Inverse Short-time Fourier Transform Research Articles

A sparse time-frequency reconstruction approach from the synchroextracting domain

Synchroextracting, including frequency-extracting and transient-extracting, offers a sparse time-frequency (TF) representation for multi-component signals. However, it is susceptible to amplitude modulation (AM) and frequency modulation (FM) when reconstructing the raw signal through the TF ridge. This paper proposes a new signal reconstruction approach (SRA) in the synchroextracting domain to address this limitation. This approach performs synchroextracting on the short-time Fourier transform (STFT) domain. We incorporate the extracting operator in the inverse STFT to establish the mathematical relationship between the synchroextracting representation and the retrieved signal, thus enabling the reconstruction of each mode in the synchroextracting domain. The proposed SRA is theoretically derived, and its reconstruction performance is evaluated in the frequency-extracting and transient-extracting domains. Two synthetic signals are utilized to demonstrate that compared with some advanced reconstruction methods, the SRA has a high reconstruction accuracy, strong noise robustness, and is less affected by AM-FM features and the window length. The application of the bat signal further clarifies the advantages of the SRA and its feasibility in practical applications. Moreover, this study also provides a new reconstruction framework and reference for other synchroextracting-type methods.

Mine Microseismic Signal Denoising Based on a Deep Convolutional Autoencoder

Mine microseismic signal denoising is a basic and crucial link in microseismic data processing, which influences the accuracy and reliability of the monitoring system, and is of great significance with regard to safety during mining. Therefore, this study introduces a deep learning method to improve the mapping function and sparsity of signals in the time-frequency domain and constructs a denoising framework based on a deep convolutional autoencoder to address the denoising problem of mine microseismic signals. First, all noisy microseismic signals are normalized to ensure the nonlinear expression ability of the constructed denoising framework. Then, the normalized signals are transformed into the time-frequency domain using the short-time Fourier transform (STFT), and the real and imaginary parts of time-frequency coefficients serve as the input of the deep convolutional autoencoder to output the masks of the effective and noise signals. Next, these masks are applied to the time-frequency coefficients of the noisy microseismic signals, and the time-frequency coefficients of the potentially effective and noise signals are estimated. Finally, inverse STFT is used to transform these time-frequency coefficients to the time domain to obtain the final denoised effective and noise signals. The constructed framework automatically learns rich features from synthetic data to separate the effective and noise signals, thereby achieving the purpose of fast and automatic denoising. The experimental results show that compared with the wavelet threshold and ensemble empirical mode decomposition, the denoising framework considerably improves the signal-to-noise ratio of mine microseismic signals with less waveform distortion. Moreover, it can achieve a better denoising effect efficiently even in the case of a low SNR, which has obvious advantages. The constructed denoising framework is suitable for microseismic monitoring signals of various mine dynamic disasters and provides strong technical support for intelligent monitoring and early warning concerning production risks in mines.

Blind extraction of acoustic signals from rolling bearing composite faults based on ISCA-IMCKD

In production practice, the signal gathered by a sensor often includes strong ambient noise, and its composition is complex. Focusing on the problem that traditional methods are difficult to separate and extract fault frequencies from strong background noise, a novel compound fault blind extraction method based on improved sparse component analysis (ISCA) and improved maximum correlation kurtosis deconvolution (IMCKD)-named ISCA‐IMCKD- is suggested. Initially, the signal that the sensor has collected is shifted into time-frequency area signal by short-time Fourier transform (STFT). In addition, the single source domain characteristic data is screened by improved single source point detection to determine the number of sources. Second, the ISCA method is optimized by using cosine distance improved fuzzy C-means clustering, which is utilized to further process the characteristic data to calculate the mixing matrix. Moreover, the estimated source signal is initially extracted according to the membership degree of clustering results. Finally, the estimated source signal is shifted into the time area by inverse STFT transform, and the IMCKD is employed to enhance the characteristics of the projected source signals. Meanwhile, the initially estimated source signal is completely separated, and the defect frequencies of the composite faults are finally extracted by envelope analysis. Simulation experiments and measured data are employed to certify the viability of the proposed means. The defect detection of rolling bearings is finished while the time cost is significantly saved.

