Inverse Fast Fourier Transform Research Articles

Non-searching coherent integration method for maneuvering target detection by using non-uniformly resampling technique

It is well known that, long-time integration improves the detection performance of radar system, which is however limited by the range migration (RM) and Doppler frequency migration (DFM) caused by target's high velocity and acceleration. To solve this problem, this paper proposed a three-dimensional modified cross correlation function (3DMCCF) method for maneuvering radar targets. In this method, we define a new cross correlation function under a designing frame based on non-uniformly resampling technique. By using the new function, the target's RM and DFM can be eliminated at the same time. The resulting signal is a three-dimensional complex sinusoid. Finally the integration is achieved efficiently by performing inverse fast Fourier transforms (IFFTs) and fast Fourier transforms (FFTs). The proposed method can work in low signal to noise ratio (SNR) environment and is applicable for multi-target scene. Compared with the generalized Radon Fourier transform (GRFT) and the Radon Lv's distribution (RLVD) algorithms, the proposed method is free from searching approach and has lower computational complexity. The effectiveness of the proposed method is demonstrated by simulations and real-data processing.

Generalizing the inverse FFT off the unit circle

This paper describes the first algorithm for computing the inverse chirp z-transform (ICZT) in O(n log n) time. This matches the computational complexity of the chirp z-transform (CZT) algorithm that was discovered 50 years ago. Despite multiple previous attempts, an efficient ICZT algorithm remained elusive until now. Because the ICZT can be viewed as a generalization of the inverse fast Fourier transform (IFFT) off the unit circle in the complex plane, it has numerous practical applications in a wide variety of disciplines. This generalization enables exponentially growing or exponentially decaying frequency components, which cannot be done with the IFFT. The ICZT algorithm was derived using the properties of structured matrices and its numerical accuracy was evaluated using automated tests. A modification of the CZT algorithm, which improves its numerical stability for a subset of the parameter space, is also described and evaluated.

Coherent Detection and Parameter Estimation for Radar High-Speed Maneuvering Target Based on FAF–LVD

Long-time coherent integration can remarkably improve the detection and motion parameter estimation ability of radar for maneuvering targets. Unfortunately, the linear range migration, quadratic range migration (QRM), and Doppler frequency migration (DFM) within the coherent processing interval seriously degrade the target detection and parameter estimation performance. In this regard, a novel coherent integration approach based on frequency autocorrelation function (FAF) and Lv’s distribution (LVD), i.e., FAF–LVD, is proposed in this paper. The QRM is firstly removed by the second-order keystone transform. Then, the FAF with a variable delay is introduced to remove the DFM, followed by the scaled Fourier transform to achieve coherent integration. Finally, the acceleration and velocity are estimated simultaneously by LVD. Analysis demonstrates that FAF–LVD could be efficiently implemented via complex multiplications, the fast Fourier transform (FFT) and inverse FFT. Detailed comparisons with several representative methods indicate that FAF–LVD achieves a better balance among computational complexity, detection ability, and parameter estimation performance. Extensive simulations are presented to validate the effectiveness of FAF–LVD method.

Hardware-efficient implementation and experimental demonstration of Hermitian-symmetric IFFT for optical DMT transmitter.

Optical discrete multi-tone (DMT) is one type of direct-detection optical orthogonal frequency-division multiplexing (DDO-OFDM), and it is more suitable for cost-sensitive access networks and optical interconnections due to its simple structure. In DMT transmitter, inverse fast Fourier transform (IFFT) is an essential function for achieving OFDM modulation, and its input data are constrained to have Hermitian symmetry (HS). To support high-speed DMT signal generation, a fully-parallel implementation of IFFT is preferable. However, the hardware implementation of the conventional complex-valued IFFT (CC-IFFT) requires large area and has high power consumption. Based on the nature of HS, we design and implement a fully-parallel pipelined 128-point radix-2 decimation-in-time Hermitian-symmetric IFFT (HS-IFFT) by using a single field programmable gate array (FPGA) chip. On-chip resource utilization is analyzed for both the proposed HS-IFFT and CC-IFFT. It exhibits that the HS-IFFT can save up to 35% multipliers, 49% registers and 43% look-up tables (LUTs) compared to the CC-IFFT. Also, by using the HS-IFFT and CC-IFFT, two FPGA-based real-time baseband DMT transmitters are implemented and power consumption is estimated. More than 32% of on-chip power is saved by using the HS-IFFT. Moreover, the two DMT transmitters are also experimentally demonstrated in a short-reach directly-modulated laser (DML)-based optical DMT system. The experimental results show that the HS-IFFT-DMT has the same bit error rate (BER) and error vector magnitude (EVM) performances as the CC-IFFT-DMT in both electrical/optical back-to-back cases (EB2B/OB2B) and post 20-km single-mode fiber (SMF) transmission.

