DFT Filter Banks Research Articles

A conjugate frequency modulation FRM method: Applications in polyphase DFT filter bank

In this paper, we study the application of frequency response masking (FRM) technology in polyphase discrete Fourier transform (DFT) filter bank (FB). Due to the inability of FRM methods with conventional structure to simultaneously meet the needs of sharp transition band polyphase DFT FB to improve the signal-to-interference ratio of channelized signals and reduce the complexity of FBs, an improved conjugate frequency modulation frequency response masking (CFM-FRM) method is proposed. The proposed CFM-FRM method solves the problem by frequency modulation, and consumes less multipliers by taking advantage of the orthogonality between sub-filters in CFM-FRM FB. The efficient realization of CFM-FRM based polyphase DFT FB is derived and the multi-size configuration method is illustrated via coefficient decimation. We analyze the adaptability of related FRM works to polyphase DFT FB. The simulation and analysis show that the CFM-FRM method is applicable to polyphase DFT FB, the CFM-FRM based polyphase DFT FB has less multipliers than related methods in other works, and the performances of multi-size FBs meet the requirements.

A Parallel Solution of Timing Synchronization in High-Speed Remote Sensing Data Transmission

Considering the problem that the timing synchronization calculation in high-speed remote sensing signal reception is complex and it is difficult for it to be parallel, this paper deduces and designs a parallel timing error estimation and correction scheme. This paper presents the design of polyphase DFT filter banks with non-maximum decimation. The feedforward timing error estimation and correction method is then improved to enhance synchronization performance. Finally, an implementation scheme for parallel timing error estimation and correction is proposed using the polyphase filter bank time domain decomposition method and the filter polyphase model. In the estimation module, the parallel implementation structure of the joint second-order and fourth-order cyclic statistics methods is designed, which improves the estimation accuracy. In the correction module, a fractional delay filtering method with higher accuracy is adopted in order to improve the calibration accuracy and reduce the computational complexity. The timing synchronization of a high-speed remote sensing signal with timing error is simulated and verified. The experimental results show that the parallel method proposed in this paper greatly reduces the processing speed of subband data, and has a good synchronization performance, which is close to the theoretical limit in the demodulation error rate. This paper utilizes a multi-phase DFT filter bank architecture to achieve parallel timing synchronization, which presents a novel approach for the future parallel reception of high-speed remote sensing signals.

Frequency Estimation with Co-prime DFT Filter Bank and Half Nyquist Frequency Shift

When processing wide sense stationary (WSS) signals, the sampled data rate of conventional MN bands DFT filter bank is at least MN, while the co-prime DFT filter bank (co-prime DFTFB) only needs M+N, that sharply lowers the sampling rate. Here, M and N are co-prime pair of integers. However, practical FIR filter imperfections and correlation detection mode arouse spurious peaks in signal power spectrogram, that greatly limits the application of co-prime DFTFB. In this paper, we propose a modified co-prime DFTFB by adding a real valued multiplier to the original one, where M and N are both odd numbers. Together with original co-prime DFTFB, we get a 2MN bands filter bank. In the simulation section, two BPSK signals with random carrier frequencies are employed. The results of detection probability versus SNR curves through 500 Monte Carlo experiments verify the effectiveness of our method.

A Methodology for the Design of Fault Tolerant Parallel Digital Channelizers on SRAM-FPGAs

Digital channelizers (DCs) based on the Discrete Fourier Transform (DFT) and polyphase filter banks are widely used in on-board processing (OBP) platforms to extract narrowband sub-channels from a wideband signal efficiently. In high-capacity communication satellite platforms there are always multiple DCs extracting narrowband signals from multiple wideband signals in parallel. Field-programmable gate arrays (FPGAs) are a popular option for the implementation of DCs due to their parallel computing capabilities and good re-configurability, but FPGAs suffer single-event upsets (SEUs) on the space platform. This paper focuses on the efficient protection of parallel DCs with enhanced coding techniques. We first prove that a linear relationship between parallel DCs can be introduced and maintained among the multiple outputs. However, traditional coding schemes cannot be directly applied for the detection of faulty DCs due to the quantization noise introduced by fixed point implementations. To address this issue, we propose an enhanced coding scheme by averaging in the space and time domains to minimize the effect of quantization noise, introducing thresholds and a majority voter to further improve the detection probability. Both theoretical analysis and fault injection experiments prove the effectiveness of the proposed protection scheme. Experimental results show that all the SEUs that cause an SNR lower than 20dB can be detected and recovered, and the resource overheads are about 1.6 times and 1.3 times of that of the unprotected DCs for systems with 8 DCs and 16 DCs, respectively.

