 5. Transient processes of the fast FLL with an open
loop for different Kw values:
⋅ ⋅ ⋅ ⋅ ⋅ 0; ----- 0,5; 0,9
4
3
2
1
0 5 10 15 20 25 30
Time, s
F
re
qu
en
cy
,
G
H
z
Òåõíîëîãèÿ è êîíñòðóèðîâàíèå â ýëåêòðîííîé àïïàðàòóðå, 2013, ¹ 6
28
SIGNALS TRANSFER AND PROCESSING SYSTEMS
Adaptive filtering
The main disadvantage of the estimator [10]
is its sensitivity to interferences (in particular
higher harmonics) and noises, especially in low
frequency range. It is reasonable to use preliminary
filtering of input (reference) signal to reduce
the influence of such factors [10—12]. It is the
possibility to estimate the instantaneous frequency
in the proposed fast FLL that allows the filter
bandwidth adaptation to be carried out. It means
that coefficients {aj}, {bj} of the transfer function
Hj = Hb({bj})/Ha ({aj}) should be modified at each
step j by filter synthesis laws
{aj} = ℑa(ω*x,j), {bj} = ℑb(ω*x,j).
Hence, the bandwidth depends on the obtained
frequency estimate. The adaptive filter as an ele-
ment of the fast FLL is shown in Fig. 6.
As the preliminary research has shown, it is
preferable to use the first order Butterworth filter
as a low-pass IIR due to the advantages of the
former in operating speed and stability. Thus, it
is this filter we focus on hereafter.
The first fundamental reason to use the filter is
that it allows maintaining the maximum signal-to-
noise ratio (SNR) which can be reached because
the filter cutoff frequency (fco) equals the signal
frequency. This can be seen from the graph of the
transient processes in Fig. 7 for SNR=10 dB. The
figure clearly shows that the system is virtually
inoperable with such noise level without the filter.
Using the nonadaptive filter adjusted to nomi-
nal frequency significantly reduces the frequency
tracking error for the low-frequency signal, but
worsens the precision for the high-frequency signal
by suppressing it. The adaptive filter decreases the
tracking error for the low-frequency signal even
more, and significantly improves precision for
the high-frequency signal. Minor loss at nominal
frequency, as compared to the non-adaptive filter,
is caused by instantaneous frequency fluctuations
and, respectively, cut-off frequency fluctuations.
It should be noted, that the presence of the filter
virtually does not delay the transient process of
the frequency jump.
The second positive effect of the adaptive fre-
quency filtering is the suppression of higher har-
monics, which enables to perform error estimation
of the main tone frequency of periodic nonsinusoi-
dal signals. This effect is considered further, on
an example of a triangular signal without noise.
Fig. 8 shows transient processes of the system
with and without filter. One can see that the
adaptive filter provides a sufficiently higher pre-
cision of tracking of the first harmonic frequency
of the triangular signal. Fig. 9 shows a fragment
of tracking of the output sinusoidal signal to the
triangular reference signal. As can be seen from
the figure, the thansient process lasts no more than
two cycles of lower frequency signal.
Properties of the frequency estimation
algorithm with pre-filtering
Above mentioned positive features of the new
FLL first of all depend on the precision of the
frequency estimation of the disturbed reference
signal. Therefore, the behavior of pre-filter and
estimator as a pair must be analyzed in more detail
for different input processes.
