rectangular pulse train equation

In the limit, as becomes very large, the . Equation 3-42. FLAT-TOP SAMPLING . (3.30) g t = ∑ k = - ∞ ∞ p t - k T 0 where p ( t) is a rectangular pulse, as defined in (3.27). (3-41) for the summation in Eq. The simplest waveform for a radar system is probably a rectangular waveform, sometimes also referred to as single frequency waveform. Figure 3 Power is just the time rate of change of the energy flow (energy per unit time). Its RMS value is given in (11). Fourier series coefficient magnitudes for a rectangular pulse train with pulse width U and period V. The duty cycle is D = U/V. As the sampling aperture increases i.e. • A periodic signal x(t), has a Fourier series if it satisfies the following conditions: 1. x(t) is absolutely integrable over any period, namely 2. x(t) has only a finite number of maxima and minima over any period 3. x(t) has only a finite number of discontinuities over any period In fact, it can be any pulse, even lasting for more than T seconds. Show activity on this post. Show activity on this post. Tips p(t) A. 2 Figure 2-18 Impulse sampling. Rectangular Pulse Train and Sinc Function. from publication: Time Division Multiplexing Front-Ends for Multiantenna Integrated Wireless Receivers | The . Alternative definitions of the function define ⁡ to be 0, 1, or undefined. For four-level lasers, an increase in efficiency of pulse train generation appears for the active materials for which depopulation . Fourier Transform of a unit impulse train Consider an impulse train The Fourier series of this impulse train can be shown to be: (t) = ED where coo = and D Therefore using results from the last slide (slide 1 1), we get: t 20k) L7.2 P694 Lecture 3 Slide 12 13 Jan 2020 EA2.3- —200 — E ectronics 2 Function is odd, with. Because of the periodicity of it is very common when plotting the DTFT to plot it over the range of just one period: . Here, binary 1 is represented by a rectangular positive pulse. increase of pulse width ----- there will be more loss in high frequency components. A 1.0 KHz signal is flat top sampled at the rate of 1800 samples/sec and the samples are applied to an ideal rectangular LPF with cut-off frequency of 1100 Hz, then the output of the filter contains > I need to generate a Periodic Rectangular pulse train (+1 -1) Type . Namely, three modulating functions are considered: a train of rectangular waves, a single case, do not suffer diffractive or dispersive effects during their propagation: see, e.g., [1-9]. This answer is not useful. Homework Equations F(w) = integral from -infinity to +infinity of: f(t)exp(-iwt)dw The Attempt at a Solution Pulse duration A Interpulse interval B Pulse period T = A + B Duty cycle D = A/T Pulse frequency fo = 1/T Pulse radian frequency ωo = 2πfo Pulse amplitude Vo Fourier Series Equation where the Fourier parameters are: The Fourier parameters for the Pulse Train The Fourier Series for the Pulse Train V B T Amplitude in Volts Time in seconds A o . In other words, the zeros (the crossings of the magnitude spectrum with the axis) move closer to the origin. Consider a regularly repeating train of optical pulses with repetition rate f =1/T as shown below. y = pulstran (t,d,func) generates a pulse train based on samples of a continuous function, func. Note that the width of the pulse can change! Periodic trains: (a) pulse train and (b) impulse train. Determine the Fourier transform of a rectangular pulse shown in the following figure Example:-a/2 a/2 h t x(t) /2 22 /2 2 sin( ) sin( ) 2 2 2 sinc 2 a aa jj jt a h Xhedt ee j a ha ha a a ha ωω ω ω ω ω ω ω ω ω π − − − == − − == = ∫ Equation (3-43) is the general expression for the DFT of the rectangular function as shown in Figure 3-24. Determine the impulse response of the matched filter. In this Demonstration, the pulse period is fixed at one second and the height is fixed at unity. It was proved that such a generation efficiency is significantly higher than efficiency of monopulses generation, especially for three-level lasers. Here, H(f) is the Fourier transform of the rectangular pulse. Since c(t) is a rectangular pulse train, c n has been expressed in equation 1 using a sinc function as: The output signal can therefore be expressed as: The frequency domain representation is therefore: The spectrum of the output signal is therefore as shown below. Figure 4. This Demonstration illustrates the following relationship between a rectangular pulse and its spectrum: 1. -SE. Therefore, as an example, the first term should be "func(t-0.5)" so that the train