Fractional cosine, sine, and Hartley transforms

In previous papers, the Fourier transform (FT) has been generalized into the fractional Fourier transform (FRFT), the linear canonical transform (LCT), and the simplified fractional Fourier transform (SFRFT). Because the cosine, sine, and Hartley transforms are very similar to the FT, it is reasonable to think they can also be generalized by the similar way. We introduce several new transforms. They are all the generalization of the cosine, sine, or Hartley transform. We first derive the fractional cosine, sine, and Hartley transforms (FRCT/FRST/FRHT). They are analogous to the FRFT. Then, we derive the canonical cosine and sine transforms (CCT/CST). They are analogous to the LCT. We also derive the simplified fractional cosine, sine, and Hartley transforms (SFRCT/SFRST/SFRHT). They are analogous to the SFRFT and have the advantage of real-input-real-output. We also discuss the properties, digital implementation, and applications (e.g., the applications for filter design and space-variant pattern recognition) of these transforms. The transforms introduced in this paper are very efficient for digital implementation. We can just use one half or one fourth of the real multiplications required for the FRFT and LCT to implement them. When we want to process even, odd, or pure real/imaginary functions, we can use these transforms instead of the FRFT and LCT. Besides, we also show that the FRCT/FRST, CCT/CST, and SFRCT/SFRST are also useful for the one-sided (t ∈ [0, ∞]) signal processing     

A New Transceiver Scheme for OFDMA System Based on Discrete Cosine Transform and Phase Modulation

A high peak-to-average power ratio of the transmit signal is a major drawback of multicarrier transmissions, such as orthogonal frequency division multiplexing (OFDM) and orthogonal frequency division multiple access (OFDMA). An alternative approach to mitigate the peak-to-average power ratio (PAPR) problem is based on signal transformation using phase modulation (PM). A phase modulation based systems have the advantage of constant envelope (CE) signals and the ability to improve the diversity of multipath channels. In this paper, a different implementation of discrete Fourier transform DFT-OFDMA system which is based on discrete cosine transform (DCT) is proposed. The DCT-OFDMA system is then used to develop a new transceiver system called DCT-OFDMA-PM which refers to discrete cosine OFDMA with phase modulation. The PM input signal to be modulated must be real which can be produced using DCT-OFDMA with pulse amplitude modulation (M-PAM). The new system involves a signal transformation prior to amplification. This gives the advantage of CE (i.e. 0 dB PAPR). The proposed system is implemented with frequency domain equalization (FDE) to obtain high diversity gains over the frequency multipath channel. Simulation the PM-based systems with multipath fading can outperform that with single path fading.     

基于自适应正交小波基的图像分解

简单介绍了傅利叶变换以及傅立叶加窗变换的局限性，以及小波变换的提出对这一局限性的有效解决。重点介绍了小波变换基本原理，正交小波基的概念，以及正交小波分解回复算法。并用程序实现了正交小波基的统一解析构造方法。最后，利用小波算法对图像的水平和垂直细节进行提取，并给出了分解结果。     

Discrete Sine and Cosine Transforms in Single Carrier Modulation Systems

In the DFT-based single carrier frequency division multiple access (SC-FDMA) modulation system, the discrete Fourier transform (DFT) is usually exploited to divide the frequency channel. In this paper, we propose to use discrete sine/cosine transforms in place of the DFT for SC-FDMA. Eight SC-FDMA systems based on various DST/DCT types are studied. The bit error rate (BER) and the peak to average power ratio (PAPR) are used to evaluate performance of these eight DST/DCT-based SC-FDMA systems in comparison with the conventional DFT-based SC-FDMA system in an AWGN environment. Simulation results show that the DST/DCT-based SC-FDMA systems with the use of localized FDMA scheme can provide better BER performance and yet keep the same PAPR performance as compared to the DFT-based SC-FDMA system.     

分数频Fourier级数的信号分解

在传统的Fourier级数（FS）的基础上，提出了一种新的分数频FS（FFFS）的信号表示方法。该方法突破正交性要求下的频率为基频整数倍的限制，使得对信号的处理更加灵活、细致。首先给出了FFFS的定义，提出了获取分数频的试验法和二分频法；然后对压缩带宽、逼近项数、与原函数逼近度和Gibbs现象等性能与传统的Fs进行比较，发现FFFS有相当的优越性。     

FPGA Implementation of FFT Algorithm for OFDM Based IEEE 802.16d （Fixed WiMAX） Communications

The IEEE 802.16d communication standard uses orthogonal frequency division multiplexing （OFDM）. In the widely used OFDM systems, the fast Fourier transform （FFT） and inverse fast Fourier transform pairs are used to modulate and demodulate the data constellation on the sub-carriers. In this paper, a high level implementation of a high performance FFT for OFDM modulator and demodulator is presented. The design has been coded in Verilog and targeted into Xilinx Spartan3 field programmable gate arrays. Radix-22 algorithm is proposed and used for the OFDM communication system. The design of the FFT is implemented and applied to fixed WiMAX--IEEE 802.16d communi- cation standard. The results are tabulated and the hardware parameters are compared. The proposed architecture is least in number of multipliers used and the memory size, and second to the least in number of adders used.     