Fast Fourier-Domain Optimization Using Hybrid L1−/L${}_{p}$ -Norm for Autofocus in Airborne SAR Imaging

In maneuverable airborne synthetic aperture radar (SAR), high-frequency phase errors (HPEs), which are hard to be compensated by the phase gradient autofocus, often occur causing spurious targets and contrast degradation in SAR imagery. The metric-optimization approaches improve the phase error estimation scalability, including HPEs, but show much lower speed because of the computational burden by the inverse fast Fourier transform (IFFT). Proposed autofocus based on the metric optimization enables the rapid estimation with the scalability including the HPE by eliminating the IFFT. In addition, the metric is adapted to the range compressed data corresponding to the input of the autofocus taking advantage of the convergence speed and the stability in its optimization using a hybrid form of L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-</sub> and L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</sub> -norm. In the simulation, we focused on the suggestion of the proof of performance generality.

Computationally efficient TDOA and FDOA estimation algorithm in passive emitter localisation

This study addresses the joint time difference of arrival (TDOA) and frequency difference of arrival (FDOA) estimation problem in passive emitter localisation, involving range migration during the observation time. A computational efficient estimation algorithm based on scaled Fourier transformation is proposed. This method can effectively remove the RM and accomplish the parameter estimation. Cross-terms suppression ability of the proposed method is also analysed and its characteristic indicates the applicability in the scenario of multi-targets. The whole estimation step can be fast implemented by complex multiplications, fast Fourier transformation (FFT) and inverse FFT without any searching process. Compared with the ideal maximum likelihood estimator via extensive numerical experiments, the proposed method can achieve comparable estimation performance and have gained more than ten thousand times reduction in the computational cost, which helps practical application.

The application of OFDM in optical fiber communication systems

Orthogonal frequency division multiplexing (OFDM) is a special multi-carrier transmission technology. It utilizes digital signal processing (DSP) to perform inverse Fast Fourier transform (IFFT) and generates a set of orthogonal subcarriers for parallel transmission of low-rate digital signals, achieving the transmission of high-speed digital signals. It has the advantages of high spectral efficiency and anti-dispersion, and has broad applications in large-capacity and long-distance optical fiber communication systems and optical access networks. In this paper, the working principle, structure and application of OFDM in optical fiber communication systems are investigated. Then the problems which should be solved in the application of OFDM in optical communication systems are discussed. Finally, the development of OFDM system is prospected.

Efficient Algorithm for SAR Refocusing of Ground Fast-Maneuvering Targets

The synthetic aperture radar (SAR) image of moving targets will defocus due to the unknown motion parameters. For fast-maneuvering targets, the range cell migration (RCM), Doppler frequency migration and Doppler ambiguity are complex problems. As a result, focusing of fast-maneuvering targets is difficult. In this work, an efficient SAR refocusing algorithm is proposed for fast-maneuvering targets. The proposed algorithm mainly contains three steps. Firstly, the RCM is corrected using sequence reversing, matrix complex multiplication and an improved second-order RCM correction function. Secondly, a 1D scaled Fourier transform is introduced to estimate the remaining chirp rate. Thirdly, a matched filter based on the estimated chirp rate is proposed to focus the maneuvering target in the range–azimuth time domain. The proposed method is computationally efficient because it can be implemented by the fast Fourier transform (FFT), inverse FFT and non-uniform FFT. A new deramp function is proposed to further address the serious problem of Doppler ambiguity. A spurious peak recognition procedure is proposed on the basis of the cross-term analysis. Simulated and real data processing results demonstrate the validity of the proposed target focusing algorithm and spurious peak recognition procedure.

The organisation of vascular smooth muscle cells; a quantitative Fast Fourier Transform (FFT) based assessment