Supervised Single Channel Speech Enhancement Method Using UNET

This paper proposes an innovative single-channel supervised speech enhancement (SE) method based on UNET, a convolutional neural network (CNN) architecture that expands on a few changes in the basic CNN architecture. In the training phase, short-time Fourier transform (STFT) is exploited on the noisy time domain signal to build a noisy time-frequency domain signal which is called a complex noisy matrix. We take the real and imaginary parts of the complex noisy matrix and concatenate both of them to form the noisy concatenated matrix. We apply UNET to the noisy concatenated matrix for extracting speech components and train the CNN model. In the testing phase, the same procedure is applied to the noisy time-domain signal as in the training phase in order to construct another noisy concatenated matrix that can be tested using a pre-trained or saved model in order to construct an enhanced concatenated matrix. Finally, from the enhanced concatenated matrix, we separate both the imaginary and real parts to form an enhanced complex matrix. Magnitude and phase are then extracted from the newly created enhanced complex matrix. By using that magnitude and phase, the inverse STFT (ISTFT) can generate the enhanced speech signal. Utilizing the IEEE databases and various types of noise, including stationary and non-stationary noise, the proposed method is evaluated. Comparing the exploratory results of the proposed algorithm to the other five methods of STFT, sparse non-negative matrix factorization (SNMF), dual-tree complex wavelet transform (DTCWT)-SNMF, DTCWT-STFT-SNMF, STFT-convolutional denoising auto encoder (CDAE) and casual multi-head attention mechanism (CMAM) for speech enhancement, we determine that the proposed algorithm generally improves speech quality and intelligibility at all considered signal-to-noise ratios (SNRs). The suggested approach performs better than the other five competing algorithms in every evaluation metric.

Inter-Frequency Phase Difference for Phase Reconstruction Using Deep Neural Networks and Maximum Likelihood

This paper presents improvements to two-stage algorithms for estimating the short-time Fourier transform (STFT) phase from only the amplitude by using deep neural networks (DNNs). The phase is difficult to reconstruct due to its sensitivity to the waveform shift and wrapping issue. To mitigate these problems, two-stage approaches indirectly estimate the phase through phase derivatives, i.e., instantaneous frequency (IF) and group delay (GD). In the first stage, the IF and GD are estimated from the amplitude using DNNs, and then in the second stage, the phase is reconstructed by maintaining the IF/GD information. Conventional methods for the second stage do not consider the importance of high-amplitude time–frequency bins, e.g., the least squares-based method, or lack a solid model, e.g., the average-based method. To address these problems, we propose improvements to the second stage of two-stage algorithms by using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">von Mises</i> distribution-based maximum likelihood and weighted least squares. We also provide theoretical discussions for the phase reconstruction, including the investigations of the properties of the GD and roles of the IF/GD information in the inverse STFT. On the basis of the analysis, we propose a new phase-based feature, i.e., inter-frequency phase difference (IFPD), and demonstrate its application in two-stage phase reconstruction algorithms. We conducted subjective and objective experiments to compare the performances of our proposed and conventional methods. The results confirm that the proposed method using the IFPD performs better than other methods for all metrics.

STFT-Domain Neural Speech Enhancement With Very Low Algorithmic Latency

Deep learning based speech enhancement in the short-time Fourier transform (STFT) domain typically uses a large window length such as 32 ms. A larger window can lead to higher frequency resolution and potentially better enhancement. This however incurs an algorithmic latency of 32 ms in an online setup, because the overlap-add algorithm used in the inverse STFT (iSTFT) is also performed using the same window size. To reduce this inherent latency, we adapt a conventional dual-window-size approach, where a regular input window size is used for STFT but a shorter output window is used for overlap-add, for STFT-domain deep learning based frame-online speech enhancement. Based on this STFT-iSTFT configuration, we employ complex spectral mapping for frame-online enhancement, where a deep neural network (DNN) is trained to predict the real and imaginary (RI) components of target speech from the mixture RI components. In addition, we use the DNN-predicted RI components to conduct frame-online beamforming, the results of which are used as extra features for a second DNN to perform frame-online postfiltering. The frequency-domain beamformer can be easily integrated with our DNNs and is designed to not incur any algorithmic latency. Additionally, we propose a future-frame prediction technique to further reduce the algorithmic latency. Evaluation on noisy-reverberant speech enhancement shows the effectiveness of the proposed algorithms. Compared with Conv-TasNet, our STFT-domain system can achieve better enhancement performance for a comparable amount of computation, or comparable performance with less computation, maintaining strong performance at an algorithmic latency as low as 2 ms.

