Tukey Window Research Articles

Improvement of Fresnel Diffraction Convolution Algorithm

With the development of digital holography, the accuracy requirements for the reconstruction phase are becoming increasingly high. The transfer function of the double fast transform (D-FFT) algorithm is distorted when the diffraction distance is larger than the criterion distance dt, which reduces the accuracy of solving the phase. In this paper, the Fresnel diffraction integration algorithm is improved by using the low-pass Tukey window to obtain more accurate reconstructed phases. The improved algorithm is called the D-FFT (Tukey) algorithm. The D-FFT (Tukey) algorithm adjusts the degree of edge smoothing of the Tukey window, using the peak signal-to-noise ratio (PSNR) and the structural similarity (SSIM) to remove the ringing effect and obtain a more accurate reconstructed phase. In a simulation of USAF1951, the longitudinal resolution of the reconstructed phase obtained by D-FFT (Tukey) reached 1.5 μm, which was lower than the 3 μm obtained by the T-FFT algorithm. The results of Fresnel holography experiments on lung cancer cell slices also demonstrated that the phase quality obtained by the D-FFT (Tukey) algorithm was superior to that of the T-FFT algorithm. D-FFT (Tukey) algorithm has potential applications in phase correction, structured illumination digital holographic microscopy, and microscopic digital holography.

Analysis of Filtered Multicarrier Modulation Techniques Using Different Windows for 5G and Beyond Wireless Systems

In contemporary wireless communication systems, multicarrier modulation schemes have become widely adopted over single-carrier techniques due to their improved capacity to address challenges posed by multipath fading channels, leading to enhanced spectral efficiency. Orthogonal frequency division multiplexing (OFDM), a prevalent multicarrier scheme in 4G, is favored for its ease of implementation, interference resilience, and high data rate provision. But it falls short of meeting the requirements for 5G and beyond due to limitations such as out-of-band (OOB) emissions and cyclic prefixes. This paper introduces the filter bank multicarrier (FBMC) and universal filtered multicarrier (UFMC) with quadrature amplitude modulation (QAM) and phase shift keying (PSK) waveforms through Additive White Gaussian Noise channel (AWGN), Rayleigh fading channel and Rician channel. The objective of this paper is to enhance the performance of UFMC with reduced complexity through the new filtering approach for achieving optimal outcomes. The proposed scheme, incorporating Tukey filtering technique, demonstrates superior performance in reducing peak-to-average power ratio (PAPR) and improving bit error ratio (BER) compared to the original UFMC signal without necessitating additional power increments. Specifically, the UFMC system with Tukey filtering achieves a notable net gain of 5 dB. Simulation results demonstrate that utilizing various filter types in FBMC and UFMC systems, combined with QAM modulation, significantly reduces OOB emissions compared to conventional systems. In aspect to BER, Tukey window showed almost 10−6 at 15 dB SNR in UFMC which is better than FBMC.

Balancing ensemble averaging and signal stationarity when processing acoustic data recorded during a rocket launch

There are many important details to consider when collecting acoustical data during a rocket launch including system noise floor, dynamic range and transducer sensitivity. In this talk, the choice of signal processing parameters will also be shown to be important. Since the pressures are created by turbulence, ensemble averaging is key to reducing random variation. As such, the use of a Hanning window with 50% overlap would be customary for performing this type of processing. However, as the rocket lifts off, the source location moves, and the data can only be considered stationary for short blocks of time. Therefore, the ability to average is limited by non-stationarity. To balance these competing phenomena, an adjustable windowing function such as the Tukey window may be more appropriate than Hanning. Noise data collected at two different launches will be used to compare of the Hanning window with 50% overlap to that using of the Tukey window with a taper of α = 0.25, which filters 12.5% of the signal at each extremity, with 87.5% overlap. The use of both window types will be compared when estimating auto spectral densities and integrated overall levels. The effect of blocksize will also be determined.