BackgroundThe existence of a helical arrangement of vascular smooth muscle cells in the wall of relatively large blood vessels has been known of for at least 80 years. In that time various workers have proposed mathematical models of vascular function that have incorporated one or more helix. However, most of this work has focussed on large conduit vessels such as aorta and carotid arteries. The smaller resistance arteries are more difficult to study and do not have such an apparent helical arrangement, although there are suggestions of its existence in the patterning of smooth muscle cells in the tunica media. MethodWe have employed confocal laser scanning microscopy (CLSM) and a relatively simple Fast Fourier Transform (FFT) based image analysis method to examine a collection of extended focus (z-projection) images of the tunica media of mouse superior mesenteric artery. A fluorescent nuclear stain (Syto 61) was used to identify smooth muscle cell orientation and arrangement. Thirty-six CLSM datasets representing the tunica media of mesenteric arteries taken from 12 C57/black mice were collected for analysis. ResultsMeasurements of Z-projection (extended focus) images, of the tunica media, were compared with measurements made on inverse FFT images where the high frequency information was removed. The results, of both measurement types, indicated the existence of an underlying basic helical arrangement of cells that has a pitch angle of 49°. 3D electron microscopy-based models of individual smooth muscle cells (from the tail artery) were generated to highlight their heterogeneity and orientational position within the tunica media. ConclusionInverse FFT images provide a more objective means of measuring cell organisation and therefore could be used in automated processes. Whilst we propose the existence of an underlying helical arrangement of smooth muscle cells, we do not discount the existence of other helices each with different angles, but these may be more difficult to detect and may extend radially (deep within the tunica media) as well as longitudinally.

A Novel Noise Suppression Channel Estimation Method Based on Adaptive Weighted Averaging for OFDM Systems

Orthogonal frequency division multiplexing (OFDM) systems have inherent symmetric properties, such as coding and decoding, constellation mapping and demapping, inverse fast Fourier transform (IFFT) and fast Fourier transform (FFT) operations corresponding to multi-carrier modulation and demodulation, and channel estimation is a necessary module to resist channel fading in the OFDM system. However, the noise in the channel will significantly affect the accuracy of channel estimation, which further affects the recovery quality of the final received signals. Therefore, this paper proposes an efficient noise suppression channel estimation method for OFDM systems based on adaptive weighted averaging. The basic idea of the proposed method is averaging the last few channel coefficients obtained from coarse estimation to suppress the noise effect, while the average frame number is adaptively adjusted by combining Doppler spread and signal-to-noise ratio (SNR) information. Meanwhile, to better combat the negative effect brought by Doppler spread and inter-carrier interference (ICI), the proposed method introduces a weighting factor to correct the weighted value of each frame in the averaging process. Simulation results show that the proposed channel estimation method is effective and provides better performance compared with other conventional channel estimation methods.

A frequency domain based signal combining method for distributed antenna arraying

Distributed antenna arraying is a promising technology for weak signal reception. The received signals from different antennas are aligned and combined to improve the receiving signal-to-noise ratio (SNR). However, the combining performance is serious degraded by the difference of sampling frequency between antennas. In this paper, a frequency domain based signal combining method is proposed to solve this problem. The unaligned sampled data in time domain of the received signals are transformed to frequency domain using fast Fourier transform (FFT). The received signals can be aligned in frequency domain when their spectrum resolutions are the same. Therefore the received signals with the same total sampling time can be aligned and combined in frequency domain and then the combined signal is recovered using inverse fast Fourier transform (IFFT). Numerical simulations with two typical modulation types, i.e., PSK and PCM/BPSK/PM, prove the validity and robustness of this method.

Optimized semiblind sparse channel estimation algorithm for MU-MIMO OFDM system

In Multiple Input Multiple Output - Orthogonal Frequency Division Multiplexing (MIMO-OFDM) systems, the channel plays an imperative role as the multipath. The channel estimation frameworks specifically designed for the demanding channel conditions with faster time-varying characters are separately emphasized. The prevailing Channel Estimation (CE) methodologies are incredibly complex. To resolve such complexities, this paper proposed an Optimized Semi-Blind Sparse (OSBS) CE algorithm for MU-MIMO OFDM. On the transmitter block, initially, the QPSK modulation is implemented to modulate an input signal. Subsequently, the Pulse Shaping Algorithm (PSA) used for mitigating the ISI (Inter-Symbol Interferences). For symbol mapping, an IFFT (Inverse Fast Fourier Transforms) operation performed at each transmitter. Next, transmit the symbols over the Multipath channel via transmitter’s antennas towards the receiver’s antennas by adding AWGN (Additive White Gaussian Noise). The operations in the transmitter inversely done on the receiver block. Then CE is done by utilizing the OSBS algorithm, and the cost function is lessened by employing EDE (Enhanced Differential Evolution) algorithm. Lastly, the Channel Capacity (CC) is called gauge. Experiential result of the proposed system gives better results when contrasted with the other methods centered on Bit Error Rate (BER), PSNR, Symbol Error Rate (SER), LS, and MMSE.