of rectangular pulses starts at "t=0". . Substituting Eq. A possible pulse load of 100 P R for 10 ms does not give us permission to directly apply 1000 P R for 1 ms. pulse, it is convenient to first periodically extend the isolated pulse to obtain a periodic pulse train having period T s and then multiply the periodic pulse train by a rectangular function to extract an isolated RZ pulse. Commutator determines the synchronization and sequence of the channels (signals) to be sampled. Fig.4 : (a) Spectrum of some arbitrary signal. (However, except for the final result we never make use of the fact that it is a rectangular pulse. • Example: the rectangular pulse train Fourier Series Representation of Periodic Signals xt T xt t R()(),+= ∀∈ • Then, x(t) can be expressed as where is the fundamental frequency(rad/sec) of the signal and The Fourier Series () ,jk t0 k k xt ce tω ∞ =−∞ /2 /2 1 () , 0,1,2,o T jk t k T cxtedtk T − ω − Option (a) 6. The above equation states that the output signal is produced by adding together many pulses, each centered at a particular sample, and also scaled by the amplitude of the sample x(n). I want to find the formula for the Fourier series f T ( t) of a particular rectangular pulse train with the following properties: Period = P, a positive integer. Recently on a Q&A forum, I answered some questions about pulse waveforms and harmonics. (3-38), our expression for X(q) becomes. The exact shape of the wave is determined by the duty cycle or pulse width of the oscillator output. This effect is frequently seen when the input signal is a square wave or rectangular pulse train with a high repetition rate. As the harmonics of the baseband signal, extend out to infinity, so too do the sidebands of the modulated signal. Hello, I am attempting to create a pulse train for my model. For example, the DTFT of the rectangular pulse will most often be shown . (c1). T = 5; t=-5*T:1/2*T:5*T; y=5*rectpuls (t,T); See rectpuls documentation. b) Plot this rectangular pulse train using Matlab. 2.3.1 The Rectangular Pulse The rectangular pulse is defined as (2.22) Π LT ( t) = { A - LT 2 ≤ t ≤ LT 2 0 otherwise where A is the amplitude of the pulse and L is an integer. Details. 10=1/τ 20=2/τ 30=3/τ 0.25=τ/Τ% v(t)= 2Vτ T o sinc(N2πf o T o) N=1 ∞ ∑ cos(Nπt) This is Each pulse in xp(t) has width T and amplitude 1/T. y ( t) = p ( t) × y δ ( t).. ( 1) To get the sampled spectrum, consider Fourier transform on both sides for equation 1 Y [ ω] = F. T [ P ( t) × y δ ( t)] The square wave in Figure 3 is a pulse signal with 50% duty-cycle. A rectangular pulse has height H and total length t0 in time. 1. example y = pulstran (t,d,p) generates a pulse train that is the sum of multiple delayed interpolations of the prototype pulse in vector p. example The DTFT of a discrete cosine function is a periodic train of impulses: I updated the above plot on 6-Jan-2010 to show the location of the impulses. The spectrum of this rectangular pulse is shown in fig.4(b). However, this model could be easily expanded to include more motor units and common inputs. Here, c(t) is the periodic train of pulse of width t and frequency f s. We know that the exponential Fourier series for any periodic waveform is expressed as, Also, for the periodic pulse train of c(t), we have, So, we have. We will write the square pulse or box function as rect_T(t), indicating that the rectangle function is equal to 1 for a period of T (from -T/2 to +T/2) and 0 elsewhere: Using the definition of the Fourier Transform ( Equation [1] on the intro page ), the integral is evaluated: Because the basic 10-1 Assume the p-to-p amplitude is 5. a) Using Table 4.3 express the truncated exponential form of Fourier series for this signal. That's because rectpuls is not meant to take in a symbol, it has to take in numbers. . CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): of temporal modulation effects in Bessel beams different pulse shapes. The rectpuls function generates a sampled aperiodic, unit-height rectangular pulse centered about t = 0 and with a default width of 1. Example 1.1 For the unit amplitude rectangular pulse train shown in Fig. This might be of interest to others, especially students in digital media or non-technical fields who need to have an idea about this math and related jargon.In most fields of study, the duty cycle is the fraction of the whole period… The common input voltage is represented as y t+1 in equation (3), where it is modeled as a rectangular pulse train with a specified pulse width and amplitude (A p). where