Frequency-dependent Q simulation and viscoacoustic reverse time migration based on the fractional Zener model

Seismic attenuation is a basic physical property of the earth, which significantly affects the characteristics of seismic wavefields. Accurately simulating wave propagation in the earth is essential to image subsurface structures. Some prevailing methods (e.g., the standard linear solid and fractional Laplacian equation) to describe seismic wave propagation in attenuating media are mainly based on the constant- Q model (CQM), which is valid at room temperature and pressure. However, laboratory measurements suggest that the quality factor Q is a function of frequencies in some regions. To simulate the frequency-dependent Q effect, we derive a viscoacoustic wave equation from the stress-strain relationship of the fractional Zener model (FZM) with variable fractional orders. During the implementation, we separate the real and imaginary parts of the modulus and introduce a low-rank decomposition method to solve the FZM equation. Because the amplitude dissipation and phase dispersion are decoupled, we establish a compensated reverse time migration ( Q-RTM) algorithm to mitigate adverse effects caused by seismic attenuation and improve the quality of seismic migration in frequency-dependent attenuating media. A two-layer model and the BP gas chimney model are used to perform Q-RTM tests. A low-pass filter with a Tukey window function is applied to suppress numerical instability during the compensation. Numerical results demonstrate that our FZM Q-RTM approach can produce high-resolution images with corrected reflector positions and amplitudes. Because the CQM equation ignores the frequency dependence of Q, it may lead to overcompensation in Q-RTM.

A study of different tapering windowing functions and referencing curve for the improvement of sound field using wave-field synthesis

Wavefield synthesis is a well-known sound field reproduction technique. The correct synthesis of the desired sound field ideally requires a continuous source distribution over an enclosed surface. Due to practical limitations, a finite length of secondary source array is used. This results in distortion in the reproduced sound field due to the diffraction effect from the edge loudspeakers. To alleviate this problem, tapering window functions are utilized. In this paper, the influence of various windowing functions on the reproduced fields for different secondary source geometry and virtual source type is studied, and different parameters are used to make a quantitative comparison between the performance of different windowing functions. Further, the effect of the different referencing curves for the synthesis of correct amplitude is also presented. From the simulation results, it was found that the Tukey window function provides a wider sweet spot area with a minimal amplitude ringing effect. The selection of a proper referencing curve depends on the array geometry and the type of virtual source.

Appropriate Window Function and Window Length in Multifrequency Velocity Estimator for Rapid Motion and Locality of Layered Myocardium.

The heart wall has a multilayered structure and moves rapidly during ejection and rapid filling periods. Local strain rate (SR) measurements of each myocardial layer can contribute to accurate and sensitive evaluations of myocardial function. However, ultrasound-based velocity estimators using a single-frequency phase difference cannot realize these measurements owing to insufficient maximum detectable velocity, which is limited by a quadrature frequency. We previously proposed a velocity estimator using multifrequency phase differences to improve the maximum detectable velocity. However, the improvement is affected by a spatial discrete Fourier transform (DFT) window length that represents the locality of the velocity estimation. In this article, we theoretically describe that shortening the window increases the interference between different frequency components and decreases the maximum detectable velocity. The tradeoff between the maximum detectable velocity and the window length was confirmed through simulations and a water-tank experiment. Under the tradeoff, the Hanning window, which was used in previous studies, is not always appropriate for the local measurement of the velocity, which sometimes exceeds 100 mm [Formula: see text] depending on the subject, direction of the ultrasound beam to the heart wall, and cardiac periods. In the in vivo measurement with the short window, the Tukey window with a large flat part that has a high-frequency resolution and ameliorates the discontinuity at both edges of the windowed signal was appropriate to measure the maximum velocity. This study offers the potential for local measurements of each myocardial layer using the multifrequency velocity estimator with the appropriate window function and window length.

Performance of Oversampled Polyphase Filterbank Inversion via Fourier Transform: Continuous Signals

Signal channelization enables efficient frequency domain processing and is a mainstay of astronomical signal processing, but applications that require high time resolution necessitate reconstruction of the original wide band signal. In a previous paper, a near-perfect method of reconstructing a time-limited input signal from the output of an oversampled polyphase filterbank (PFB) was described. Here, we consider the case where continuous signals are processed. We show that the most simplistic approach, which utilizes non-overlapping windows and a fast Fourier transform (FFT) channelizer, introduces large errors whose magnitude can equal the signal. The ringing introduced by truncation at the end of a block, combined with the cyclic nature of FFTs, leads to errors that are concentrated at block boundaries. These localized errors can be heavily suppressed by utilizing overlapping windows and nearly completely eliminated by apodizing the data blocks with a Tukey window. After these improvements, the much smaller residual error is concentrated at the PFB channel boundaries and is due to adjacent channels having different gain slopes at the channel boundary. Increasing the channel passband equalizes the gain slope at the channel boundary, and the error is reduced further. With these changes, errors as low as −100[Formula: see text]dB are achieved, and the method of reconstructing the channelized data meets the stringent signal purity requirement for astronomical applications such as radio pulsar timing.