A Spectral Analyzer Based on Dual Coprime DFT Filter Banks and Sub-Decimation

A Spectral Analyzer Based on Dual Coprime DFT Filter Banks and Sub-Decimation

Supraharmonic estimation by polyphase DFT filter bank

As a side effect caused by new technologies, supraharmonics attracted the attention of researchers in recent years. Mitigation and analysis of supraharmonics distortions are of great importance to guarantee the power quality (PQ) available in the power grids since such distortions can cause serious damage to the grid-connected equipment. However, there are few works in literature reporting techniques for supraharmonics analysis, and PQ equipment is rarely capable of performing measurements in the supraharmonic range. This work proposes a supraharmonic estimation system utilizing a digital filter bank through a multirate digital signal processing technique. The polyphase decomposition applied in the decimating filter bank enables the simplification of the system implementation. Both synthetic and real signals are used to evaluate the technique in analyzing supraharmonic distortions. The proposed method shows a good application prospect in accurately measuring supraharmonics and with a significant reduction in computational complexity compared with the method presented in the IEC 61000-4-30 standard.

Improving Generalized Discrete Fourier Transform (GDFT) Filter Banks with Low-Complexity and Reconfigurable Hybrid Algorithm

With ever-increasing wireless network demands, low-complexity reconfigurable filter design is expected to continue to require research attention. Extracting and reconfiguring channels of choice from multi-standard receivers using a generalized discrete Fourier transform filter bank (GDFT-FB) is computationally intensive. In this work, a lower compexity algorithm is written for this transform. The design employs two different approaches: hybridization of the generalized discrete Fourier transform filter bank with frequency response masking and coefficient decimation method 1; and the improvement and implementation of the hybrid generalized discrete Fourier transform using a parallel distributed arithmetic-based residual number system (PDA-RNS) filter. The design is evaluated using MATLAB 2020a. Synthesis of area, resource utilization, delay, and power consumption was done on a Quartus 11 Altera 90 using the very high-speed integrated circuits (VHSIC) hardware description language. During MATLAB simulations, the proposed HGDFT algorithm attained a 66% reduction, in terms of number of multipliers, compared with existing algorithms. From co-simulation on the Quartus 11 Altera 90, optimization of the filter with PDA-RNS resulted in a 77% reduction in the number of occupied lookup table (LUT) slices, an 83% reduction in power consumption, and an 11% reduction in execution time, when compared with existing methods.

Wearable Hearing Device Spectral Enhancement Driven by Non-Negative Sparse Coding-Based Residual Noise Reduction.

This paper proposes a novel technique to improve a spectral statistical filter for speech enhancement, to be applied in wearable hearing devices such as hearing aids. The proposed method is implemented considering a 32-channel uniform polyphase discrete Fourier transform filter bank, for which the overall algorithm processing delay is 8 ms in accordance with the hearing device requirements. The proposed speech enhancement technique, which exploits the concepts of both non-negative sparse coding (NNSC) and spectral statistical filtering, provides an online unified framework to overcome the problem of residual noise in spectral statistical filters under noisy environments. First, the spectral gain attenuator of the statistical Wiener filter is obtained using the a priori signal-to-noise ratio (SNR) estimated through a decision-directed approach. Next, the spectrum estimated using the Wiener spectral gain attenuator is decomposed by applying the NNSC technique to the target speech and residual noise components. These components are used to develop an NNSC-based Wiener spectral gain attenuator to achieve enhanced speech. The performance of the proposed NNSC–Wiener filter was evaluated through a perceptual evaluation of the speech quality scores under various noise conditions with SNRs ranging from -5 to 20 dB. The results indicated that the proposed NNSC–Wiener filter can outperform the conventional Wiener filter and NNSC-based speech enhancement methods at all SNRs.

