A real time digital receiver for correlation measurements in atomic systems
V. Mugundhan, Maheswar Swar, Subhajit Bhar, Saptarishi Chaudhuri
AA real time digital receiver for correlation measurements inatomic systems
V. Mugundhan ∗ , Maheswar Swar † , Subhajit Bhar ‡ and Saptarishi Chaudhuri § Raman Research Institute,C.V. Raman Avenue, Sadashivanagar,Bangalore - 560080, India ∗ [email protected], † [email protected], ‡ [email protected], § [email protected] Abstract —We present the development and char-acterization of a generic, reconfigurable, low-cost ( <
350 USD) software-defined digital receiver system(DRS) for temporal correlation measurements inatomic spin ensembles. We demonstrate the useof the DRS as a component of a high resolutionmagnetometer. Digital receiver based fast Fouriertransform spectrometers (FFTS) are generally su-perior in performance in terms of signal-to-noiseratio (SNR) compared to traditional swept-frequencyspectrum analyzers (SFSA). In applications wherethe signals being analyzed are very narrow band infrequency domain, recording them at high speedsover a reduced bandwidth provides flexibility tostudy them for longer periods. We have built theDRS on the STEMLab 125-14 FPGA platform andit has two different modes of operation: FFT Spec-trometer and real time raw voltage recording mode.We evaluate its performance by using it in atomicspin noise spectroscopy (SNS). We demonstrate thatthe SNR is improved by more than one order ofmagnitude with the FFTS as compared to that ofthe commercial SFSA. We also highlight that withthis DRS operating in the triggered data acquisitionmode one can achieve spin noise (SN) signal withhigh SNR in a recording time window as low as 100msec. We make use of this feature to perform timeresolved high-resolution magnetometry. While thereceiver was initially developed for SNS experiments,it can be easily used for other atomic, molecular andoptical (AMO) physics experiments as well.
I. I
NTRODUCTION
Digital receivers are a class of electronic sys-tems where operations like amplification, filter-ing, integration etc. are performed as a series ofmathematical operation on embedded components like FPGAs, Microprocessors or GPUs. Comparedto their analog counterparts, digital receivers areimmune to variations in gain and temperature.However, digital systems have quantization noise,sampling rate and phase noise which can beminimized by choosing high bit-width ADCs andlow drift clock sources. These characteristics makedigital receivers an attractive option in applicationswhere precision measurements are required [1],[2]. AMO experiments are one such example.Digital receivers are being used in AMO ex-periments for process control [3] (e.g. tempera-ture, current and wavelength control in lasers),synchronous detection [4] and in compact mag-netic resonance spectroscopy systems [5]. How-ever, synchronous detection may not be feasiblein many AMO experiments including spin noisespectroscopy (SNS) [6]–[8]. The typical strengthof the raw SNS signal is < nV / √ Hz whichis far less compared to the previous studies[3]–[5]. Therefore, the SNS signal has to be recordedcontinuously (or on trigger) to improve the SNR.In this paper, we discuss the development andutilization of a versatile digital receiver to measurethe spin noise (SN) in atomic vapor systems.We have performed a comparative study withthe results of our previous work in [6]. We alsodemonstrate its utility in real-time precision mag-netometry. This digital receiver will be used as acomponent of a novel, miniaturized magnetometerbased on SNS techniques.The paper is organized as follows: We introducespin noise spectroscopy and the digital receiver1 a r X i v : . [ phy s i c s . i n s - d e t ] J a n system developed for its measurement in sectionII. The firmware architectures of the former isdescribed in section III. The methods adopted tomitigate the effects of electro-magnetic interfer-ence (EMI) in the measurements are describedin section IV. In section V, we present the SNSdata obtained by using our DRS as well as acomparison with the results obtained from SFSA.Further, we demonstrate triggered data acquisitionand time resolved magnetometry using our DRS.We conclude in section VI after a brief discussionon further applications and future scope of thedeveloped receiver.II. D IGITAL R ECEIVERS FOR S PIN NOISESPECTROSCOPY
In this section, we describe the spin noise spec-troscopy technique as well as detection schemesby introducing our digital receiver.