p(t) denotes the pulse shape of our choice.. is a rectangular pulse of width a and height h = 1/a. Share. Theoretically, the sampled signal can be obtained by convolution of rectangular pulse p (t) with ideally sampled signal say y δ (t) as shown in the diagram: i.e. It would be great if you could help me with the scripts. periodic rectangular pulse train (This example is to be found in almost all the textbooks on communication theory). Figure 2. example y = pulstran (t,d,func,fs) uses a sample rate of fs. f T ( t) = { 1 0 ≤ t ≤ 1 0 else, 0 ≤ t ≤ P. I have watched a zillion how-tos and read . Note that the frequency of cos(mat) is m/2, hence eleven frequencies are considered from 0 Hz to 5 Hz in increments of 0.5 Hz. Ez(x,y) can be obtained from Ex (x,y) and Ey (x,y) as already explained, and H field can be obtained from the relation, 0 i E H The rectangular function (also known as the rectangle function, rect function, Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as ⁡ = = {, | | >, | | =, | | <. Formula for Fourier series for rectangular pulse train? In other words, the first element of 'd' must be half the width of the function (i.e. Bookmark this question. I ran the Transient Noise simulation using ADE L for 1000s (usingt Transient Noise analysis in order to directly acquire ADE L -> result -> main form -> PSD once the simulation finishes). The frequency domain representation of the rectangular pulse is (2.23) F { Π LT ( t) } = A ∫ LT 2 LT 2 e - j 2 π ft dt = ALT sin ( π LTf) π LTf The amplitudes of the harmonics for this example drop off much more rapidly (in this case they go as 1/n 2 (which is faster than the 1/n decay seen in the pulse function Fourier Series (above)). For the rectangular waveform, the pulse width is the reciprocal of the bandwidth. •Rectangular Sampling. I would like to generate a pulse train of Gaussian pulse in time domain with a certain width (let's say 20 ns in the above example) with a repetition interval of (let's say 100 ns). If you're looking for just periodic pulse trains, like the example you gave - here's a pulse train that is on for 5 cycles then off for five cycles: N = 100 # sample count P = 10 # period D = 5 # width of pulse sig = np.arange(N) % P < D Giving plot(sig) You can replace np.arange(N)with your linspacehere. You have to set T to an actual number (width of the rectpuls). After the first stage, the impulses in the impulse train occur at multiples of the sampling period. The rectangular function (also known as the rectangle function, rect function, Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as ⁡ = = {, | | >, | | =, | | <. This Demonstration illustrates the following relationship between a rectangular pulse and its spectrum: 1. An application of a periodic impulse train is in the ideal sampling process. (The proof of the last line in the equation above is beyond the scope of these notes - sorry.) The Fourier transform of a rectangular pulse $$ x(t) = \begin{cases} 1, & \text{for $|t| \le \tau /2$ } \\ 0, & \text{otherwise} \end Stack Exchange Network Stack Exchange network consists of 178 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their . Where; VD is my voltage applied. Example Complex exponential Fourier series of a rectangular pulse train Given the same rectangular pulse train considered for the trigonometric Fourier series expansion (amplitude = A, duty cycle = ô/T o ), the complex exponential Fourier expansion coefficients are found by evaluating the following integral. I am new to introducing pulses and would like an equation to place on my electrcial potential module to create the following: Rectangular wave: a) On for 0.1 sec at a voltage (VD), on a 1 second duty cycle (so on for 10% of a cycle) b) repeating 10 times. pulse train to generate an impulse train of samples. Channel temperature can be estimated with Equation (8) using these data. In Let the spectrum of s(t) be the rectangular pulse train as shown in fig.4(a) and the spectrum of h(t) i.e., H(f) is shown in fig.4(b). As an example, a unit amplitude rectangular pulse of duration . F(w) is the Fourier transform of f(t). Pulse loads in single pulses or pulse trains, with a permissible mean power as shown in Equation R1-6 or R1-7, always have to take into consideration the voltage strength. Consider a Rectangular wave with period of 8 seconds and pulse width of 2 seconds. Knowing the RMS value of a pulse waveform we can easily calculate the RMS value of a periodic square signal. So this leads us to define two different types of power. is multiplied by the pulse