Fig. 6. Adaptive filter
structure
6
4
2
0 20 40 60
Time, µs
F
re
qu
en
cy
,
G
H
z
Fig. 7. Transient processes of the fast FLL with
sinusoidal reference signal:
⋅ ⋅ ⋅ ⋅ ⋅ without filtering; ----- with a nonadaptive filter;
with an adaptive filter
1,2
0,8
0,4
0 40 80 120
Time, µs
F
re
qu
en
cy
,
G
H
z
Fig. 8. Transient processes of the fast FLL with
triangular reference signal:
⋅ ⋅ ⋅ ⋅ ⋅ without filtering; with an adaptive filter
Fig. 9. Visualisation of adaptation process
⋅ ⋅ ⋅ ⋅ ⋅ output signal; — reference signal
1,0
0,5
0
–0,5
–1,0
1,00 1,25 1,50
Time, µs
A
m
pl
it
ud
e,
V
Òåõíîëîãèÿ è êîíñòðóèðîâàíèå â ýëåêòðîííîé àïïàðàòóðå, 2013, ¹ 6
29
SIGNALS TRANSFER AND PROCESSING SYSTEMS
Frequency estimation errors in the presence
of the harmonic interference
The appearance of an additional harmonic ξ
with different frequency fξ and power Pξ consid-
erably decreases the estimation accuracy because
the algorithm does not have any filtering proper-
ties. Fig. 10 shows the graph of the estimation
mean which depends on the frequency ratio and
the signal to interference power ratio mf(fξ/fS,
Pξ/PS) when the noise is absent. Estimations
randomness is caused by randomization of the
signal and the interference initial phases and the
standard deviation lies within 9% zone relative
to the nominal frequency. The obtained surface
of the estimation mean mf(⋅) is characterized by
smoothness, and one-dimensional dependencies
mf (fξ/fS) at Pξ/PS = const are characterized by
high enough linearity.
It was found that frequency estimations are
virtually independent of the window size and the
sampling frequency, if such frequency is much
higher than fS and fξ.
It should be noted, that in this situation there
is no point in studying the pre-filtering, because
it is quite enough to determine the signal to in-
terference power ratio from amplitude-frequency
characteristic of the filter and directly address the
function mf(fξ/fS, Pξ/PS).
Influence of frequency deviation
on estimation precision
In the case of the locally non-stationary signal,
when its actual instantaneous frequency (IF) is
significantly varied within a single window, the
estimation depends on the variation degree. For
example, in the case of the linear deviation, the
frequency estimation approximately equals to the
medium value between the initial (fb) and the
final (fe) frequencies of the window:
f* = (fb + fe )/2 + ∆f*.
The character of deviation ∆f* is shown in
Fig. 11. The charts for each window size (8, 16,
32, 64) are different because of the difference in
phase distances between the samples.
Reasonability of the input signal pre-filtering
In actual practice, the correlative noise proc-
ess is formed by pre-filtering before using the
frequency estimation algorithm. An input pa-
rameter for research is the signal-to-noise ratio
SNR = Ps/s2
g, where s2
g is the variance of the
additive white Gaussian noise.
The graph of the estimation mean (Fig. 12)
for the 1st order low-pass filter (LPF) shows a
sufficiently larger working area near nominal fre-
quency in comparison to the case, when the LPF
is not used.
This can also be confirmed by the mean square
error (MSE) of frequency estimation (Fig. 13, a).
The surface is characterized by the reduction of the
argument of the MSE function minimum, while
SNR is increasing. This means that greater signal
suppression by the filter is allowed.
Some decrease of the error mean can be achieved
by reducing the sampling frequency and the
number of samples in the window. But we must
remember that reducing the number of samples
generally causes the increase of the MSE.
The 2nd order LPF can be considered as more
efficient in use. The MSE surface for such filter
is shown in Fig. 13, b. Such MSE value, in com-
parison to Fig. 13, a, decreases 2 to 3 times at the
Fig. 10. Estimation mean for the harmonic interference
mf, GHz
2,5
2,0
1,5
1
0,5
3 2 1 0
fξ/f
S 0
1
2
3
Pξ/
PS
Fig. 12. The estimation mean for the 1st order
preliminary LPF (fco — cutoff frequency)
mf, GHz
1,04
1,00
0,96
5 10 15 20
SNR
0
1
2
3
fco
, GHz
60
40
20
0
–20
0 0,4 0,8 1,2 1,6 2,0
fb/fe
Fig. 11. Frequency estimation with deviation for
different window size
64
32
16
8
∆m
f,
M
H
z
Òåõíîëîãèÿ è êîíñòðóèðîâàíèå â ýëåêòðîííîé àïïàðàòóðå, 2013, ¹ 6
30
SIGNALS TRANSFER AND PROCESSING SYSTEMS
points of optimum, but if the cutoff frequency fco
is less than 0.7fS, the MSE increases much sharper.