Preserving Wideband Tympanometry Information With Artifact Mitigation.

Absorbance measured using wideband tympanometry (WBT) has been shown to be sensitive to changes in middle and inner ear mechanics, with potential to diagnose various mechanical ear pathologies. However, artifacts in absorbance due to measurement noise can obscure information related to pathologies and increase intermeasurement variability. Published reports frequently present absorbance that has undergone smoothing to minimize artifact; however, smoothing changes the true absorbance and can destroy important narrow-band characteristics such as peaks and notches at different frequencies. Because these characteristics can be unique to specific pathologies, preserving them is important for diagnostic purposes. Here, we identify the cause of artifacts in absorbance and develop a technique to mitigate artifacts while preserving the underlying WBT information. A newly developed Research Platform for the Interacoustics Titan device allowed us to study raw microphone recordings and corresponding absorbances obtained by WBT measurements. We investigated WBT measurements from normal hearing ears and ears with middle and inner ear pathologies for the presence of artifact and noise. Furthermore, it was used to develop an artifact mitigation procedure and to evaluate its effectiveness in mitigating artifacts without distorting the true WBT information. We observed various types of noise that can plague WBT measurements and that contribute to artifacts in computed absorbances, particularly intermittent low-frequency noise. We developed an artifact mitigation procedure that incorporates a high-pass filter and a Tukey window. This artifact mitigation resolved the artifacts from low-frequency noise while preserving characteristics in absorbance in both normal hearing ears and ears with pathology. Furthermore, the artifact mitigation reduced intermeasurement variability. Unlike smoothing algorithms used in the past, our artifact mitigation specifically removes artifacts caused by noise. It does not change frequency response characteristics, such as narrow-band peaks and notches in absorbance at different frequencies that can be important for diagnosis. Also, by reducing intermeasurement variability, the artifact mitigation can improve the test-retest reliability of these measurements.

Design, comparison and analysis of low pass FIR filter using window techniques method

In digital communication, a filter is any device that selectively attenuates any unwanted component from a received signal. It essentially changes or reshapes the waveform of a signal in the desired manner. In this work, we have designed and studied low pass filter using Rectangular, Bartlett, Hamming, Hanning, Tukey and Kaiser Window algorithms and compared them with each other for further analysis. The parameters we used for designing the filter are sampling frequency, cut off frequency, filter order and a variable parameter, α. MATLAB toolbox for DSP, namely FDA Tool and FV Tool were employed for the realization of the design.

Extracting impedance changes from a frequency multiplexed signal during neural activity in sciatic nerve of rat: preliminary study in vitro

Objective: To establish suitable frequency spacing and demodulation steps to use when extracting impedance changes from frequency division multiplexed (FDM) carrier signals in peripheral nerve. Approach: Experiments were performed in vitro on cadavers immediately following euthanasia. Neural activity was evoked via stimulation of nerves in the hind paw, while carrier signals were injected, and recordings obtained, with a dual ring nerve cuff implanted on the sciatic nerve. Frequency analysis of recorded compound action potentials (CAPs) and extracted impedance changes, with the latter obtained using established demodulation methods, were used to determine suitable frequency spacing of carrier signals, and bandpass filter (BPF) bandwidth and order, for a frequency multiplexed signal. Main results: CAPs and impedance changes were dominant in the frequency band 200 to 500 Hz and 100 to 200 Hz, respectively. A Tukey window was introduced to remove ringing from Gibbs phenomena. A ±750 Hz BPF bandwidth was selected to encompass 99.99% of the frequency power of the impedance change. Modelling predicted a minimum BPF order of 16 for 2 kHz spacing, and 10 for 4 kHz spacing, were required to avoid ringing from the neighbouring carrier signal, while FDM experiments verified BPF orders of 12 and 8, respectively, were required. With a notch filter centred on the neighbouring signal, a BPF order of at least 6 or 4 was required for 2 and 4 kHz, respectively. Significance: The results establish drive frequency spacing and demodulation settings for use in FDM electrical impedance tomography (EIT) experiments, as well as a method for their selection, and, for the first time, demonstrates the viability of FDM-EIT of neural activity on peripheral nerve, which will be a central aspect of future real-time neural-EIT systems and EIT-based neural prosthetics interfaces.