Auditory Device Voice Activity Detection Based on Statistical Likelihood-Ratio Order Statistics

This paper proposes a technique for improving statistical-model-based voice activity detection (VAD) in noisy environments to be applied in an auditory hearing aid. The proposed method is implemented for a uniform polyphase discrete Fourier transform filter bank satisfying an auditory device time latency of 8 ms. The proposed VAD technique provides an online unified framework to overcome the frequent false rejection of the statistical-model-based likelihood-ratio test (LRT) in noisy environments. The method is based on the observation that the sparseness of speech and background noise cause high false-rejection error rates in statistical LRT-based VAD—the false rejection rate increases as the sparseness increases. We demonstrate that the false-rejection error rate can be reduced by incorporating likelihood-ratio order statistics into a conventional LRT VAD. We confirm experimentally that the proposed method relatively reduces the average detection error rate by 15.8% compared to a conventional VAD with only minimal change in the false acceptance probability for three different noise conditions whose signal-to-noise ratio ranges from 0 to 20 dB.

Sensing Fractional Power Spectrum of Nonstationary Signals with Coprime Filter Banks

The coprime discrete Fourier transform (DFT) filter banks provide an effective scheme of spectral sensing for wide-sense stationary (WSS) signals in case that the sampling rate is far lower than the Nyquist sampling rate. And the resolution of the coprime DFT filter banks in the Fourier domain (FD) is 2π/MN, where M and N are coprime. In this work, a digital fractional Fourier transform- (DFrFT-) based coprime filter banks spectrum sensing method is suggested. Our proposed method has the same sampling principle as the coprime DFT filter banks but has some advantages compared to the coprime DFT filter banks. Firstly, the fractional power spectrum of the chirp-stationary signals which are nonstationary in the FD can be sensed effectively by the coprime DFrFT filter banks because of the linear time-invariant (LTI) property of the proposed system in discrete-time Fourier domain (DTFD), while the coprime DFT filter banks can only sense the power spectrum of the WSS signals. Secondly, the coprime DFrFT filter banks improve the resolution from 2π/MN to 2π sin α/MN by combining the fractional filter banks theory with the coprime theory. Simulation results confirm the obtained analytical results.

Design of a Narrow Transition Band Dynamic Digital Channelized Receiver withoutMerging Adjacent Sub-channels

In electronic reconnaissance, effective channelization of several input signals with unknown parameters is the key requirement of the broadband receiver. Generally, since the prototype filter must be perfect, the dynamic channelized receiver based on merging adjacent sub-channels to reconstruct non-uniform filter Banks occupies too many resources and is difficult to realize. This paper proposed a sharp wideband channelized receiver based on DFT filter banks and interpolated filter banks. The proposed receiver consists of an analysis section, channel detection and arbitration section, and a synthesis section. The analysis section divides the wideband signal into multiple sub-channels. Channel detection and arbitration section output the center frequencies and the bandwidths of the input signals. In the synthesis section, after being converted to baseband, the input signals are filtered and decimated to achieve the low rate signals. The proposed method released the design of the prototype filter from the requirement of perfect reconstruction. So it is computationally efficient. Besides, time-multiplexed and interpolated filter techniques can be used to further reduce the hardware complexity. Simulation results verify the validity of the proposed method.

Personal Sound Zones by Subband Filtering and Time Domain Optimization

Personal Sound Zones (PSZ) systems aim to render independent sound signals to multiple listeners within a room by using arrays of loudspeakers. One of the algorithms used to provide PSZ is Weighted Pressure Matching (wPM), which computes the filters required to render a desired response in the listening zones while reducing the acoustic energy arriving to the quiet zones. This algorithm can be formulated in time and frequency domains. In general, the time-domain formulation (wPM-TD) can obtain good performance with shorter filters and delays than the frequency-domain formulation (wPM-FD). However, wPM-TD requires higher computation for obtaining the optimal filters. In this article, we propose a novel approach to the wPM algorithm named Weighted Pressure Matching with Subband Decomposition (wPM-SD), which formulates an independent time-domain optimization problem for each of the subbands of a Generalized Discrete Fourier Transform (GDFT) filter bank. Solving the optimization independently for each subband has two main advantages: 1) lower computational complexity than wPM-TD to compute the optimal filters; 2) higher versatility than the classic wPM algorithms, as it allows different configurations (sets of loudspeakers, filter lengths, etc.) in each subband. Moreover, filtering the input signals with a GDFT filter bank (as in wPM-SD) requires lower computational effort than broadband filtering (as in wPM-TD and wPM-FD), which is beneficial for practical PSZ systems. We present experimental evaluations showing that wPM-SD offers very similar performance to wPM-TD. In addition, two cases where the versatility of wPM-SD is beneficial for a PSZ system are presented and experimentally validated.