The application of a band-pass filter allows us
to further reduce the MSE at optimal points, but
requires a precise coordination of frequency tuning
to a range of possible signal frequencies. According
to research results for the 1st order band-pass filter
with a 20% bandwidth, the prior uncertainty range
should not exceed 0.8—1.2 relative to the true
frequency value. When the 2nd order filter is used
or the bandwidth is narrower, the requirements
for prior knowledge become stricter.
Improvement of non-harmonic signals
estimation
As it was mentioned earlier, pre-filtering is
also useful for estimation of frequency of periodic
non-harmonic signals, the main feature of which
is presence of higher harmonics. For example, the
MSE surface of estimation of square wave fre-
quency after the 1st order LPF is shown in Fig. 14.
As it can be seen, there is a gradual shift of
fco
opt towards zero, due to the negative value of the
second derivative of response of the LPF in the
high frequency range. Without pre-filtering the
errors of square wave frequency estimation (even
without the noise) exceed 50%, which proves the
reasonability of application of pre-filtering.
It was found that the value of the MSE for
trapezoidal signals (which have much smaller
harmonics), decreases 4—6 times in comparison
to the meander.
Detection of the signal frequency modulation
A great feature of the algorithm is a sufficiently
accurate estimation at intervals (windows) equal
to a period of the signal [6] and even at a half
period when the noise level is low, which brings
us nearer to the actual IF and provides the oppor-
tunity to observe its modulation over time. This
property is investigated on the example of a linear
frequency-modulated (LFM) signal processing with
pre-filtering by the 1st order LPF. The results of
measuring the IF of such signal with the frequency
that varies from 0.9 to 1.8 MHz during the time
interval of 10 ms with the sampling frequency of
16 MHz are shown in Fig. 15. The MSE is obtained
by averaging of differences at each signal sample.
Conclusions
The application of the new frequency discrimi-
nator with an estimation of instant frequencies of
reference and generated signals allows adding to
the FLL-system an adaptive filter of the reference
signal and an open regulation contour. Small lag-
ging of blocks of the instant frequency estimation
and the open regulation contour provide fast fre-
quency tracking. The speed of a transient process
reaches 3 to 5 cycles of a signal. The adaptive
80
60
40
20
0 10 20
SNR
M
S
E
f,
M
H
z
0,5 1,0 1,5
fco, GHz
Fig. 13. The mean square error for the 1st (a) and the
2nd (b) order preliminary LPF
120
80
40
0
10 20
S
N
R
M
S
E
f,
M
H
z
0,5 1,0 1,5 2,0 2,5 3,0
fco, GHz
a)
b)
Fig. 14. The MSE for the 1st order preliminary LPF
400
300
200
100
0 5 10
S
N
R
M
S
E
f,
M
H
z
0 1 2 3
fco, GHz
Fig. 15. The MSE for the LFM signal
160
120
80
40
2 6 10
SNR
M
S
E
f,
M
H
z
1,0 2
,0 3,
0 4,0
fco
, MHz
Òåõíîëîãèÿ è êîíñòðóèðîâàíèå â ýëåêòðîííîé àïïàðàòóðå, 2013, ¹ 6
31
SIGNALS TRANSFER AND PROCESSING SYSTEMS
pre-filtering allows increasing the signal to inter-
ference ratio at FLL-system input and improves
the accuracy of frequency tracking. The applica-
tion of the 2nd order band-pass pre-filter is only
reasonable for a small prior frequency ambiguity
range (not more than 20%), while in other cases
the 1st order low-pass filter is more preferable.
REFERENCES
1. Xin Jin, Runbo Fu, J. S. Nielsen. Method and apparatus
for frequency tracking in a space timetransmit diversity
receiver. Pat. USA no 2012288041A1, 2012.
2. Rembovsky A. Radio Monitoring. Springer, 2009.
3. Curran J. T., Lachapelle G., Murphy C. C. Improving
the design of frequency lock loops for GNSS receivers. IEEE
Trans. on aerospace and electronic systems, 2012, Vol. 48,
no 1, pp. 850-868.