train or switching waveform xp(t), shown in Fig. Theorem 2, p. 241 in ) to be consistent with . Computing the Fourier transform of rectangular pulse.An improved version of this video is at http://www.youtube.com/watch?v=_HJH3MekMHY Details. is generated. Theorem 2, p. 241 in ) to be consistent with . where the message signal is multiplied by a periodic train of rectangular pulses. Rectangular Pulse Function If a < x < b, then the rectangular pulse function equals 1. Pulse distortion can be a concern for any system intended to output a scaled version of an input signal. I wanted to ask that in frequency domain the rectangular pulse is a sinc function, so is this sinc function periodic or aperiodic? Euler's Equation 3: Complex Fourier Series • Euler's Equation • Complex Fourier Series • Averaging Complex Exponentials • Complex Fourier Analysis • Fourier Series ↔ Complex Fourier Series • Complex Fourier Analysis Example • Time Shifting • Even/Odd Symmetry • Antiperiodic ⇒ Odd Harmonics Only • Symmetry Examples • Summary E1.10 Fourier Series and Transforms . Equation below describes the effect of the . Hot Network Questions Credit card charge off : Can creditor take away the electrician's toolbox and the car even if the car was paid off a long time ago? Show activity on this post. 1.2, let us compute the Fourier series coefficients. Fig. Both and its alias are plotted in Fig.4.9.The example in this figure pertains to an output sampling rate which is times that of the input signal.In other words, the input signal is upsampled by a factor of using linear interpolation. Yang Yang, IE, CUHK ERG2310A: Principles of Communication Systems (2002-2003) 8 Chapter 7: Pulse Modulation Time-division multiplex (TDM) Time-division multiplexing is the method of combining several sampled signals in a definite time sequence. What Is the FS of A Pulse Signal? In other words, the zeros (the crossings of the magnitude spectrum with the axis) move closer to the origin. Also if signals that are continuous in time domain then they are aperiodic in frequency domain? The above equation is an eigenvalue equation and its solution gives the transverse components of the electric field E for the mode and the corresponding propagation constant ( ) . In practice, such waves remain unchanged in their space . The latter pulse implies √10 times higher voltage since V=√( P . Transcribed image text: A rectangular pulse train can be modeled by the following Fourier series in M+1 frequency terms M x(t) 5 sin(mn/2) +5 Σ cos(mat) 2 MT/2 (1) m=1 2. When the duty cycle is low, the signal energy is spread over many harmonics (many of the sine-wave basis functions are non-zero). Equation 1 t i+1 = t i + Dt (Equation 1) Note: you need to fix the cell for delta t in Equation 1. 1.2: Periodic rectangular pulse train x p ()t has a period T However, this mid-point property, as defined here, is required (see e.g. from publication: Floquet Spectral Almost-Periodic Modulation of Massive Finite and Infinite Strongly Coupled . Step 3. As the pulse becomes flatter (i.e., the width of the pulse increases), the magnitude spectrum loops become thinner and taller. However, in natural sampling the top of each Solution: Let x 1 (t) represent the positive rectangular pulse with duration T as shown in figure 6.31(a). Its RMS value can be calculated from equation (5), where D = 1/2. As the pulse becomes flatter (i.e., the width of the pulse increases), the magnitude spectrum loops become thinner and taller. Conceptually, this occurs because the triangle wave looks much more like the 1st harmonic, so the contributions of the higher harmonics are less. The pulse, p(t), is a rectangular pulse of height, A, and width equal to T seconds. Rectangular pulse trains are used in a wide variety of test and measurement applications in both research and industry. Returning our dummy variable q to its original value of 2pm/N, Equation 3-43. Now, it may be noted that since c(t) is a rectangular pulse train, therefore C n for this waveform will be expressed as, • PAM- Pulse Amplitude Modulation: - The pulse may take any real voltage value that is proportional to the value of the original waveform. It is a term is used in synthesizer programming, and is a typical waveform available on many synthesizers. Write down the equation for F(w) in terms of f(t). In paper, I have to convolve with a Dirac comb. The interval of nonzero amplitude is defined to be open on the right: rectpuls(-0.5) = 1 while rectpuls(0.5) = 0. As a search-radar scans past a target, it will remain in the . Fill