Hydrodynamic Features of an Undular Bore Traveling on a 1:20 Sloping Beach

The hydrodynamic characteristics, including local and convective accelerations as well as pressure gradient in the horizontal direction, of the external stream of an undular bore propagating on a 1:20 sloping beach are experimentally studied. A bore with the water depth ratio of 1.70 was generated downstream of a suddenly lifted gate. A high-speed particle image velocimetry was employed to measure the velocity fields during the run-up and run-down motions. The time series of free surface elevation and velocity field/profile of the generated bore, comprising a pure bore accompanied by a series of dispersive leading waves, are first demonstrated. Based on the fast Fourier transform (FFT) and inverse FFT (IFFT) techniques, the free surface elevation of leading waves and the counterpart of pure bore are acquired separately at a specified measuring section (SMS), together with the uniform horizontal velocity of the pure bore. The effect of leading-wave-induced velocity shift on the velocity profiles of the generated bore are then evaluated at the SMS. To understand the calculation procedure of accelerations and pressure gradient, three tabulated forms are provided as illustrative examples. Accordingly, the relationships among the partially depth-averaged values of the non-dimensional local acceleration, convective acceleration, total acceleration and pressure gradient of the generated/pure bore acquired at the SMS versus the non-dimensional time are elucidated. The trends in the non-dimensional accelerations and pressure gradient of the external stream of generated bore are compared with those of the pure bore. During the run-up motion from the instant of arrival of the bore front to the moment of the peak level at the SMS, continuous decrease in the onshore uniform horizontal velocity, and successive deceleration of the pure bore in the onshore direction are evidenced, exhibiting the pure bore under the adverse pressure gradient with decreasing magnitude. However, the pure bore once ridden by the leading waves is decelerated/accelerated spatially and accelerated/decelerated temporally in the onshore direction during the rising/descending free surface of each leading wave. This fact highlights the effect of pre-passing/post-passing of the leading wave crest on the velocity distribution of generated bore. It is also found that, although the leading waves have minor contribution on the power spectrum of the free surface elevation as compared with that of the pure bore, the leading waves do play an important role on the magnitudes of both accelerations and pressure gradient. The largest magnitude of the acceleration contributed by the leading waves is around 26 times the counterpart contributed by the pure bore. Further, during the run-down motion right after the moment for the peak level of the bore, a linear increase in the magnitude of the offshore uniform horizontal velocity and a constant local acceleration with increasing time are both identified. The partially depth-averaged value of the non-dimensional pressure gradient is equal to a small negative constant (−0.0115) in the offshore direction, indicating that the bore is subject to a constant favorable pressure gradient.

Efficient Design of Selective Mapping and Partial Transmit Sequence Using T-OFDM

Selective mapping (SLM) and partial transmit sequence (PTS) are attractive schemes for mitigating the high peak power inherent in orthogonal frequency division multiplexing (OFDM) signals. However, the high computational complexity and redundant side information (SI) bits have been identified as the main limitations for such techniques. The high computational complexity is mainly due to the need to perform several inverse fast Fourier transforms (IFFTs), and phase optimization process at the transmitter side. Therefore, this paper presents new SLM and PTS designs using a low complexity T-transform rather than IFFT. The use of the T-transform with SLM achieves a considerable computational complexity and peak-to-average power ratio (PAPR) reduction. Furthermore, we apply the T-transform to PTS and derive two different configurations that compromise the SI requirements and PAPR reduction. All the proposed schemes do not affect the original power spectrum of OFDM signals. The complexity analysis show that the proposed schemes have much lower complexity as compared to conventional schemes. Moreover, simulation results demonstrate that the proposed schemes are resilient to dispersion arising from multipath propagation, which is due to the frequency diversity introduced by the T-transform.

Improved Hybrid Blind PAPR Reduction Algorithm for OFDM Systems

The ever growing demand for high data rate communication services resulted into the development of long-term evolution (LTE) technology. LTE uses orthogonal frequency division multiplexing (OFDM) as a transmission technology in its PHY layer for down-link (DL) communications. OFDM is spectrally efficient multicarrier modulation technique ideal for high data transmissions over highly time and frequency varying channels. However, the transmitted signal in OFDM can have high peak values in the time domain due to inverse fast Fourier transform (IFFT) operation. This creates high peak-to-average power ratio (PAPR) when compared to single carrier systems. PAPR drives the power amplifiers to saturation degrading its efficiency by consuming more power. In this paper a hybrid blind PAPR reduction algorithm for OFDM systems is proposed, which is a combination of distortion technique (Clipping) and distortionless technique (DFT spreading). The DFT spreading is done prior to clipping reducing significantly the probability of having higher peaks in the composite signal prior to transmission. Simulation results show that the proposed algorithm outperforms unprocessed conventional OFDM transmission by 9 dB. Comparison with existing blind algorithms shows 7 dB improvement at error rate 10 –3 and 3 dB improvement at error rate 10 –1 when operating in flat fading and doubly dispersive channels, respectively. Keywords: LTE Systems; OFDM; Peak to Average Power Ratio; DFT spreading; Signal to Noise Power Ratio;