A. Spectroscopy Technique
Study of SN of an atomic ensemble has variedapplications, ranging from precision magnetome-try, non-perturbative optical detection to metrol-ogy and quantum sensing. The fluctuation in thespin population of an atomic system in time leadsto temporal changes in the refractive index ofthe medium. A linearly polarized and far detunedprobe laser beam can detect this temporal varia-tions of the refractive index in its polarization an-gle. We use a polarimetric detection system wherethe polarization fluctuation of the probe laser beamis detected in a balanced photodetector [9]. Thepower spectrum of the polarization fluctuation(second order correlation function - g (2) ) gives theinformation about the spectral properties of theatomic spin ensemble. In a typical experimentalconditions we apply a uniform magnetic fieldperpendicular to the propagation direction of theprobe beam. The atomic spins precess around themagnetic field with a Larmor frequency which isproportional to the strength of the magnetic field.Therefore, the peak of the spectrum appears at theLarmor frequency. Also, the width of the signalis inversely proportional to the transverse spinrelaxation time ( ∼
100 kHz in our experimentalconditions).Our SNS experimental set-up is shown in Fig.1.A probe laser beam which is detuned by ≈
10 GHz from the strongest optical transition in neutralrubidium (Rb) atoms, is used to probe the spinfluctuations of the atoms in the vapor cell heatedto temperatures ranging between 350 K and 400K. The spin fluctuations causes polarization fluc-tuations of the probe laser. The polarimetric detec-tion scheme employing a half wave plate (HWP),polarizing beam splitter (PBS), and a balancedphoto-detector (BPD) is capable of measuring thispolarization fluctuation. A uniform magnetic field( B ⊥ ), produced using a pair of magnetic coils inHelmholtz configuration, is applied on the atomicvapor which is perpendicular to the propagationdirection of the probe laser beam. The outputsignal of the BPD is recorded using the digitalreceiver described in this article and reported insection V.Previously we used a commercially availableSFSA to detect the SN signal from the bal-anced photo-detector. It has a superheterodynestage whose mixer provided a swept local oscil-lator (LO) signal, such that the radio-frequency(RF) signal is translated to a fixed intermediatefrequency (IF). Since the LO has to be sweptacross a range of frequencies, the sweep timeincreases with frequency span. This reduces thedwell time at each frequency resulting in a de-creased sensitivity. From the experimental pointof view, this leads to poor SNR. Moreover, if thesignal is expected to show variations smaller thanthe sweep-time, it cannot be detected. SFSAs alsohave a low frequency cut-off (in our case 100 kHz)below which the output amplitude and frequencymeasurements are not possible. We have ongoingexperiment to perform SNS on laser cooled atomsto investigate spin dynamics in quantum regime,where a triggered data recording of a SN signalover a short duration ( ∼ few ms) is required. Inthis case a SFSA can not be used.There have been recent experiments reportingmeasurements of SNS in quantum dots [10] aswell as in atomic vapors [11], where the useof non-reconfigurable and somewhat expensivedigital receivers are reported. However, the digitalreceiver described in this paper, allows us to over-come the aforementioned limitations of SFSA,with certain trade-offs. Fig. 1: A typical spin noise spectroscopy (SNS) set-up of rubidium (Rb) atomic vapor. L- plano-convexlens, VC- vapor cell (contains Rb atomic vapor), M- dielectric mirror, HWP- half wave plate, PBS-polarizing beam-splitter, BPD- balanced photodetector, B ⊥ - orthogonal magnetic field. B. Digital Receivers for SNS
We developed a digital receiver capable of op-erating in two modes, as listed below.I A fast Fourier transform spectrometer (FFTS)to probe the entire frequency range of inter-est,II A real time data recorder (RTDR) with trig-ger capabilities.Both the aforementioned modes are imple-mented on the STEMLab 125-14 developmentboard. This board is selected for our applicationbecause it has two 14 bit analog-to-digital con-verter (ADC) channels, with each channel pro-viding a dynamic range better than 80 dB. Ithas an analog bandwidth of 62.5 MHz, and isDC coupled. The heart of the board is a XilinxZynq 7010 System on Chip (SoC), with inte-grated programmable logic (PL) cells and ARMmicroprocessor based processing system (PS). Thesignal processing algorithms in this work are im-plemented on the PL side, while user control anddata transmission programs are implemented onthe PS side.III. F IRMWARE D ESCRIPTION