Multi Line Transmit Beamforming Combined With Adaptive Apodization.

Increased frame rate is of high importance to cardiac diagnostic imaging as it enables examination of fast events during the cardiac cycle and improved quantitative analysis, such as speckle tracking. Multi-line transmission (MLT) is one of the methods proposed for this purpose. In contrast to the single-line transmission (SLT), where one focused beam is sent in each direction, MLT beams are simultaneously transmitted and focused in several (2,4,6..) directions improving the framerate accordingly. The simultaneous transmission is known to cause cross-talk artifacts due to the interference between the main-lobes and the side-lobes of the transmitted and received beams. Usually, the artifacts are attenuated using a Tukey window apodization, but the lateral resolution is degraded. Several other methods, such as minimum variance beamforming and filtered delay multiply and sum beamforming were proposed to deal with these artifacts.The assumption examined in this study is that a receive apodization can be chosen adaptively from a number of apodization windows in order to provide better artifact rejection and to increase the spatial resolution. The entire study was performed on experimental MLT dataset including wire and tissue mimicking phantoms, as well as in vivo cardiac data. The results demonstrate that application of a predefined apodization bank outperforms Tukey windowing alone, in terms of both resolution and receive crosstalk artifact rejection. Moreover, the achieved spatial resolution is superior to the non-apodized SLT, as measured from wire phantoms. The proposed method can also be combined with wider transmit beams, suitable for multi line acquisition.

H i anisotropies associated with radio-polarimetric filaments

LOFAR detected toward 3C 196 linear polarization structures which were found subsequently to be closely correlated with cold filamentary HI structures. The derived direction-dependent HI power spectra revealed marked anisotropies for narrow ranges in velocity, sharing the orientation of the magnetic field as expected for magneto hydrodynamical turbulence. Using the Galactic portion of the Effelsberg-Bonn HI Survey we continue our study of such anisotropies in the HI distribution in direction of two WSRT fields, Horologium and Auriga; both are well known for their prominent radio-polarimetric depolarization canals. At 349 MHz the observed pattern in total intensity is insignificant but polarized intensity and polarization angle show prominent ubiquitous structures with so far unknown origin. Apodizing the HI survey data by applying a rotational symmetric 50 percent Tukey window, we derive average and position angle dependent power spectra. We fit power laws and characterize anisotropies in the power distribution. We use a Gaussian analysis to determine relative abundances for the cold and warm neutral medium. For the analyzed radio-polarimetric targets significant anisotropies are detected in the HI power spectra; their position angles are aligned to the prominent depolarization canals, initially detected by WSRT. HI anisotropies are associated with steep power spectra. Steep power spectra, associated with cold gas, are detected also in other fields. Radio-polarimetric depolarization canals are associated with filamentary HI structures that belong to the cold neutral medium (CNM). Anisotropies in the CNM are in this case linked to a steepening of the power-spectrum spectral index, indicating that phase transitions in a turbulent medium occur on all scales. Filamentary HI structures, driven by thermal instabilities, and radio-polarimetric filaments are associated with each other.

Global field synchronization in gamma range of the sleep EEG tracks sleep depth: Artifact introduced by a rectangular analysis window

BackgroundInvestigating functional connectivity between brain networks has become an area of interest in neuroscience. Several methods for investigating connectivity have recently been developed, however, these techniques need to be applied with care. We demonstrate that global field synchronization (GFS), a global measure of phase alignment in the EEG as a function of frequency, must be applied considering signal processing principles in order to yield valid results. New methodMultichannel EEG (27 derivations) was analyzed for GFS based on the complex spectrum derived by the fast Fourier transform (FFT). We examined the effect of window functions on GFS, in particular of non-rectangular windows. ResultsApplying a rectangular window when calculating the FFT revealed high GFS values for high frequencies (>15Hz) that were highly correlated (r=0.9) with spectral power in the lower frequency range (0.75–4.5Hz) and tracked the depth of sleep. This turned out to be spurious synchronization. With a non-rectangular window (Tukey or Hanning window) these high frequency synchronization vanished. Both, GFS and power density spectra significantly differed for rectangular and non-rectangular windows. Comparison with existing method(s)Previous papers using GFS typically did not specify the applied window and may have used a rectangular window function. However, the demonstrated impact of the window function raises the question of the validity of some previous findings at higher frequencies. ConclusionsWe demonstrated that it is crucial to apply an appropriate window function for determining synchronization measures based on a spectral approach to avoid spurious synchronization in the beta/gamma range.