APNet: An All-Frame-Level Neural Vocoder Incorporating Direct Prediction of Amplitude and Phase Spectra

This paper presents a novel neural vocoder named APNet which reconstructs speech waveforms from acoustic features by predicting amplitude and phase spectra directly. The APNet vocoder is composed of an amplitude spectrum predictor (ASP) and a phase spectrum predictor (PSP). The ASP is a residual convolution network which predicts frame-level log amplitude spectra from acoustic features. The PSP also adopts a residual convolution network using acoustic features as input, then passes the output of this network through two parallel linear convolution layers respectively, and finally integrates into a phase calculation formula to estimate frame-level phase spectra. Finally, the outputs of ASP and PSP are combined to reconstruct speech waveforms by inverse short-time Fourier transform (ISTFT). All operations of the ASP and PSP are performed at the frame level. We train the ASP and PSP jointly and define multilevel loss functions based on amplitude mean square error, phase anti-wrapping error, short-time spectral inconsistency error and time domain reconstruction error. Experimental results show that our proposed APNet vocoder achieves an approximately 8x faster inference speed than HiFi-GAN v1 on a CPU due to the all-frame-level operations, while its synthesized speech quality is comparable to HiFi-GAN v1. The synthesized speech quality of the APNet vocoder is also better than that of several equally efficient models. Ablation experiments also confirm that the proposed parallel phase estimation architecture is essential to phase modeling and the proposed loss functions are helpful for improving the synthesized speech quality.

Analysis-by-synthesis based training target extraction of the DNN for noise masking

In conventional speech enhancement methods, the target of noise mask in the time-frequency domain is based on deep neural networks (DNN), such as ideal ratio mask and phase-sensitive mask, in which they do not consider the dependency of spectrum. In this paper, an ideal real-valued ratio mask (IRVRM) extraction method is proposed based on the analysis-by-synthesis (ABS) for utilizing the dependency of spectrum. In the synthesis process, the enhanced speech is obtained by inverse short-time Fourier transform (ISTFT) of the masked spectrum, whereas in the analysis process, the IRVRM is determined by maximizing speech quality of the reconstructed speech from mask space. The ABS loop algorithm is proposed to reduce computational complexity, namely, the best mask in the specifically generated subspace is conducted in each loop. After the ABS loop, the approximated IRVRM is conducted. This IRVRM is further utilized as the training target of the DNN. The experimental results show that when the extracted IRVRM with the ABS loop is employed as the training target of the DNN, the speech quality is effectively improved in the DNN-based noise masking.

Improving Frame-Online Neural Speech Enhancement With Overlapped-Frame Prediction

Frame-online speech enhancement systems in the short-time Fourier transform (STFT) domain usually have an algorithmic latency equal to the window size due to the use of overlap-add in the inverse STFT (iSTFT). This algorithmic latency allows the enhancement models to leverage future contextual information up to a length equal to the window size. However, this information is only partially leveraged by current frame-online systems. To fully exploit it, we propose an overlapped-frame prediction technique for deep learning based frame-online speech enhancement, where at each frame our deep neural network (DNN) predicts the current and several past frames that are necessary for overlap-add, instead of only predicting the current frame. In addition, we propose a loss function to account for the scale difference between predicted and oracle target signals. Experiments on a noisy-reverberant speech enhancement task show the effectiveness of the proposed algorithms.

Fetal ECG extraction using short time Fourier transform and generative adversarial networks

Objective. Fetal ECG (FECG) plays an important role in fetal monitoring. However, the abdominal ECG (AECG) recorded at the maternal abdomen is affected by various noises, making the extraction of FECG a challenging task. The main objective is to present a novel approach to FECG extraction using short time Fourier transform (STFT) and generative adversarial networks (GAN). Methods. Firstly, the AECG signals are transformed from one-dimensional (1D) time domain to two-dimensional (2D) time-frequency domain by using the STFT. Secondly, the 2D-STFT coefficients of FECG are estimated by the GAN model in the time-frequency domain. Finally, after the inverse STFT, the FECG can be reconstructed in the time domain. Main results. Experimental results on two databases demonstrate the effectiveness of the proposed method. Specifically, the SE, PPV and F 1 of the proposed method on PCDB are 92.37 ± 3.78%, 93.69 ± 3.96% and 93.02 ± 3.81%, respectively. And the SE, PPV and F 1 on ADFECGDB are 90.32 ± 10.70%, 89.79 ± 9.26% and 90.05 ± 9.81%, respectively. Significance. Unlike the previous studies based on the elimination of maternal ECG in the 1D time domain, the novelty of the proposed method relies on extracting the FECG directly from the AECG in the 2D time-frequency domain. It sheds some light to the topic of FECG extraction.