In this section, we describe the firmware archi-tecture of the two operational modes of the DRS. A. Fast Fourier Transform Spectrometers (FFTS)
Fourier transform is used to find the spectralcontent of a time domain signal [12]. Fast Fouriertransform (FFT) is an algorithm which reducesthe complexity involved in calculating the Fouriertransform from a O ( n ) to O ( n log n ) problem byusing the periodicity and the symmetry propertiesof the former [13], [14]. This in general reducesthe number of operations required to obtain thespectrum and results in resource savings whenimplemented in embedded devices e.g. FPGA orin Microprocessors.The SNR is proportional to √ βτ , where β is thebandwidth, and τ is the integration time [15]. For aconventional spectrum analyzer, there are two timescales involved: t s , the sweep time, and t d , thedead time. So, if a sweep contains N s points, theamount of time required for obtaining the powerat each frequency becomes t s /N s . In cases wherethe data is to be acquired using interfaces suchas GPIB, USB, or ethernet, t d includes the timetaken for the spectrum analyzer to transfer the datato the DAQ system, during which time no newacquisition can occur.In case of an FFTS, the estimation of thepower spectrum involves complex weighting andsummation of all time domain samples of theburst used to perform the FFT. If a streamingalgorithm is used, data acquisition, performing Fig. 2: Top level block diagram of the FFTS. PS and related interfaces are shown as green blocks. Thered dashed lines indicate the flow of the master clock at 125 MHz, which is derived from the ADCdata clock. The data and clock inputs from the ADC to the FPGA are Low Voltage ComplementaryMetal Oxide Semiconductor (LVCMOS) signals.FFT and data transfer can happen simultaneouslyresulting in zero dead time. Thus for a singlespectrum, with the same spectral resolution, anFFTS ideally provides √ N s improvement in theSNR as compared to SFSA[16].The base firmware version of the Stem-Lab 125-14 provides a burst mode version of the FFTS.However, we required capability to perform thisoperation in streaming mode, and average thespectra on the FPGA itself. This allows us to keepdata rates below 30 MBps, beyond which loss-lessdata transfer via ethernet becomes difficult, due tobottlenecks in communication between the PL andthe PS sides of the SoC. The block diagram of ourFFTS implementation is shown in Fig.2.The analog signal is sampled by the on-boardADC at 125 MHz. The digitized data is capturedsynchronously on the FPGA, converted to 2’scomplement format and passed on to the spec-trometer block.The spectrometer block is implemented usingSimulink System Generator. The signed data ob-tained so far is polyphase filtered using an 8 tap FIR filter[17]. The output of the filterbank is an18 bit fixed-point number, with a binary point atthe 17th bit. This is input to the biplex FFT blockIP core [18], available from the CASPER signalprocessing library [19], [20]. A 4096 points FFTis performed resulting in a spectral resolution of ≈ dv signal isasserted high and the power spectrum is presentedto the subsequent blocks for transmission to theDAQ. For example, if 1000 such spectra aresummed, the resulting integration time is ≈ AXISBRAM WRITER
IP block [21]. Once the spectrumis written into the BRAM, a finished signal
TABLE I: The different options available in the RTDR firmware.
Option Description baseband Records signal in dc - 625 kHz base-band; LO is disabledIF Records signal in an IF band spanning from f lo to f lo + 625 kHztriggered Records a signal burst for a programmable predefined time on rising edge of trigger pulsecontinuous Records data continuously indicating this is asserted and posted to the sts register.The FPGA present on-board provides accessonly to the PS Ethernet, therefore the transfer ofdata to the DAQ is mediated by executing a Ccode on the PS. The sts , cfg and AXI BRAMREADER provide memory mapped access to thePL. cfg register is used to provide a master resetand configuration information to the PL. sts reg-ister provides information on the BRAM addresspointer and holds the state of the finished signal. On the assertion of the finished signal,the PS starts reading the contents of the BRAM.The BRAM data is packetized as
UDP packetswith packet and spectrum count information andis transmitted to the DAQ using linux socketfunctions.We characterize the developed spectrometer us-ing continuous wave (CW) and SN signals. For theCW tests, signals at different frequencies and dif-ferent powers are fed to the system and recorded.These tests are carried out to estimate the SNRof the spectrometer at different frequencies and toidentify the linear regime. The power measured bythe FFTS is found to linearly vary with the inputpower.