in column for Time (sec.) Spectrum of a perfectly rectangular pulse The envelope of this plot follows a function of the basic form: γ = sin ( x) x This single can then be modulated onto an RF waveform to give a spectrum. The Periodic Rectangular Pulse This is the example given above. For 33%, 50%, and 67% RZ, expressions for the iso-lated pulses E i(t)(i =33,50,67) are given in (3)-(5). Pulse becomes flatter ( i.e., the pulse width of 2 seconds in this,... The following relationship between a rectangular wave with period of t is as... Of 2 seconds if you could help me with the scripts fig.4 ( ). Trainxt ( t ) represent the positive rectangular pulse ; this is < a href= '' https: ''. A radar system is a rectangular pulse has height h and total length T0 in.! Power is just the time rate of change of the channels ( signals ) to be 0,,... That as a search-radar scans past a target, it will remain in the limit, becomes! Flow ( energy per unit time ) exact shape of the function define ⁡ to be 0, 1 or. Modulated signal be any pulse, even lasting for more than t seconds ; s because rectpuls is meant! Closer to the origin this leads us to define two different types of pulse train, often the output! Pdf < /span > Chapter 10 cyclic period of t is applied as shown Fig. One second and the duty cycle is D = 1/2 is used in synthesizer programming, and is a function. Variable q to its original value of 2pm/N, equation 3-43 the magnitude spectrum loops become and... T and amplitude 1/T pulse ; this is the general expression for final... Width of the energy flow ( energy per unit time ) in every is! I have to set t to an actual number ( width of 2 seconds fact that it is common! Is this sinc function periodic or aperiodic notes - sorry. the pulse of... ( w ) in terms of F ( w ) in terms of F w... Ask that in frequency domain any system intended to output a scaled version of input! To ask that in frequency domain the rectangular pulse of duration series coefficient magnitudes for rectangular... Different types of power the DFT of rectangular functions | Chapter Three rectangular... To convolve with a cyclic period of t is applied as shown in fig.4 ( )... The magnitude spectrum loops become thinner and taller Chapter 10 ( i.e., the of... In efficiency of monopulses generation, especially for three-level lasers, p. 241 ). For a rectangular pulse train limit, as defined here, is required ( see.! Often be shown property, as illustrated in Figure 3-24 sinc function periodic or?. Of fs times higher voltage since V=√ ( P Modulation of Massive Finite Infinite... A system is a term is used in synthesizer programming, and a... The duty cycle is D = 1/2 =ΠT ( t/Tp ) information is lost, the. Of 2pm/N, equation 3-43 Receivers | the, a unit amplitude rectangular pulse will most often be shown sampling... Will most often be shown ( signals ) to be sampled signal is also called the rectangle function, function..., sometimes also referred to as single frequency waveform by pressing „ F4‟ distortion can be any pulse, lasting! Linear Interpolation as Resampling | Physical Audio signal... < /a > Details in front of the periodicity of is... The last line in the, binary zero is represented by a pulse. Train, often the rectangular pulse train equation output signal is also a rectangular pulse train paper, have... Of duration remain in the limit, as illustrated in Figure 1.3, t =ΠT... Rectangular pulses and height h = 1/a define ⁡ to be sampled is applied as shown Fig. Impulses ( delta functions ) uniformly spaced T0 seconds apart Figure 3-24 of. A search-radar scans past a target, it can be estimated with equation ( 5 ) where... In time domain then they are aperiodic in frequency domain the rectangular pulse its. Length T0 in time domain then they are aperiodic in frequency domain series coefficient magnitudes for a system. 2, p. 241 in ) to be 0, 1, or undefined information is,... Closer to the origin of an input signal however, this mid-point property, becomes. Harmonics of the periodicity of it is very common when plotting the DTFT the. Unit amplitude rectangular pulse and its spectrum: 1 fig.4 ( b ) of one... Is given in ( 11 ) is just the time rate of fs that in frequency domain referred to single... Figure 3 is a term is used in synthesizer programming, and is a typical available. It can be estimated with equation ( 8 ) using these data is... And sequence of the pulse increases ), the pulse width U and period V. the duty cycle well. Multiantenna Integrated Wireless Receivers | the Integrated Wireless Receivers | the frequency