End-to-End Monaural Speech Separation with a Deep Complex U-Shaped Network

Conventional time–frequency (TF) domain source separation methods mainly focus on predicting TF-masks or speech spectrums, where complex ideal ratio mask (cIRM) is an effective target for speech enhancement and separation. However, some recent studies employ a real-valued network, such as a general convolutional neural network (CNN) and a recurrent neural network (RNN), to predict a complex-valued mask or a spectrogram target, leading to the unbalanced training results of real and imaginary parts. In this paper, to estimate the complex-valued target more accurately, a novel U-shaped complex network for the complex signal approximation (uCSA) method is proposed. The uCSA is an adaptive front-end time-domain separation method, which tackles the monaural source separation problem in three ways. First, we design and implement a complex U-shaped network architecture comprising well-defined complex-valued encoder and decoder blocks, as well as complex-valued bidirectional Long Short-Term Memory (BLSTM) layers, to process complex-valued operations. Second, the cIRM is the training target of our uCSA method, optimized by signal approximation (SA), which takes advantage of both real and imaginary components of the complex-valued spectrum. Third, we re-formulate STFT and inverse STFT into derivable formats, and the model is trained with the scale-invariant source-to-noise ratio (SI-SNR) loss, achieving end-to-end training of the speech source separation task. Moreover, the proposed uCSA models are evaluated on the WSJ0-2mix datasets, which is a valid corpus commonly used by many supervised speech separation methods. Extensive experimental results indicate that our proposed method obtains state-of-the-art performance on the basis of the perceptual evaluation of speech quality (PESQ) and the short-time objective intelligibility (STOI) metrics.

Multichannel speech separation using hybrid GOMF and enthalpy-based deep neural networks

Speech signal is commonly debased by room reverberation and included noises in genuine climates. This paper focuses on disengaging objective speech signals in reverberant conditions from multichannel input signals. To overcome all the existing drawbacks, this work proposes an efficient technique like, multichannel speech signal separation using a new hybrid method that combines grasshopper optimization-based matrix factorization (GOMF) and enthalpy-based DNN (EDNN). To predict and remove the unwanted noise into the multichannel input signal, this paper presents a narrative classification framework in the manner of following steps namely, STFT, GOMF-based rank estimation, identify signal eigenvalues, noise removal, feature extraction well as classification. At first, STFT is utilized to plan the multichannel blend waveforms to complex spectrograms. Then, GOMF is used to estimates the obvious speech signals and noise. After the estimation, important features are extracted. Feature extraction is based on spatial feature, spectral feature, and directional features. To attain the enhanced classification outcomes, the spectrogram is reconstructed based on enthalpy-based deep neural network (EDNN). At last, convert the resultant speech spectrogram back to the extracted output signal based on inverse STFT. Experimental results show that our proposed approach accomplishes the most extreme SNR outcome of − 6dB of 24.0523. Comparable to the DNN-JAT, which achieves 18.50032. The RNN and NMF-DNN had the worst SNR 13.45434 and 12.29991. The proposed outcome is compared with various algorithms and some existing works. Compared with other existing works our proposed methodology achieves higher outcomes.

Joint time–frequency mask and convolutional neural network for real-time separation of multipath in GNSS deformation monitoring

As one of the leading technologies of real-time dynamic deformation monitoring, global navigation satellite system (GNSS) has been widely used in deformation monitoring. Multipath error is the primary error source that limits the application of GNSS high-precision deformation monitoring, which cannot be eliminated by the double-differenced technique. It is a problem to separate and mitigate multipath in the GNSS deformation monitoring series in real-time. Therefore, we propose an approach to solve this problem, named time–frequency mask and convolutional neural network (TFM–CNN). The specific processes are as follows: (1) TFM–CNN network construction. We add a full-band deformation to the multipath and obtain the spectrogram of the signal by the short-time Fourier transform (STFT); meanwhile, the ideal ratio mask (IRM) is used to obtain the corresponding time–frequency mask matrix based on the spectrogram; furthermore, one-dimensional CNN mines the mapping relationship between the spectrogram and the time–frequency mask matrix. (2) Multipath separation. We obtain the spectrogram of the GNSS real-time deformation monitoring series by STFT. Then, we estimate its time–frequency mask matrix by the network. The matrix is multiplied by the spectrogram of the monitoring series to obtain the spectrogram of the multipath. Finally, we perform the inverse STFT to obtain the multipath in the GNSS monitoring series. The experimental results show that by training GNSS data in only a specific direction (such as the north direction), the mapping relationship between the spectrogram of multipath and the time–frequency mask matrix can be obtained, which can effectively separate multipath of the GNSS monitoring series in different observation environment in real-time. TFM-CNN significantly improves the monitoring accuracy and achieves millimeter level dynamic deformation monitoring.