Hearing Aid Speech Enhancement Using Phase Difference-Controlled Dual-Microphone Generalized Sidelobe Canceller

This paper proposes a new technique for improving a generalized sidelobe canceller (GSC) for dual-microphone speech enhancement to be applied in an auditory device such as a hearing aid. Here, the GSC is implemented on a 32-channel uniform polyphase discrete Fourier transform filter bank, where the overall algorithm processing delay is 8 ms to meet hearing aid requirements. The proposed method can improve the fixed beamformer (FBF) and control the adaptive algorithm in the noise canceller (NC) using the phase difference obtained from dual-microphone signals. For this, spatial cues such as the phase differences are used to estimate the target-to-non-target directional signal ratio (TNR). A target-directional speech enhancing spectral gain-attenuator is calculated based on the estimated TNR, which is then incorporated to improve the FBF in the GSC. Furthermore, the weight update of the adaptive NC in the GSC is formulated using the phase difference-based TNR. The experimental results show that the auditory speech enhancement system that employs the proposed dual-microphone GSC algorithm provides better perceptual quality and intelligibility scores than conventional methods such as a beamformer, phase-error-based filter (PEF), GSC, or PEF-controlled GSC under multiple noise conditions of signal-to-noise ratio range 0-20 dB.

Low complexity reconfigurable channelizers using non-uniform filter banks

A Software Defined Radio (SDR) channelizer needs reconfigurable sharp filter banks with low implementation complexity. In this paper, the design of non-uniform Modified Discrete Fourier Transform filter bank (MDFT FB) is proposed to be used in SDR channelizer. The frequency response masking technique is used to design the prototype filter which gives sharp filters with lower hardware complexity, compared to the finite impulse response filters. The canonic signed digit (CSD) representation is used in the design, to convert the continuous filter coefficients into discrete coefficients. Multi-objective artificial bee colony algorithm is utilized to improve the performance degradation when the CSD represented filter coefficients are used. Further, the shift inclusive differential technique with common sub-expression elimination is used to reduce the number of adders. Xilinx ISE is used to verify the hardware requirement, for the implementation of the non-uniform MDFT FB. Hence low complexity reconfigurable SDR channelizers using non-uniform MDFT FB is proposed in this paper.

Design of hardware-efficient digital hearing aids using non-uniform MDFT filter banks

This paper proposes the design of a simple digital hearing aid using non-uniform modified discrete Fourier transform filter bank. Here, the non-uniform filter bank is obtained by first designing a uniform filter bank and then merging suitable bands to obtain the desired non-uniform structure. In hearing aids, narrow channels with adjustable gains can be allocated to those frequency regions of the audiogram with sharp transition, whereas wider passband channels can be allocated to frequency regions with slower transitions. The latter can be done by merging the bands in those regions. It is shown in this paper that matching error, delay and hardware complexity in terms of the number of multipliers required for the prototype filter are lower than the existing techniques for all types of hearing losses.

FPGA implementation of a reconfigurable channelization for simultaneous multichannel DRM30/FM receiver

It is becoming more and more popular to support multiple radio broadcasting standards, such as Frequency Modulation (FM) and Digital Radio Mondiale for Amplitude Modulation (DRM30), on one channelization system for content and metadata indexing applications. However, existing works mainly focus on supporting only one standard, because different standards usually have different channel characteristics in term of bandwidth and carrier location. This paper presents a flexible and resource-efficient architecture that can simultaneously channelize the entire FM and DRM30 bands. In particular, a coarse/finergrained division based approach is proposed to implement the multi-standard channelization. Therefore, the parameters of each output channel, such as center frequency and output sampling rate, can be independently configured at run-time. Finally, the proposed architecture, which consists of one polyphase Discrete Fourier Transform (DFT) filter bank, one tuning unit, and one resampling filter, is implemented in a single field programmable gate array (FPGA). The experiment results indicate that the proposed design can support both FM and DRM30 standards, and requires less FPGA resources than the existing works which can only support one standard.