B. Real Time Data Recorder (RTDR)
The FFTS discussed thus far, provides a simpleand compact measurement option for SNS. Inscenarios where the SN signal is short lived intime, a real time triggered data acquisition andprocessing protocol is required.We developed a low bandwidth, raw voltagerecorder. In Fig.3, we show a top-level blockdescription of the same. Table I outlines the vari-ous options available in the data recorder. Here,we use both the input channels, where one isfrom the BPD and the other is a signal genera-tor (BK PRECISION Model no. 4040B), whichis used as the local oscillator (LO). As in the FFTS firmware, the signals from the ADC areconverted to 2’s complement and multiplied toobtain an intermediate frequency (IF) signal. TheIF signal is usually close to dc and tracking thevariations in the former using the master clockoperating at 125 MHz would result in sub-optimalusage of resources. Hence, we use a cascadedintegrated comb (CIC) filter for down-samplingthe signal[22], [23]. When the factor by whichthe signal has to be down-sampled is large, CICfilters, used as a front end for FIR filters result indecreased number of filter taps required for anti-aliasing.The response of the CIC filter is not uniformwithin the band of interest. To compensate forthis, a FIR filter with a complementary responseis cascaded to it. The FIR filter is implemented asa half-band filter, resulting in an output data ratethat is half of that of the input. A 256 tap Kaiserwindow, with β = 10 , is used to shape the filterpass band. When both the filters are cascaded, theresulting combination has an uniform amplituderesponse over the band of operation and an out ofband rejection ≥
90 dB.The data from the multiplier as it enters theCIC filter is at 125 MSPS. This is decimated by50, resulting in a data rate of 2.5 MSPS at theoutput of the CIC filter and an aggregate data rateof 1.25 MSPS after the FIR filter, resulting in abase-band data of 625 kHz.We use four counters in the firmware for time-keeping purposes: a trigger counter (TC), a freerunning counter (FRC) at 125 MHz rate, a over-flow counter (OC) and a packet counter (PC). TheTC keeps track of the triggers received by theRTDR, while the FRC keeps track of the timesince the power on. The 32 bit OC counts thenumber of FRC overflows. These counters allowus to obtain the time between two trigger eventsand also its occurance instances since the start ofacquisition. The PC helps us to ensure no data wasmissed during packet framing and transmission.
Fig. 3: Firmware description of the triggered raw voltage recorder. The dotted blue lines represent theflow of control signals and status signals to and from the memory mapped AXI registers. The greenblocks represent signal processing elements of the design.The data, along with the counter values, iswritten to a BRAM and read out by the PS andtransmitted using ethernet.CW signals at various frequencies within the 0-62.5 MHz band were injected at different powerlevels from -90 to 10 dBm. As shown in Fig.4, theoutput power scales linearly with the input power,irrespective of the frequency.IV. E
LECTROMAGNETIC I NTERFERENCE (EMI)
AND ITS MITIGATION
The ambient EMI can hinder the detection ofweak signals. Some common sources of unavoid-able EMI are 50/60 Hz AC lines, switching regula-tors and LO harmonics. Strong EMI affects the dy-namic range of the receiver system at frequencies < ≈ σ threshold. -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10-100-80-60-40-20020 O u t pu t P o w er ( d B m )
100 kHz100 kHz fit500 kHz500 kHz fit1 MHz1 MHz fit10 MHz10 MHz fit30 MHz30 MHz fit60 MHz60 MHz fit -90 -80 -70 -60 -50 -40 -30 -20 -10 0 10
Input Power (dBm) -50510 R e s i du a l s ( d B ) Fig. 4: Characterization of the DRS (in both RTDR and FFTS modes) with signals of various power fedacross the frequency range of operation. The ’+’ markers indicate the data and the solid lines representthe first order polynomial fits. The bottom plot shows the residuals. The black dashed lines encompassthe linear range of the DRS.