A Tacholess Order Tracking Method Based on Inverse Short Time Fourier Transform and Singular Value Decomposition for Bearing Fault Diagnosis.

Order tracking has been widely used to diagnose failures of variable speed rotating machines. The performance of the TOT (Time-Frequency Domain Tacholess Order Tracking) methods is based on the correct separation of the target component strictly related to the shaft rotation frequency. Currently, most of the methods have focused on obtaining the instantaneous frequency with accuracy. In this paper, a new TOT method has been proposed that combines the inverse short-time Fourier transform (ISTFT) with singular value decomposition (SVD). The target component closely related to the shaft rotation frequency is selected and filtered approximately in the time-frequency domain. Hence, the ISTFT is adopted to reverse the target component into the time domain. Next, SVD is used to refine the roughly filtered target component. Finally, the phase of the refined signal is extracted to resample the original signal. The performance of the method was tested using real vibration signals collected from a large-scale test rig of a high-speed train traction system.

Dual-Transform Source Separation Using Sparse Nonnegative Matrix Factorization

In this article, we propose a new source separation method in which the dual-tree complex wavelet transform (DTCWT) and short-time Fourier transform (STFT) algorithms are used sequentially as dual transforms and sparse nonnegative matrix factorization (SNMF) is used to factorize the magnitude spectrum. STFT-based source separation faces issues related to time and frequency resolution because it cannot exactly determine which frequencies exist at what time. Discrete wavelet transform (DWT)-based source separation faces a time-variation-related problem (i.e., a small shift in the time-domain signal causes significant variation in the energy of the wavelet coefficients). To address these issues, we utilize the DTCWT, which comprises two-level trees with different sets of filters and provides additional information for analysis and approximate shift invariance; these properties enable the perfect reconstruction of the time-domain signal. Thus, the time-domain signal is transformed into a set of subband signals in which low- and high-frequency components are isolated. Next, each subband is passed through the STFT and a complex spectrogram is constructed. Then, SNMF is applied to decompose the magnitude part into a weighted linear combination of the trained basis vectors for both sources. Finally, the estimated signals can be obtained through a subband binary ratio mask by applying the inverse STFT (ISTFT) and the inverse DTCWT (IDTCWT). The proposed method is examined on speech separation tasks utilizing the GRID audiovisual and TIMIT corpora. The experimental findings indicate that the proposed approach outperforms the existing methods.

FLGCNN: A novel fully convolutional neural network for end-to-end monaural speech enhancement with utterance-based objective functions

This paper proposes a novel fully convolutional neural network (FCN) called FLGCNN to address the end-to-end speech enhancement in time domain. The proposed FLGCNN is mainly built on encoder and decoder, while the extra convolutional-based short-time Fourier transform (CSTFT) layer and inverse STFT (CISTFT) layer are added to emulate the forward and inverse STFT operations. These layers aim to integrate the frequency-domain knowledge into the proposed model since the underlying phonetic information of speech is presented more clearly by time–frequency (T-F) representations. In addition, the encoder and decoder are constructed by the gated convolutional layers so that the proposed model can better control the information passed on in the hierarchy. Besides, motivated by the popular temporal convolutional neural network (TCNN), the temporal convolutional module (TCM) which is efficient in modeling the long-term dependencies of speech signal is inserted between encoder and decoder. We also optimize the proposed model with different utterance-based objective functions to exploit the impact of loss functions on performance, because the entire framework can realize the end-to-end speech enhancement. Experimental results have demonstrated that the proposed model consistently gives better performance improvement than the other competitive methods of speech enhancement.

Underdetermined convolutive blind source separation in the time–frequency domain based on single source points and experimental validation

To effectively separate underdetermined convolutive mixtures, an accurate and robust underdetermined convolutive blind source separation (BSS) method in the time–frequency domain based on single source points (SSPs) is proposed. Firstly, convolutive BSS in the time domain is transformed into instantaneous BSS in the time–frequency domain by short-time Fourier transform (STFT). Secondly, hierarchical clustering is carried out after the extraction and identification of SSPs by using sparse coding technology. Thirdly, source separation in the frequency domain is obtained based on Lp norm minimization and then alignments are permutated and scales are compensated. Finally, inverse STFT is adopted to reconstruct the separated signals in the time domain. Furthermore, numerical case studies and experimental case studies on a cylindrical test bed are carried out to validate the effectiveness of the proposed method. Generally, this paper provides an accurate and robust underdetermined convolutive BSS technique for mixing matrix estimation, source identification and contribution evaluation, which can provide significant evidence for vibration and noise monitoring and control.