Resolution Doubled Co-Prime Spectral Analyzers for Removing Spurious Peaks

Co-prime DFT filter banks provide an effective tool of spectral analysis in case that the sampling rate is far lower than the Nyquist sampling rate. However, since the practical prototype filters are not ideal, spurious peaks will occur in multiple locations when the frequency offsets of the stimulus components are close to half of the frequency resolution of the co-prime spectrum. As a result, the quality of the original co-prime panorama spectrum will degrade greatly. This paper proposes a modified analyzer by synthesizing the original co-prime analyzer and a 0.5 frequency resolution shifted analyzer, which is derived from the original one by applying two simple operations on each low-rate data channel. Following some decision criterion between the original co-prime analyzer and the shifted analyzer, the synthesized analyzer not only removes all the annoying spurious peaks but also doubles the spectral resolution. Numerical comparisons are presented throughout to illustrate the above improvements.

Design of FRM-based MDFT filter banks in the canonic signed digit space using modified meta-heuristic algorithms

An optimal totally multiplier-less sharp transition width Modified Discrete Fourier Transform (MDFT) filter bank is proposed in this work. Since, here, the aim is to design a low complexity sharp transition width MDFT filter bank, the filters of the filter bank are designed using Frequency Response Masking technique to reduce the number of multipliers and hence the complexity. To replace multipliers with adders and shifters, the filter coefficients are converted into the Canonic Signed Digit space. In order to reduce the number of adders and shifters in the multiplier-less implementation, restricted number of non-zero bits is used in the conversion. This may degrade the performances of the MDFT filter bank. The performances are improved using modified meta-heuristic algorithms. A new hybrid algorithm which combines the qualities of Harmony Search Algorithm and Gravitational Search Algorithm is proposed in this work to optimise the performance of the MDFT filter bank.

Velocity filtering for attenuating moving artifacts in videos using an ultra-low complexity 3-D linear-phase IIR filter

An ultra-low complexity three-dimensional (3-D) linear-phase infinite-extent impulse response (IIR) velocity filter is proposed for attenuating moving artifacts in videos while enhancing objects moving on smooth approximately-linear trajectories. The proposed 3-D linear-phase IIR velocity filter consists of an ultra-low complexity 3-D wide-angle linear-phase IIR cone filter bank between two two-dimensional (2-D) spatial variable-shift filters. The ultra-low complexity 3-D wide-angle linear-phase IIR cone filter bank consists of a one-dimensional (1-D) temporal modified discrete Fourier transform filter bank and 2-D spatial allpass, IIR highpass and allstop filters. A typical 3-D linear-phase IIR velocity filter of order $$4\times 4\times 510$$4×4×510, applied to enhance a heavily corrupted test video signal, requires only 26 real multiplications and 60 real additions to process a sample and provides a scene-complexity-independent signal-to-interference-and-noise ratio improvement of 13.86 dB. The proposed 3-D linear-phase IIR velocity filter is employed to attenuate sunlight flicker patterns in shallow underwater videos, and experimental results are presented to confirm the effectiveness of the proposed method and its robustness to motion estimation errors.

Design of low complexity sharp MDFT filter banks with perfect reconstruction using hybrid harmony-gravitational search algorithm

The design of low complexity sharp transition width Modified Discrete Fourier Transform (MDFT) filter bank with perfect reconstruction (PR) is proposed in this work. The current trends in technology require high data rates and speedy processing along with reduced power consumption, implementation complexity and chip area. Filters with sharp transition width are required for various applications in wireless communication. Frequency response masking (FRM) technique is used to reduce the implementation complexity of sharp MDFT filter banks with PR. Further, to reduce the implementation complexity, the continuous coefficients of the filters in the MDFT filter banks are represented in discrete space using canonic signed digit (CSD). The multipliers in the filters are replaced by shifters and adders. The number of non-zero bits is reduced in the conversion process to minimize the number of adders and shifters required for the filter implementation. Hence the performances of the MDFT filter bank with PR may degrade. In this work, the performances of the MDFT filter banks with PR are improved using a hybrid Harmony-Gravitational search algorithm.