一种正弦波发生器的设计方法

介绍一种用数字方式获得正弦波的方法,该方法不需要使用存储器,完全通过计算得到正弦波的波形数据,而且得到正弦波的同时还可以得到相位正交的余弦波.通过实验仿真表明调节电路中的参数还可以调节输出幅度、频率和精度.这种电路可以用于离散傅里叶变换的计算和某些数字通信系统中,为正弦波、余弦波的设计提供一种新思路.     

A simple transmit diversity system for fading channels using shaped sinusoidal functions

This paper proposes a transmit-diversity system using a pair of orthogonal pulses. The system uses a set of orthonormal-basic functions, which contains four shaped-sinusoidal pulses with the same frequency. The first two elements in the set are shaped sine and cosine pulses. The second two elements are the same sine and cosine pulses but they are shaped with the Hilbert transform of the shaping pulse of the first two elements. The modulator in the proposed system produces two modulated symbols for each data symbol. It uses the first two elements in the proposed set in modulating the first modulated symbol and the second two elements in modulating the second modulated symbol. The modulated symbols are transmitted though two antennas. The diversity order of the proposed system is twice the number of antennas in the receiver. In the proposed system, no space-time coding is used and the channel gains change every symbol period. This is different from the Multiple-Input-Multiple-Output (MIMO) system. The receiver of the proposed system consists of two matched filters for each receiving antenna. No special detectors or interference cancelation techniques are used because there is no interference between the outputs of the matched filters.     

扩频通信系统中一种实现数字下变频器的算法

介绍了在扩频通信系统中一种产生数字下变频器(DDC)正交本振信号的方法--CORDIC算法,它在产生正弦值和余弦值时不需要太多的ROM资源,只需要简单的移位和加法等迭代操作,很容易在VLSI芯片上实现;文中也给出了用该算法实现DDC的VLSI结构.     

Low-power direct digital frequency synthesis for wirelesscommunications

A low-power direct digital frequency synthesizer (DDFS) architecture is presented. It uses a smaller lookup table for sine and cosine functions compared to already existing systems with a minimum additional hardware. Only 16 points are stored in the internal memory implemented in ROM (read-only memory). The full computation of the generated sine and cosine is based on the linear interpolation between the sample points. A DDFS with 60-dBc spectral purity 29-Hz frequency resolution, and 9-bit output data for sine function generation is being implemented in 0.8-μm CMOS technology. Experimental results verify that the average power dissipation of the DDFS logic is 9.5 mW (at 30 MHz, 3.3 V)     

基于FPGA的OFDM调制解调系统设计与实现

正交频分复用(OFDM)是第四代移动通信的核心技术,该技术在高速数据传输中得到了广泛的应用。文章给出了正交频分复用系统的基本模型和该系统所采用的调制与解调方法;根据OFMD的特点,本设计提出了一种基于IFFT/FFT的OFDM调制解调器的低成本FPGA的实现方法。在ISE环境下完成对OFDM无线通信系统中快速傅里叶变换算法的仿真,仿真结果表明快速傅里叶变换在OFDM技术中具有一定的使用价值。实践证明,该方法具有设计简单、快速、高效和实时性等特点。     

基于FPGA的正交数控振荡器(NCO)的设计与实现

在研究数控振荡器NCO工作原理的基础上,通过分析对比几种不同的NCO设计方法,采用了算法简单、节省资源的基于ROM查找表的设计方法。针对正交数控振荡器NCO的主要部件正余弦存储表、可变模计数器进行了算法设计和电路设计,并在Altera公司的FPGA上进行了验证,波形仿真结果表明了电路设计的正确性。采用查找表的方法可以有效提高系统功能的可扩展性和系统的可集成性,使得NCO功能模块可以通过配置存储表、频率控制字来满足多种应用场合下的NCO设计需要,可以广泛地应用于各种现代通信系统中。     

超宽带射频接收机的研制

超宽带(UWB)短距离无线通信技术是当前国内外研究的热点,直接序列超宽带(DS-UWB)方案和多带－正交频分复用(MB-OFDM UWB)方案是两个主要候选方案,其中多带-正交频分复用方案是较受重视的方案.本文针对MB-OFDM UWB系统,提出了一种双载波-正交频分复用(DC-OFDM UWB)的射频解决方案.该方案采用了两个相邻的子载波实现宽带通信,两个子载波是在中频部分采用合路/分路的方式,以降低硬件实现难度和系统的复杂度.设计了UWB射频接收机中的低噪声放大器(LNA)、频率合成器和解调器等关键部件,并建立了DC-OFDM UWB接收机实验演示平台.测试结果表明,研制的射频接收机满足FCC规定的射频指标要求,该方案也适用于其它的宽带通信系统中.     