Signal Enhancement of Acoustic Signature of Lutjanidae Family Species in Indian Waters

The present study is to carry out the enhancement of the acoustic signals of Lutjanidae species often found in abundance, in tropic shallow waters. Since most of the studies on Lutjanidae is about its physical structure both internal and external, and its population in sea ie., catches in tons per year. This research work is the first attempt on the acoustical study of Lutjanidae family species call signal. Five species of Lutjanidae family are considered for this study which includes L. analis, L. apodus, L. synagris, L. griseus, and L. jocu). The earlier literature which studied the acoustic toning of marine species vocalization using empirical mode decomposition method [1]. Here in this research, (i) signals with background noise and (ii) enhanced signals are considered for comparison. The enhancement of acoustic signals of Lutjanidae family species is useful as acoustic reference for those working in the field of biological signal processing. The enhancement of the signal is achieved by the logical applications and applying Short Time Fourier Transform (STFT), inverse STFT. From the above two cases considered, the frequency range of 50 to 2500 Hz approximately is clearly noticed in the spectrogram, power spectral density and it shows the frequency of all species looks similar. By listening the sound produced by the species, it is observed to be of type knocking sound.

Supervised single channel dual domains speech enhancement using sparse non-negative matrix factorization

In this paper, we propose a novel single-channel speech enhancement algorithm that applies dual-domain transforms comprising of dual-tree complex wavelet transform (DTCWT) and short-time Fourier transform (STFT) with a sparse non-negative matrix factorization (SNMF). The first domain belongs to the DTCWT, which is utilized on the time domain signals to conquer the weakness of signal distortions brought about by the downsampling of the discrete wavelet packet transform (DWPT) and delivered a set of subband signals. The second domain alludes to the STFT, which is exploited to each subband signal and built a complex spectrogram. At last, we apply the SNMF to the magnitude spectrogram for extracting speech components. In short, the DTCWT decomposes the time-domain noisy signal into a set of subband signals and afterward applied STFT to each subband signal, and we get nonnegative matrices by taking the absolute value of the complex matrix. From this point forward, we apply SNMF to each nonnegative matrix and identify the speech components. Finally, the estimated signal can be achieved through a subband binary ratio mask (SBRM) by applying the inverse STFT (ISTFT) and, subsequently, the inverse DTCWT (IDTCWT). The proposed approach is assessed utilizing the GRID audio-visual and IEEE databases, and diverse kinds of noises such as stationary, non-stationary, and quasi-stationary. The exploratory outcomes demonstrate that the proposed algorithm improved objective speech quality and intelligibility altogether at all considered signal to noise ratios (SNRs), compared to the other seven speech enhancement methods of STFT-SNMF, STFT-SNMFSE, MLD-STFT-SNMF, STFT-GDL, STFT-CJSR, DTCWT-SNMF, and DWPT-STFT-SNMF.

Reconfigurable Range-Doppler Processing and Range Resolution Improvement for FMCW Radar

A reconfigurable range-Doppler processing method for FMCW radar is presented. By concatenating beat-frequency signals from more than one sweep, a continuous beat-frequency signal for the whole coherent processing interval (CPI) can be created. As a result, continuous targets’ observation time is extended beyond that of a single chirp duration, leading to range resolution improvement. The created continuous beat-frequency signal can be split in the digital domain to any two-dimensional slow-time and fast-time matrices with the same number of elements as in the original signals, which offers a realization of a software-defined pulse/sweep repetition rate in range-Doppler processing. The signal concatenation is done in the short-time Fourier transform (STFT) domain, where the beat-frequency slices are extrapolated to compensate for the observation time lost in the transient region between sweeps, and then a phase correction is applied to each frequency-slice as appropriate, followed by an inverse STFT (ISTFT). The proposed technique is verified with simulation and experiments with an FMCW radar for stable and moving target scenarios. We found that the method allows for range resolution improvement without the transmission of additional bandwidth and also allows for the ability to observe different resolution granularities in parallel from one CPI. It additionally allows the decoupling of the transmitted PRF from the Doppler processing PRF, permitting the facility to observe different unambiguous Doppler velocity intervals from one CPI, without compromising on the total CPI processing gain.