Anisotropies in the HI gas distribution toward 3C 196

The local Galactic HI gas was found to contain cold neutral medium (CNM) filaments that are aligned with polarized dust emission. These filaments appear to be dominated by the magnetic field and in this case turbulence is expected to show distinct anisotropies. We use the Galactic Effelsberg--Bonn HI Survey (EBHIS) to derive 2D turbulence spectra for the HI distribution in direction to 3C196 and two more comparison fields. Prior to Fourier transform we apply a rotational symmetric 50% Tukey window to apodize the data. We derive average as well as position angle dependent power spectra. Anisotropies in the power distribution are defined as the ratio of the spectral power in orthogonal directions. We find strong anisotropies. For a narrow range in position angle, in direction perpendicular to the filaments and the magnetic field, the spectral power is on average more than an order of magnitude larger than parallel. In the most extreme case the anisotropy reaches locally a factor of 130. Anisotropies increase on average with spatial frequency as predicted by Goldreich and Sridhar, at the same time the Kolmogorov spectral index remains almost unchanged. The strongest anisotropies are observable for a narrow range in velocity and decay with a power law index close to --8/3, almost identical to the average isotropic spectral index of $-2.9 < \gamma < -2.6$. HI filaments, associated with linear polarization structures in LOFAR observations in direction to 3C196, show turbulence spectra with marked anisotropies. Decaying anisotropies appear to indicate that we witness an ongoing shock passing the HI and affecting the observed Faraday depth.

Motor current signatures and their envelopes as tools for fault diagnosis

AbstractInduction motor inter-turn short circuit stator fault is identified using motor current signals with the help of Discrete Wavelet Transform along with Power Spectral Density. This methodology is adopted for motor current signals and their envelopes in order to identify a better tool for fault diagnosis. First, the analysis is performed using the original stator current signal, which has the fundamental frequency components along with the slip frequency and other harmonic/fault components. The fundamental component in the stator current can be eliminated by using the envelope of the signal. The transient in the wavelet decomposition can be suppressed by modifying the current envelope. This is done by pre-multiplying the original envelope with the Tukey window. The Power Spectral Density is calculated for both the signatures. Comparison of these two methods show that the proposed analysis based on modified envelope using Discrete Wavelet Transform along with Power Spectral Density offers better resu...

Ventricular Fibrillation Waveform Changes during Controlled Coronary Perfusion Using Extracorporeal Circulation in a Swine Model.

BackgroundSeveral characteristics of the ventricular fibrillation (VF) waveform have been found predictive of successful defibrillation and hypothesized to reflect the myocardial energy state. In an open-chest swine model of VF, we modeled “average CPR” using extracorporeal circulation (ECC) and assessed the time course of coronary blood flow, myocardial metabolism, and myocardial structure in relation to the amplitude spectral area (AMSA) of the VF waveform without artifacts related to chest compression.MethodsVF was induced and left untreated for 8 minutes in 16 swine. ECC was then started adjusting its flow to maintain a coronary perfusion pressure of 10 mmHg for 10 minutes. AMSA was calculated in the frequency domain and analyzed continuously with a 2.1 s timeframe and a Tukey window that moved ahead every 0.5 s.ResultsAMSA progressively declined during untreated VF. With ECC, AMSA increased from 7.0 ± 1.9 mV·Hz (at minute 8) to 12.8 ± 3.3 mV·Hz (at minute 14) (p < 0.05) without subsequent increase and showing a modest correlation with coronary blood flow of borderline statistical significance (r = 0.489, p = 0.0547). Myocardial energy measurements showed marked reduction in phosphocreatine and moderate reduction in ATP with increases in ADP, AMP, and adenosine along with myocardial lactate, all indicative of ischemia. Yet, ischemia did not resolve during ECC despite a coronary blood flow of ~ 30% of baseline.ConclusionAMSA increased upon return of coronary blood flow during ECC. However, the maximal level was reached after ~ 6 minutes without further change. The significance of the findings for determining the optimal timing for delivering an electrical shock during resuscitation from VF remains to be further explored.

Ultrasound Elasticity Imaging System with Chirp-Coded Excitation for Assessing Biomechanical Properties of Elasticity Phantom.