改进的算术傅立叶变换（AFT）算法

算术傅立叶变换（AFT）是一种非常重要的傅立叶分析技术。AFT的乘法量少（仅为O（N））,算法结构简单,非常适合VLSI设计,具有广泛的应用。但AFT的加法量很大,为O（N∧2）,因此减少AFT的加法运算是很重要的工作。本文通过分析AFT的采样特点,给出了奇函数和偶函数的AFT的改进算法。然后在此基础上给出了一般函数的AFT的改进算法。改进算法比原算法的加法运算量降低了一半,因此计算速度快了一倍。本文改进的偶函数和奇函数的AFT算法还分别可以用来计算离散余弦变换（DCT）和离散正弦变换（DST）。     

Direct digital frequency synthesizers with polynomial hyperfolding technique

A new approach to design the phase to sine mapper of a direct digital frequency synthesizer (DDFS) is presented. The proposed technique uses an optimized polynomial expansion of sine and cosine functions to achieve either a 60-dBc spurious free dynamic range (SFDR), with a second-order polynomial, or a 80-dBc SFDR, with third-order polynomials. Polynomial computation is done by using new canonical-signed-digit (CSD) hyperfolding technique. This approach exploits all the symmetries of polynomials parallel computation and uses CSD encoding to minimize hardware complexity. CSD hyperfolding technique is also presented in the paper. The performances of new DDFS compares favorably with circuits designed using state-of-the-art Cordic algorithm technique.     

用于多媒体广播的正交频分复用模块集成系统

在０．１８μｍ工艺或更小的线宽下,可把各单个子系统有效地集成在同一块芯片上。通过讨论新工艺条件下具有语音视频图像处理功能的高速编码正效频分复用调制（ＯＦＤＭ）集成系统设计的可能方案,并剖析实例,对其离散余弦变换、快速傅里叶变换及前向纠错编码进行了分析。     

基于CORDIC算法的线性调频直接数字合成实现

本文介绍了一种应用CORDIC算法的线性调频直接数字合成(DDS)的实现方法。由于DDS输出的余弦波形直接由极坐标系中的幅度值和角度值确定,而CORDIC算法将极坐标系直接转换为包含正、余弦值的直角坐标系,从而实现频率数字调制。通过计算机仿真和FPGA硬件实现表明,采用这种算法的DDS是高精度和高效的。     

Integer sinusoidal transforms for image processing

The sine and cosine transforms, which are popular transforms for image coding, are members of a sinusoidal transform family. Each member of the family is the optimal KLT of a Markov process. This paper derives the conditions under which the order-8 sinusoidal transforms can be approximated by orthogonal integer transforms which can be implemented using integer arithmetic. Some integer transforms are derived as examples. The results show that for the popular even sine-1, even sine-2 and the cosine transforms, there is an infinite number of integer transforms and some have their transform component magnitudes less than eight. In LSI implementation, if low implementation cost and fast computation speed are paramount, then an integer transform of small component magnitudes can be chosen. If better performance is desired, integer transforms whose elements have larger magnitudes can be used. The availability of many integer transforms provides a design engineer the freedom to trade-off performance against simple implementation and speed.     

DFT-based optical offset-QAM OFDM: analytical,numerical, and experimental studies

We investigate discrete Fourier transform-based offset quadrature amplitude modulation (offset-QAM) orthogonal frequency division multiplexing (OFDM) technology. We derive a closed-form expression for the de-multiplexed signal and analyze the influence of crosstalk on implementation algorithms and system performance. It is found that channel estimation in offset-QAM OFDM is different from that in conventional OFDM (C-OFDM) due to the residual crosstalk terms and requires particular study. We propose simple and efficient channel estimation algorithms and show, in a 38-Gbit/s offset-16QAM OFDM experiment with 840-km single-mode fiber, that these algorithms can enable the system performance close to the theoretical limit. By using these algorithms, we compare this technology with C-OFDM and Nyquist FDM (N-FDM) and numerically and experimentally show that DFT-based offset-QAM OFDM can greatly enhance the net data rate for fiber transmissions compared to C-OFDM and exhibit lower complexity than N-FDM. These advantages together with the successfully developed implementation algorithms make this technology very promising for optical communication systems.     

Parallel vector processing of multidimensional orthogonal transforms for digital signal processing applications

This paper presents vector and parallel algorithms and implementations of one- and two-dimensional orthogonal transforms. The speed performances are evaluated on Cray X-MP/48 vector computer. The sinusoidal orthogonal transforms are computed using fast real Fourier transform (FFT) kernel. The non-sinusoidal orthogonal transform algorithms are derived by using direct factorizations of transform matrices. Concurrent processing is achieved by using the multitasking capability of Cray X-MP/48 to transform long data vectors and two-dimensional data vectors. The discrete orthogonal transforms discussed in this paper include: Fourier transform (DFT), cosine transform (DCT), sine transform (DST), Hartley transform (DHT), Walsh transform (DWHT) and Hadamard transform (DHDT). The factors affecting the speedup of vector and parallel processing of these transforms are considered. The vectorization techniques are illustrated by an FFT example.This work is supported in part by the National Science Foundation, Pittsburgh Supercomputing Center (grant number ECS-880012P) and by the PEW Science Education Program.