2D grid architectures for the DFT and the 2D DFT

New algorithms for the DFT and the 2-dimensional DFT are presented. The DFT and the 2-dimensional DFT matrices can be expressed as the Kronecker product of DFT matrices of smaller dimension. These algorithms are synthesized by combining the efficient factorization of the Kronecker product of matrices with the highly hardware efficient recursive implementation of the smaller DFT matrices, to yield these algorithms. The architectures of the processors implementing these algorithms consist of 2-dimensional grid of processing elements, have temporal and spatial locality of connections. For computing the DFT of sizeN or for the 2D DFT of sizeN=N ₁ byN ₁, these algorithms require 2N multipliers and adders, take approximately computational steps for computing a transform vector, and take approximately computation steps between the computation of two successive transform vectors.     

Recursive optimal pruning with applications to tree structuredvector quantizers

A pruning algorithm of P.A. Chou et al. (1989) for designing optimal tree structures identifies only those codebooks which lie on the convex hull of the original codebook's operational distortion rate function. The authors introduce a modified version of the original algorithm, which identifies a large number of codebooks having minimum average distortion, under the constraint that, in each step, only modes having no descendents are removed from the tree. All codebooks generated by the original algorithm are also generated by this algorithm. The new algorithm generates a much larger number of codebooks in the middle- and low-rate regions. The additional codebooks permit operation near the codebook's operational distortion rate function without time sharing by choosing from the increased number of available bit rates. Despite the statistical mismatch which occurs when coding data outside the training sequence, these pruned codebooks retain their performance advantage over full search vector quantizers (VQs) for a large range of rates.     

Split-radix algorithm for 2D DFT

A general split-radix algorithm is presented to compute 2D discrete Fourier transforms of sequence length q'2^m by q'2 ^m where q is an odd integer. By setting different values of q, DFT's of various sequence lengths can be efficiently computed. When q=3 for example, savings in the number of operations can be achieved in comparison with that needed by other algorithms     

Calculation of bit error rates in all-optical signal processingapplications exploiting nondegenerate few-wave mixing in semiconductoroptical amplifiers

We present a theoretical analysis of the noise properties in a nonlinear semiconductor optical amplifier. We concentrate on amplifiers operating as nonlinear media mediating four-wave mixing processes. We calculate error probabilities for different configurations that use four-wave mixing in all-optical signal manipulation such as frequency conversion and time domain demultiplexing. We identify a data induced nonlinear interference process as having a major adverse impact on the performance of nonlinear semiconductor optical amplifiers and propose the use of a variable decision threshold to overcome it. We compare the performance of the variable threshold to that using an optimal fixed threshold and show significant improvement in performance. We treat the cases of NRZ modulated data as well as the case of short optical pulses and demonstrate a vast advantage for the short pulses in terms of the required input field intensities and the achievable bit error rates     

PAC-Bayesian framework based drop-path method for 2D discriminative convolutional network pruning

Deep convolutional neural networks (CNNs) have demonstrated its extraordinary power on various visual tasks like object detection and classification. However, it is still challenging to deploy state-of-the-art models into real-world applications, such as autonomous vehicles, due to their expensive computation costs. In this paper, to accelerate the network inference, we introduce a novel pruning method named Drop-path to reduce model parameters of 2D deep CNNs. Given a trained deep CNN, pruning paths with different lengths is achieved by ordering the influence of neurons in each layer on the probably approximately correct (PAC) Bayesian boundary of the model. We believe that the invariance of PAC-Bayesian boundary is an important factor to guarantee the generalization ability of deep CNN under the condition of optimizing as much as possible. To the best of our knowledge, this is the first time to reduce model size based on the generalization error boundary. After pruning, we observe that the convolutional kernels themselves become sparse, rather than some being removed directly. In fact, Drop-path is generic and can be well generalized on multi-layer and multi-branch models, since parameter ranking criterion can be applied to any kind of layer and the importance scores can still be propagated. Finally, Drop-path is evaluated on two image classification benchmark datasets (ImageNet and CIFAR-10) with multiple deep CNN models, including AlexNet, VGG-16, GoogLeNet, and ResNet-34/50/56/110. Experimental results demonstrate that Drop-path achieves significant model compression and acceleration with negligible accuracy loss.