4. Xiao-Qiang Guo, Wei-Yang Wu, He-Rong Gu. Phase
locked loop and synchronization methods for gridinterfaced
converters: a review. Przegląd Elektrotechniczny (Electrical
Review), 2011, Vol. 87, no 4, pp. 182-187.
5. Rodríguez P., Luna A., Candela I., Mujal R., Teodorescu
R., Blaabjerg F. Multiresonant frequency-locked loop for grid
synchronization of power converters under distorted grid
conditions. IEEE Trans. on industrial electronics, 2012, Vol.
58, no 1, pp. 127-138.
6. Prokopenko I.G., Omelchuk I.P., Chyrka Y.D. Radar
signal parameters estimation in the MTD tasks. International
Journal of Electronics and Telecomunications, 2012, Vol. 58,
no 2, pp. 159-164.
7. Talbot D. Frequency acquisition techniques for Phase-
locked loops. IEEE Press, 2012.
8. East P. W. Fifty years of instantaneous frequency
measurement. IET Radar, Sonar and Navigation, 2011,
Vol. 6, no 2, pp. 112-122.
9. I.G. Prokopenko, I.P. Omelchuk. Method for harmonic
signal frequency estimation. Pat. UA no 2345679, 2009.
10. Weigang Sun, Huainan Ma, Wenshen Wang. Mutual
loop circuit device for decimal fraction frequency division
lock. Pat. CN no 201004621Y, 2008.
11. Haykin S. Adaptive filter theory, 3rd edition. Prentice
Hall, 1995.
12. Kušljevic M. D. A simple method for design of adaptive
filters for sinusoidal signals. IEEE Trans. on instrumentation
and measurement, 2008, Vol. 57, no 10, pp. 2242-2249.
Received 30.09 2013
І. Г. ПРОКОПЕНКО, І. П. ОМЕЛЬЧУК, Ю. Д. ЧИРКА, В. Ю. ВОВК
Óêðàїíà, ã. Êèїâ, Нàціîíàëьíèé àâіàціéíèé óíіâåðñèòåò
E-mail: prokop-igor@yandex.ru, omelip@ukr.net
ШВИÄÊЕ ВІÄСЛІÄÊОВÓВАННЯ ЧАСÒОÒИ
Пðîïîíóєòьñÿ мåòîд âідñëідêîâóâàííÿ чàñòîòè ïåðіîдèчíîãî ñèãíàëó. Підâèщåííÿ òîчíîñòі ïідëàшòóâàííÿ
чàñòîòè дîñÿãàєòьñÿ зàâдÿêè âèêîðèñòàííю íîâîãî шâèдêîãî чàñòîòíîãî дèñêðèміíàòîðà íà îñíîâі îціíîê
мèòòєâîї чàñòîòè. Òàêîж дîâîдèòьñÿ дîціëьíіñòь ïîïåðåдíьîї фіëьòðàції âõідíîãî ñèãíàëó ó âèïàдêó íåëі-
íіéíèõ ñïîòâîðåíь, ãàðмîíічíèõ зàâàд òà ñèëьíîãî шóмó.
Ключові слова: ФАПЧ, швидкість, оцінювання частоти, завада, адаптивний фільтр, розімкнений контур.
И. Г. ПРОКОПЕНКО, И. П. ОМЕЛЬЧУК, Ю. Д. ЧИРКА, В. Ю. ВОВК
Óêðàèíà, ã. Êèåâ, Нàцèîíàëьíыé àâèàцèîííыé óíèâåðñèòåò
E-mail: prokop-igor@yandex.ru, omelip@ukr.net
БЫСÒРОЕ ОÒСЛЕЖИВАНИЕ ЧАСÒОÒЫ
Предлагается метод отслеживания частоты периодического сигнала. Повышение точности подстрой-
ки частоты достигается благодаря использованию нового быстрого частотного дискриминатора на базе
оценок мгновенной частоты. Также доказывается целесообразность предварительной фильтрации вход-
ного сигнала в случае нелинейных искажений, гармонических помех и сильного шума.
Ключевые слова: ФАПЧ, скорость, оценивание частоты, помеха, адаптивный фильтр, разомкнутый
контур.
|