finite_difference

this is code for other 16QAM with awgn

说明：  波叠加的matlab源程序，来源于因特网。 谢谢大家！(wave superposition of Matlab source, and from the Internet. Thank you!)

Fuzzy knowledge-based system identification and modeling process is composed of two parts: variable identification and parameter identification. In variable identification, the significant variables of the system are identified among the set of possible variables. In parameter identification, the parameters of the knowledge-based system that describe the relationship between input and the output variables are identified. Parameter identification method consist of two steps: 1-find fuzzy clusters to establish the number of fuzzy rules 2-optimize the rule consequents. This code perform a fuzzy clustering using subtractive clustering

Demo:演示程序（注意图像路径） ShearletCoef: 系数计算程序 mybeta: 伪极坐标 Fourier 变换（文件名是暂时的用法） phi0,psi0,psid: 低高频图像点阵显示（myu,myv用于理论分析，不被 Demo 调用） psiStock: FPsi1(2)_x（有编号）: shearlet 函数类 bump: 钟形光滑函数 ramp: 斜升光滑函数（即旧版中的 smooth） 新版比旧版提高了框架函数的连续性——对角方向上的生成函数进行了连续化。算法设计上， 伪极坐标 Fourier 变换被独立出来。(Demo: demo program (note the image path) ShearletCoef: coefficient calculation procedure mybeta: pseudo-Polar Fourier transform (the file name is temporary usage) phi0, psi0, psid: low frequency image dot matrix display (myu, myv for theoretical analysis not to be invoked Demo) psiStock: FPsi1 (2) _x (numbered): shearlet function classes bump: bell smooth function ramp: ramp smooth functions (ie legacy of smooth) than the old version of the framework to improve the continuity of functions- diagonal direction of the generating function were continuous. Algorithm design, pseudo-Polar Fourier transform is independent.)

新的2维角度估计的高分辨方法。该方法首先建立基于范数约束的最优化问题的目标函数；然后用迭代算法沿均匀面阵接收数据的方位向求最小化目标函数的稀疏解，得到方位、俯仰角耦合的空间角频率，并分离信号；最后对每个分离的信号，沿面阵俯仰向求稀疏解，得到信号的俯仰角，进而求得对应的方位角。(The new high-resolution 2-D angle estimation method. Firstly, the establishment of an objective function optimization problems based on norm constraint then iterative algorithm along with uniform orientation plane array receives data to seek to minimize the objective function is sparse solution, get directions, spatial frequency coupling angle pitch angle, and separated signals Finally for each signal separation along the sparse area array pitch to seek solutions to obtain the pitch angle of the signal, and then obtain the corresponding azimuth.)

basics for programming in matlab

离散快速分数阶傅立叶变换,抽取信号，离散算法(the Discrete Fractional Fourier Transform)

matlab book which is very useful for programmming

针对非均匀线阵，利用修正的Capon算法，不需要信源数目，就可以达到高分辨的DOA(In view of the non uniform linear array, using the modified Capon algorithm, does not need the source number, can achieve high resolution DOA )

Auto correlation function for Rayleigh channel