     

Stochastic Modelling and 3D Minimum Variance Recursive Estimation of Image Sequences

In this paper the 3D minimum variance filtering problem is considered. The proposed spatiotemporal filter is derived according to the assumption that the 3D signal can be modelled by an ensemble of smooth 3D gaussian random fields. The resulting filtering algorithm is given by an optimal combination of three 1D estimators and is endowed with an information on the location about the spatiotemporal discontinuities of the signal. This allows the filter to conciliate the two opposite requirements of an effective noise reduction and edge preservation.     

二维DFT域全相位数字滤波器设计与实现

一维全相位数字信号处理已经在谱分析、自适应、模板设计、滤波器组分析与综合等领域得到应用,但对于二维全相位理论的推导很少而且没有实现的方法.因此,本文在一维全相位信号处理方法的基础上,首先系统地分析二维全相位信号处理模式,理论推导出无窗、单窗和双窗模式下传输函数表达式;其次,首次设计出二维全相位处理的系统实现框图,并对算法复杂度进行了优化分析;还有,对二维全相位信号处理的性质进行了分析;最后,借助MATLAB实现了DFT滤波器设计并画出3D特性曲面,完成设计二维DFT全相位滤波器的理论、方法和实验验证.     

Robocup3D仿人机器人中基于频率加权的ZMP补偿算法

本文提出了一种新的ZMP补偿算法,本算法以仿人机器人的ZMP误差信号的频率分析为基础.ZMP(zero moment point)即零力矩点,是仿人机器人的一个重要的物理量,根据双足机器人系统的ZMP方程和实际的ZMP信息,在Tomoya Sato和-Kouhei提出的ZMP的补偿方法的基础上,提出一种新的补偿方法,根...     

一种3D电视背光扫描和3D红外信号发射控制新方法

液晶(LCD)电视已经相当普及,液晶显示需要背光。当前主要采用LED背光,在该背光控制中用一个MCU控制LED驱动以产生背光。随着技术的发展,3D电视在市场占有率不断提升,在3D电视中,也需要一个MCU来发射3D眼镜同步信号。基于此,本文提出一种基于一颗高性能单片机MSP430G2553实现3D电视的背光扫描和3D眼镜同步信号控制方法,3D眼镜同步信号产生采用红外发射来产生,该设计方案具有低功耗、成本低、性能可靠的优点。     

An Orthogonal Time-Frequency Extraction Approach to 2D Systolic Architecture for 1D DFT Computation

An expandable two-dimensional systolic array consisting of N homogeneous processing elements in a rectangular sturcture to compute the one-dimensional DFT transform is proposed. DFT of size N = M² can be computed in 2M steps of pipelined operations, achieving the optimal Area–Time complexity of AT² = O(N²). The architecture is based on a new approach that exploits the symbiosis between the one-dimensional systolic arrays of Kung [6] and Chang [7]. After a two-dimensional formulation with Common Factor Algorithm, recursive time and frequency extractions are applied to the column and row transforms respectively. Twiddle factor multiplication is integrated gracefully into the row recursion. The rearrangement of the input data enables the recursive operations to be pipelined orthogonally in the dual-mode processing elements. The proposed array structure is modular and expandable. A DFT of size 2^LN can be readily computed with 2^L N-size arrays abutted together without reconfiguration. VHDL modules have been written and simulated successfully for the proposed architecture.     

用DFT对连续信号谱分析的误差问题

谱分析是数字信号处理中的一个重要问题,初学者普遍对连续信号谱分析理解不深,尤其是在误差分析时缺乏统一示例,更容易产生困惑。介绍了用离散傅里叶变换(DFT)对连续信号进行谱分析的过程,并详细说明了误差产生的原因和减小误差的方法。而且通过对模拟信号谱分析的实例全面说明了各项误差的影响及解决方案,并应用Matlab直观地进行了分析和对比验证。     

3D FDTD Implementation for Scattering of Electric Anisotropic Dispersive Medium Using Recursive Convolution Method

The finite-difference time-domain method based on recursive convoltion method (RC-FDTD) for the electric anisotropic dispersive medium is discussed in detail. To exemplify the availability of the three-dimensional RC-FDTD algorithm, the backscattering Radar-Cross-Section(RCS) of a non-magnetized plasma sphere is computed, and the numerical results are the same as the one of the Shift Operater-FDTD method, and show that the RC-FDTD method is correct and efficient. In addition, the co-polarized and cross-polarized backscattering time-domain of a magnetized plasma sphere are obtained by the RC-FDTD algorithm. The results show that when the external magnetic field is implemented, the cross-polarized component appear, evidently.     