Frequency (MHz) -120-100-80-60-40 C h a nn e l P o w er ( d B m ) Fig. 5: The effect of EMI on the measured spec-trum (green trace) and after its mitigation (bluetrace). The effect of EMI mitigation is clearly vis-ible through the absence of spikes and a reductionin the noise floor by ≈
20 dB in the blue trace.V. R
ESULTS AND D ISCUSSION
Our experimental set-up is shown schematicallyin Fig.1. A uniform transverse magnetic field ( B ⊥ )was produced by the current flowing through a pairof magnetic coils in Helmholtz configuration. Thesignal from the BPD was recorded either withour digital receiver system (DRS) or a commercial The BPD used was a Newport 1807 model having a cut-offfrequency of ≈
80 MHz. spectrum analyzer (SFSA) for the purpose ofperformance comparison.In Fig.6, we show the SN spectrum of Rbatomic vapor with B ⊥ ≈ ≈ ≈ Rb and Rb, respectively. The RBW of theSFSA was the same as the channel width of theFFTS which is 30 kHz. The integration time forthe SFSA to obtain the data presented in Fig.6(top panel) was 45 seconds whereas the same forthe FFTS presented in Fig.6 (bottom panel) was10 seconds. In both the cases the spectrum wasbackground subtracted and normalized to it’s peakvalue. The SNR of the SN signal is defined asthe ratio of the strength of the strongest signalto the rms value of the background signal. Thebackground signal is obtained by recording theSN signal at zero magnetic field. Comparing thesetwo spectra, we note that the SNR for the DRS ismore than an order of magnitude better than thatfor the SFSA for the same integration time. Thisimprovement in the SNR along with the fact thatour DRS is light weight, portable, low-cost, low-power ( <
10 Watts) as compared to a commercialSFSA, makes it preferable for both laboratory andfield measurements.
Frequency (MHz) N o r m a li ze d P o w er SNR sa ~ 8.35t int ~ 45 sSNR ffts ~ 50.25t int ~ 10 s Fig. 6: Spin noise (SN) spectrum acquired fromSFSA (top panel) and FFTS (bottom panel). Notethat the SNR is ≈
50 for the FFTS for an integra-tion time 5x lower than SFSA. These two spectrawere recorded under the same experimental con-ditions, at B ⊥ ≈ . G.Since the SN spectrum peak position is theLarmour frequency ν L (= g F µ B B ⊥ /h , where g F is the g-factor of the hyperfine levels, µ B is theBohr magneton, and h is the Plank’s constant ) ,by precisely measuring the peak position of thespectrum we can estimate the strength of B ⊥ .Therefore, this measurement technique can beused as a precision magnetometry tool. Sincethe developed DRS described in this article iseasily field deployable, we would highlight theapplicability of this device to construct a robustminiaturized magnetometer. As an example, theSN spectrum recorded at various magnetic fieldstrengths are shown Fig.7. By fitting a Lorentzianto the individual spectrum, we can estimate theLarmour frequency and in turn the magnetic field.Another advantage of using this DRS is that thedevice is reconfigurable which enables triggeredreal time measurements of the SN spectra. InFig.8, we show an example of real time dataacquisition. In each of the four panels we showSN spectrum obtained using our DRS with anintegration time of as low as 100 ms after the TTLtrigger pulse. The magnetic field strength was alsochanged after each trigger pulse. Hence, we cansample the magnetic field with a time resolutionof 100 msec. The integration time of the datashown in Fig.8 was 100 ms and the correspondingspectral resolution was ≈
610 Hz resulting in an
Frequency (MHz) -0.500.51 R e l a t i v e Sp i n N o i s e P o w er ( d B ) Fig. 7: Background subtracted spin noise (SN)spectra measured for different magnetic field val-ues. The error in the measurements are ≈ ≈ ≈
5. Whereas for the data shown in Fig.7 theintegration time was 1 s and the spectral resolutionwas 30 kHz, hence an SNR ≈ ≈
100 ms. The trigger rate was ≈
10 per minute.The output from the BPD was fed to the DRS.The triggered acquisition works as follows: (a)The FPGA waits for a rising edge on the triggerinput port, (b) On the rising edge of the triggerinput, a dv signal is asserted, upon which theBRAM starts to store the data, (c) Once 256 suchsamples are written, the data is packetized andtransferred to the DAQ server. The trigger countand an absolute time stamp is included in theheader data of the Ethernet packet for assistingin data analysis.Another application of using our device is thetemporal and spatial correlation measurements ina system with laser cooled atoms and ions. In-trinsically the correlation signals are expected tobe extremely narrow in frequency domain and arepromising candidates for various quantum tech-nology applications. However, the measurementduration is typically limited to few milliseconds. Frequency (MHz) R e l a t i v e Sp i n N o i s e P o w er ( d B ) Fig. 8: Spin noise (SN) spectrum at various mag-netic field strengths from the RTDR. These seriesof spectra has an SNR ≈
