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沃希变换性质及其计算方法傅里叶变换利用的正交矢量基内矢量的支量是单位复数,它的实部及虚部依次是余弦及正弦函数。因此计算傅里叶变换要用大量的复数乘法。沃希变换利用的正交矢量基内矢量叫做沃希矢量。沃希矢量的支量只取+1和-1这两个值。因此计算沃希变换不用乘法,沃希变换的计算工作量比傅里叶变换的工作量少得多。设N=2~p,P=1,2,…,在N空间的沃希矢量基是 {Wal_~(p)_i}i=0,1,2,…,(N-1),N=2~p。例如当P=1时,两个一阶沃希矢量定义为
Walsh transform properties and its calculation method Fourier transform using the orthogonal vector basis of the vector of the unit complex number, its real and imaginary parts of the order of the cosine and sine functions. Therefore, to calculate the Fourier transform using a large number of complex multiplication. The Orthogonal Vector Base Vector used by Walsh Transform is called the Walsh Vector. Only two values of +1 and -1 are taken from the branch of the Walsh vector. Therefore, the calculation of Walsh transform without multiplication, Walsh transform calculation workload much less than the Fourier transform workload. Let N = 2 ~ p, P = 1,2, ..., and the vector of Walsh vectors in N space is {Wal_ ~ (p) _i} i = 0,1,2, ..., 2 ~ p. For example, when P = 1, two first-order Walsh vectors are defined as