Digital signal processing. 1. Digital filters and the DFT

The wide availability of inexpensive and relatively fast digital signal processing chips has given rise to a great expansion in the application of these devices in many areas, particularly consumer electronics. The ease with which digital processing operations can now be performed has allowed the realisation of highly sophisticated signal processing algorithms. The paper introduces the first of two main areas of digital signal processing, namely digital filtering and Fourier transformation. An overview is presented of both finite impulse response and infinite impulse response digital filter types. These designs are later extended to cover the concept of an adaptive filter, which automatically trains or adapts its characteristics or frequency response to compensate for signal distortions or interference. Finally, the discrete Fourier transform is introduced for measuring the frequency spectrum of a signal     

二维双原型完全过采样DFT调制滤波器组的快速设计方法

传统的2维大规模滤波器组的设计方法具有复杂度高的缺点。该文提出一种设计2维双原型滤波器组的快速方法,该方法利用近似完全重构的条件,并采用完全过采样的离散傅里叶变换(DFT)调制滤波器组来设计。新算法将两个原型滤波器的设计问题归结为一个无约束优化问题,其中目标函数为滤波器组的总体失真(传递失真和混叠失真)与原型滤波器阻带能量的加权和,利用目标函数的梯度向量,通过双迭代机制求解该优化问题。单步迭代中,利用矩阵求逆的等效条件和块Toeplitz矩阵求逆的快速算法,显著地降低了计算复杂度。理论分析和数值实验表明,新算法可以得到整体性能更好的滤波器组,计算复杂度大幅度降低,故可以快速设计大规模的2维滤波器组。     

一种低功耗2DDFT芯片的前端设计与验证

本文基于Nangate45nmCMOS开放工艺库,设计了一种适用于数字图像处理的二维离散傅里叶变换（2-DimensionalDiscreteFourierTransform,2DDFT）芯片,并对其进行了前端验证．该芯片采用时域抽取法基-2快速傅里叶算法（Radix-2FastFourierTransform）以及优化的流水线结构,使得设计难度大大降低,处理速度得到较大提升．功能验证和逻辑综合后的结果显示,该芯片能够在250MHz时钟频率下工作,只需延迟1211个时钟周期即开始输出一个由16位单精度定点数构成的32×32位复数矩阵的DFT值,且在0．9V电压下功率为143mW,表明芯片在速度、精度以及功耗上均满足低功耗数字图像处理系统的要求．     

基于二维DFT域全相位滤波的图像多分辨率分析

图像多分辨率分析在信号滤波、图像除噪、图像 融合、图像边缘检测领域中应用广泛。该文设计了一种新的 图像多分辨率分析方法,通过对全相位系统函数进行谱分解,实现了基于全相位的严格功率 互补的高低通滤波器设计, 按照全相位处理的基本理论,选择不同的正交变换方式和基窗函数可以方便地设计出具有不 同分析/合成效果的全相位波 包。实验表明,DFT域全相位分析滤波器可以实现对图像的多层分解,由合成滤波器还原得 到的图像误差几乎为零。在 图像数据压缩、自适应除噪方面具有较为广泛的应用前景。     

Design of M‐Channel IIR Uniform DFT Filter Banks Using Recursive Digital Filters

In this paper, we propose a method for designing a class of M‐channel, causal, stable, perfect reconstruction, infinite impulse response (IIR), and parallel uniform discrete Fourier transform (DFT) filter banks. It is based on a previously proposed structure by Martinez et al. [1] for IIR digital filter design for sampling rate reduction. The proposed filter bank has a modular structure and is therefore very well suited for VLSI implementation. Moreover, the current structure is more efficient in terms of computational complexity than the most general IIR DFT filter bank, and this results in a reduced computational complexity by more than 50% in both the critically sampled and oversampled cases. In the polyphase oversampled DFT filter bank case, we get flexible stop‐band attenuation, which is also taken care of in the proposed algorithm.     

基于DDS三分量感应测井信号源系统设计

介绍了直接数字频率合成（DDS）的原理,依据其基本原理设计一款基于PIC单片机控制的DDS信号源,单片机通过SPI总线方式接收来自上位机发来的频率信号,将其存入EEPROM中,并转换为40位频率控制字写入DDS芯片中使其输出所需频率信号。DDS输出的频率信号含有大量杂散信号,经过7阶椭圆滤波器滤除杂散信号得到纯净的频率信号,再经功率放大后输出至后一级大功率放大电路。实验表明该信号源输出频率范围在1Hz～1MHz,准确度可达0.01Hz,满足三分量感应测井的要求。