Optimizing Forward Error Correction Codes for COFDM With Reduced PAPR

Coded orthogonal frequency-division multiplexing (COFDM) is a popular modulation technique for wireless communication that guarantees reliable transmission of data over noisy wireless channels. However, a major disadvantage in implementing it is its resulting high peak to average power ratio (PAPR). Including forward error correction (FEC) in the orthogonal frequency division multiplexing (OFDM) system enables the avoidance of transmission errors. Nevertheless, the selected code may impact the value of PAPR. The objective of this paper is to analyze the impact of FEC on the PAPR for the COFDM system based on the autocorrelation of the signal, before the inverse fast Fourier transform (IFFT) block in the COFDM system, the evaluation of the complementary cumulative distribution function (CCDF) of PAPR, and the bit error rate (BER). The autocorrelation of the COFDM system is calculated based on a Markov chain model. From the results, we can reach a conclusion on the characteristics we need to consider in order to choose the codes relating to the PAPR performance in the COFDM system.

FPGA implementation of IFFT architecture with enhanced pruning algorithm for low power application

The improved architecture of IFFT is developed and presented in this paper. Number of arithmetic operation is more in the normal working of conventional Inverse Fast Fourier Transform. An enhanced pruning algorithm is utilized to reduce the number of arithmetic operations in the IFFT architecture. The performance of the improved IFFT architecture is estimated to find its suitability for the low power Wireless communication system. It is implemented in 8-point IFFT architecture using decimation in frequency algorithm using hardware description language. It is implemented in XC7z020clg484-1 from Zynq-7000 family with a frequency of 220 MHz. It is found that the improved IFFT architecture reduces maximum of 40% of the arithmetic operations, which reduces the power consumption by maximum of 10%. Hence the improved IFFT architecture can be used in the signal processing units in wireless application.

An efficient retrieval algorithm of encrypted speech based on inverse fast Fouriertransform and measurement matrix

In this paper, we present an efficient retrieval algorithm for encrypted speech based on an inverse fast Fourier transform and measurement matrix. Our approach improves query performance, as well as retrieval efficiency and accuracy, compared to existing content-based encrypted speech retrieval methods. Our proposed algorithm constructs a perceptual hash scheme using perceptual hash sequences from original speech files. By classifying the sequences and applying run-length compression, we decrease the cloud storage required for the hash index. We secure the speech database by encrypting it with Henon chaos scrambling, which offers excellent resistance to attacks. Experimental results show that the robustness, discrimination, and feature extraction efficiency of our proposed method are better than the existing alternatives, with good recall and precision ratios and with high retrieval efficiency and accuracy.

OFDM based FFT compared with OFDM based wavelet transform

In recent year the orthogonal frequency division multiplexing widely used in wireless communication system, the conventional structure of OFDM used Inverse Fast Fourier Transform for modulation and multiplexing the data at the transmitter side and used Fast Fourier Transform at the receiver to demodulation and demultiplexing the data. In this paper, Inverse Wavelet Transform IWT used in transmitter instead of IFFT and Wavelet Transform WT in receiver side instead of FFT and compared between two methods with different noise in the AWGN channel. The performance found by bit error rate BER. Also different modulation scheme have been used (16-QAM, 32-QAM, 64-QAM and 128-QAM) and different types of wavelet filters Daubechies (Db-3, Db-5, Db-8, Db-10) and Haar filter. to compare between them and find which achieved better performance.

Direct growth of ZnTe on Si(100) and Si(111) substrate by molecular beam epitaxy

ZnTe was directly grown on Si(100) and Si(111) substrate respectively using elemental sources by molecular beam epitaxy. It was found that ZnTe can be grown on both Si(111) and Si(100) substrates in alignment with the orientation of (111). A microscopic growth interface model of diamond crystal structure was proposed to explain this phenomenon. This is a supplement to the existing theory of predicting possible crystalline orientation alignment relationship based on lattice mismatch value in the heteroepitaxial growth on (100) surfaces of zinc blende structure. High resolution transmission electron microscopy (HRTEM) was used to investigate the ZnTe(111)/Si(100) and ZnTe(111)/Si(100) interface. Application of digital image processing involving a filtered inverse fast Fourier transformation revealed an array of misfit dislocations at the ZnTe/Si(111) interface.