waveform ( t ) shown... Row and Column values or by pressing „ F4‟ simplest waveform for rectangular. Final result we never make use of the function define ⁡ to be 0, 1, undefined! By the pulse period is fixed at unity, let us compute the Fourier series representation of channels! With equation ( 5 ), the defined here, is required ( see e.g Wireless Receivers | the simplest. Series coefficient magnitudes for a radar system is probably a rectangular pulse train ( energy per time. Occur at multiples of the pulse period is fixed at one second and the height is fixed at second! A sample rate of change of the energy is redistributed in the the channels ( signals to! I wanted to ask that in frequency domain with pulse width U and period the! Have a rounded appearance, as defined here, is required ( see e.g 8 seconds and pulse of. Express the truncated exponential form of Fourier series - rectangular pulse is shown in fig.4 b... Compute the Fourier transform of is the same function aliased on a block of size Hz Finite Infinite. 5. a ) using these data the latter pulse implies √10 times higher voltage since V=√ ( P output is! Waves remain unchanged in their space in xp ( t, t ) the. The rectangle function, boxcar function, so is this sinc function, boxcar function, so is this function. The rectpuls ) the following relationship between a rectangular waveform, the amplitude rectangular pulse train equation propertional! Shape of the energy, E, contained in every rectangular pulse train equation is shown fig.4! Because of the channels ( signals ) to be consistent with in efficiency pulse. The zeros ( the crossings of the periodic pulse trainxT ( t ), the DTFT of the periodicity it. //Www.Physics.Sfsu.Edu/~Bland/Courses/385/Downloads/Vector/Ch10.Pdf '' > < span class= '' result__type '' > < span class= result__type., D, func, fs ) uses a sample rate of change of the Row and values... > rectangular function as shown in Figure 3 is a rectangular pulse and its spectrum 1. This signal uniformly spaced T0 seconds apart in Fig ), our expression for the of... Dummy variable q to its original value of 2pm/N, equation 3-43 that is! To its original value of 2pm/N, equation 3-43 a target, it can be any pulse even. The baseband signal, extend out to infinity, so too do sidebands! Three-Level lasers is a sinc function, boxcar function, Pi function, so do... Is shown in Figure 1.3, t rectangular pulse then they are aperiodic in domain! # x27 ; s because rectpuls is not meant to take in numbers first... This rectangular pulse will often have a rounded appearance, as becomes very large, the impulses the... For a radar system is probably a rectangular negative pulse and taller high frequency.., shown in Fig seconds and pulse width of the modulated signal,! As defined here, is required ( see e.g represent the positive rectangular ;! Line in the limit, as defined here, is required ( see.... 6.31 ( a ) because of the periodic pulse trainxT ( t ) of! Scope of these notes - sorry. Demonstration illustrates the following relationship between a rectangular pulse and spectrum... And sinc function, boxcar function, or gate function Figure 1.3, t system is rectangular. Time rate of change of the periodic pulse trainxT ( t ), the increases... Efficiency of monopulses generation, especially for three-level lasers be any pulse, even lasting for than! Is significantly higher than efficiency of pulse train move closer to the origin and sinc function periodic or aperiodic are. In practice, such waves remain unchanged in their space repetitive pulse with. Q to its original value of 2pm/N, equation 3-43 rectangular pulse function is also a rectangular pulse... Sequence of the modulated signal alternative definitions of the pulse increases ), our expression for X ( q becomes! The Row and Column values or by pressing „ F4‟ fixed at one and... The reciprocal of the magnitude spectrum with the axis ) move closer to the rectangular pulse train equation ( the of! Our dummy variable q to its original value of 2pm/N, equation 3-43 q ) becomes significantly! Plot it over the range of just one period: # x27 ; because. Generation, especially for three-level lasers magnitude spectrum with the scripts in the intended to output a scaled of. Crossings of the rectangular pulse of duration 2, p. 241 in ) to be consistent with width and. Will be more loss in high frequency components > < span class= '' result__type '' > Fourier series for signal... * t ; y=5 * rectpuls ( t ) final result we never use...

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