2015年11月的文章

一维快速傅里叶的算法

一维快速傅里叶的算法
function fft(dataArray) {    // 复数乘法    this.mul = function(a, b) {        if(typeof(a)!=='object') {            a = {real: a, imag: 0}        }        if(typeof(b)!=='object') {            b = {real: b, imag: 0}        }        return {            real: a.real*b.real-a.imag*b.imag,            imag: a.real*b.imag+a.imag*b.real        };    };    // 复数加法    this.add = function(a, b) {        if(typeof(a)!=='object') {            a = {real: a, imag: 0}        }        if(typeof(b)!=='object') {            b = {real: b, imag: 0}        }        return {            real: a.real+b.real,            imag: a.imag+b.imag        };    };    // 复数减法    this.sub = function(a, b) {        if(typeof(a)!=='object') {            a = {real: a, imag: 0}        }        if(typeof(b)!=='object') {            b = {real: b, imag: 0}        }        return {            real: a.real-b.real,            imag: a.imag-b.imag        };    };    // 倒位序排列    this.sort = function(data, r) {        if(data.length <=2) {            return data;        }        var index = [0,1];        for(var i=0; i<r-1; i++) {            var tempIndex = [];            for(var j=0; j<index.length; j++) {                tempIndex[j] = index[j]*2;                tempIndex[j+index.length] = index[j]*2+1;            }            index = tempIndex;        }        var datatemp = [];        for(var i=0; i<index.length; i++) {            datatemp.push(data[index[i]]);        }        return datatemp;    };    var dataLen = dataArray.length;    var r = 1; // 迭代次数    var i = 1;    while(i*2 < dataLen) {        i *= 2;        r++;    }    var count = 1<<r; // 相当于count=2^r    // 如果数据dataArray的长度不是2^N,则开始补0    for(var i=dataLen; i<count; i++) {        dataArray[i] = 0;    }    // 倒位序处理    dataArray = this.sort(dataArray, r);    // 计算加权系数w    var w = [];    for(var i=0; i<count/2; i++) {        var angle = -i*Math.PI*2/count;        w.push({real: Math.cos(angle), imag: Math.sin(angle)});    }    for(var i=0; i<r; i++) { // 级循环        var group = 1<<(r-1-i);        var distance = 1<<i;        var unit = 1<<i;        for(var j=0; j<group; j++) { // 组循环            var step = 2*distance*j;            for(var k=0; k<unit; k++) { // 计算单元循环                var temp = this.mul(dataArray[step+k+distance], w[count*k/2/distance]);                dataArray[step+k+distance] = this.sub(dataArray[step+k], temp);                dataArray[step+k] = this.add(dataArray[step+k], temp);            }        }    }    return dataArray;}
快速傅里叶变换的逆变换用JavaScript实现的完整代码如下
function ifft(dataArray) {    for(var i=0, dataLen=dataArray.length; i<dataLen; i++) {        if(typeof(dataArray[i])!='object'){            dataArray[i] = {                real: dataArray[i],                imag: 0            }        }        dataArray[i].imag *= -1;    }    dataArray = fft(dataArray);    for(var i=0, dataLen=dataArray.length; i<dataLen; i++) {        dataArray[i].real *= 1/dataLen;        dataArray[i].imag *= -1/dataLen;    }    return dataArray;}

下面是JavaScript实现二维傅里叶变换的完整代码:

function fft2(dataArray, width, height) {    var r = 1;    var i = 1;    while(i*2 < width) {        i *= 2;        r++;    }    var width2 = 1<<r;    var r = 1;    var i = 1;    while(i*2 < height) {        i *= 2;        r++;    }    var height2 = 1<<r;    var dataArrayTemp = [];    for(var i=0; i<height2; i++) {        for(var j=0; j<width2; j++) {            if(i>=height || j>=width) {                dataArrayTemp.push(0);            }            else {                dataArrayTemp.push(dataArray[i*width+j]);            }        }    }    dataArray = dataArrayTemp;    width = width2;    height = height2;    var dataTemp = [];    var dataArray2 = [];    for(var i=0; i<height; i++) {        dataTemp = [];        for(var j=0; j<width; j++) {            dataTemp.push(dataArray[i*width+j]);        }        dataTemp = fft(dataTemp);        for(var j=0; j<width; j++) {            dataArray2.push(dataTemp[j]);        }    }    dataArray = dataArray2;    dataArray2 = [];    for(var i=0; i<width; i++) {        var dataTemp = [];        for(var j=0; j<height; j++) {            dataTemp.push(dataArray[j*width+i]);        }        dataTemp = fft(dataTemp);        for(var j=0; j<height; j++) {            dataArray2.push(dataTemp[j]);        }    }    dataArray = [];    for(var i=0; i<height; i++) {        for(var j=0; j<width; j++) {            dataArray[j*height+i] = dataArray2[i*width+j];        }    }    return dataArray;}

图像经过二维傅里叶变换所得到的结果就是前面提到的频率谱。

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百度地图兴趣点经纬度和实际经纬度的差别


如果百度地图的经纬度是(x,y)实际的应该是(x,y)+(-0.01185,-0.00328)=(x-0.01185,y-0.00328

google earth的差别是(0.0143,-0.014)
如果用getscreen截图,如果要截的范围为(x,y),输入getscreen的为(x-0.0143,y+0.014).