The biomechanical properties of soft tissues vary with pathological phenomenon. Ultrasound elasticity imaging is a noninvasive method used to analyze the local biomechanical properties of soft tissues in clinical diagnosis. However, the echo signal-to-noise ratio (eSNR) is diminished because of the attenuation of ultrasonic energy by soft tissues. Therefore, to improve the quality of elastography, the eSNR and depth of ultrasound penetration must be increased using chirp-coded excitation. Moreover, the low axial resolution of ultrasound images generated by a chirp-coded pulse must be increased using an appropriate compression filter. The main aim of this study is to develop an ultrasound elasticity imaging system with chirp-coded excitation using a Tukey window for assessing the biomechanical properties of soft tissues. In this study, we propose an ultrasound elasticity imaging system equipped with a 7.5-MHz single-element transducer and polymethylpentene compression plate to measure strains in soft tissues. Soft tissue strains were analyzed using cross correlation (CC) and absolution difference (AD) algorithms. The optimal parameters of CC and AD algorithms used for the ultrasound elasticity imaging system with chirp-coded excitation were determined by measuring the elastographic signal-to-noise ratio (SNRe) of a homogeneous phantom. Moreover, chirp-coded excitation and short pulse excitation were used to measure the elasticity properties of the phantom. The elastographic qualities of the tissue-mimicking phantom were assessed in terms of Young’s modulus and elastographic contrast-to-noise ratio (CNRe). The results show that the developed ultrasound elasticity imaging system with chirp-coded excitation modulated by a Tukey window can acquire accurate, high-quality elastography images.

Average dielectric property analysis of complex breast tissue with microwave transmission measurements.

Prior information about the average dielectric properties of breast tissue can be implemented in microwave breast imaging techniques to improve the results. Rapidly providing this information relies on acquiring a limited number of measurements and processing these measurement with efficient algorithms. Previously, systems were developed to measure the transmission of microwave signals through breast tissue, and simplifications were applied to estimate the average properties. These methods provided reasonable estimates, but they were sensitive to multipath. In this paper, a new technique to analyze the average properties of breast tissues while addressing multipath is presented. Three steps are used to process transmission measurements. First, the effects of multipath were removed. In cases where multipath is present, multiple peaks were observed in the time domain. A Tukey window was used to time-gate a single peak and, therefore, select a single path through the breast. Second, the antenna response was deconvolved from the transmission coefficient to isolate the response from the tissue in the breast interior. The antenna response was determined through simulations. Finally, the complex permittivity was estimated using an iterative approach. This technique was validated using simulated and physical homogeneous breast models and tested with results taken from a recent patient study.

SPICE model of memristive device using Tukey window function

This paper proposes a memristor SPICE model using the Tukey window (or tapered cosine window) function. Compared with the previously proposed models based on the boundary function, the proposed model is resistant to numerical errors. From the SPICE result of a relaxation oscillator, we observe that the proposed model can be effectively used to minimise the effect of round-off errors.

High-Precision D-Band FMCW-Radar Sensor Based on a Wideband SiGe-Transceiver MMIC

In this paper, a miniaturized D-band frequency-modulated continuous-wave (FMCW) radar sensor with 48-GHz bandwidth (32.8%, 122-170 GHz) and a high measurement rate of > 1 kHz for multi-target vibration measurements is presented. The sensor is based on a SiGe transceiver monolithic microwave integrated circuit manufactured via Infineon's B7HF200 bipolar production technology with an fT of 170 GHz and fmax of 250 GHz. Gilbert cell, push-pull, and varactor-based doubler concepts on manufactured chips are compared, and the most promising signal source is embedded into a transceiver chip, which forms the main component of the presented radar sensor. The maximum output power of the system is ≈ -10 dBm and a phase noise of ≈ -80 dBc/Hz is achieved. Measurements are provided to demonstrate the sensor characteristics and show the promising results of FMCW radar in highest precision distance and multi-target vibration measurement applications. Due to the covered wide bandwidth, a range resolution of 5.88 mm is achieved ( -6-dB width, Tukey window). The sensor's distance measurement repeatability is 290 nm (65 nm with 10 × averaging and 0.5-m target distance), and the distance measurement accuracy is m for a target in 65-cm distance moving 1 cm. Additionally, vibration measurement results and range-Doppler plots for advanced multi-target applications are presented.