5, and the peak positionscan be determined within an accuracy of ≈ % .Therefore, it is difficult to perform the SNS incold atoms using traditional SFSA and our DRSemerges as a promising candidate for this purpose.In fact, we have already started using the DRS de-scribed in this article in cold atom measurements.Also, since in the RTDR configuration, the DRSrecords the voltage samples directly, it gives us theflexibility to achieve high frequency resolutions,which is only limited by the timing jitter of theon-board clock.Our DRS in the RTDR mode, allows for aminimum time resolution of 800 ns when the datais treated in its raw form. When spectral analysisis carried out with a N point fourier transform, thechannel width and the time resolution is . MHzN and ns × N , respectively. Therefore, whenthe signal is inherently strong, higher time res-olutions can be obtained at the cost of reducedfrequency resolution. However, for intrinsic SNsignal from atomic vapor presented in this article,the SNR deteriorates for shorter integration timeswhich affects the precision of the measurements.Therefore, for the purpose of demonstration, weintegrate the SN signal for 100 ms time windowand obtain a precision in measured magnetic fieldof the order of 800 µ G.To demonstrate the response of the detectionsystem to fast varying magnetic fields, we con-ducted an experiment [26], where we added acoherent drive [27] using a pair of Raman beams, which enhanced the SN signal strength millionfold, improving the SNR. We then varied themagnetic field from 3.35 G to 3.85 G, syn-chronously with the coherent drive field frequency,and recorded the signal using our DRS. The resultsfrom this experiment is shown in Fig. 9, whereeach pixel along time and frequency axis is ≈ µs and 610 Hz, respectively. We see that the DRSsimultaneously tracks the “step” changes in themagnetic field, as well as its drifts in milli-secondtimescales.We highlight that a time resolved measurementof magnetic field has applications ranging fromgeophysics [28] to physiology[29], [30]. The timestamp contained in the received data (see SectionIII B), can be used to determine the absolute timevariation of the magnetic field strength.VI. C ONCLUSIONS
We presented the development of a softwaredefined digital receiver system (DRS) with two op-erating modes for spin noise spectroscopy (SNS)experiments. The highlight of this work is that weshow the applicability of SNS in precision mag-netometry and measure fast temporal variationsin the magnetic field. This receiver is fully re-configurable and had a short development time ata low cost.The FFTS mode allows for user programmableintegration times. The RTDR mode was specif-ically developed for high spectral and temporalresolution studies of spin noise (SN) signals fromboth hot and cold atoms. Such a mode, where hightime resolution voltage data can be recorded, doesnot exist in SFSA. The FFTS can also be used tosupplement the RTDR mode as follows: using theFFTS, the user will be able to explore the spectrumover a wide range of frequencies and once the peaklocation is known, the RTDR can be used to obtaina time-frequency resolved picture of the signal ofinterest.Future directions for the system developmentinclude using a DDS core which can internallygenerate the LO signals to facilitate a two channelimplementation, replace the DAQ computer with aARM based microprocessor system viz. RaspberryPi for system miniaturization.The receiver described here was developed to bea part of a compact, portable SNS magnetometer.
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14
Time (s) F re qu e n c y O ff s e t f r o m L O ( k H z ) M ag n e t i c F i e l d ( G ) R e l a t i v e Sp i n N o i s e P o w er ( d B ) Fig. 9: Waterfall plot of the DRS output when the magnetic field was swept from ∼ CKNOWLEDGMENTS
The authors acknowledge partial support pro-vided by Ministry of Electronics and InformationTechnology (MeitY), Govt. of India under grantfor “Center for Excellence in Quantum Technol-ogy” with Ref. No. 4(7)/2020-ITEA. Authors alsoacknowledge Department of Science and Technol-ogy (DST), Govt. of India, Prof. Hema Ramachan-dran, Prof. Dibyendu Roy, Electronics Engineer-ing Group (EEG) and central workshop facility,Raman Research Institute. We extend our thanksto the CASPER signal processing community andDr. Pavel Demin for maintaining many usefulopen-source IP cores. We are grateful to Xilinxfor donation of Vivado Design Suite, through theirUniversity Program. R
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