有关信噪比的一个问题

炎海飞雪

大家帮忙看看，我前面设的SNR=2,但是随后用两个比较成熟的公式计算的结果都是6.17，按matlab中的说明，也应该是4吧，这是怎么回事？公式用错了，还是我对wnoise函数理解的有问题？

附1：代码
%测试数据的选取
[x,signal] = wnoise(3,11,snr,init);%generate the signal containing 2^11 dots.,x is the origin singnal and signal is the noising signal.
s=signal;
N=2^11;
wname='db7';
jN=2;  %分解的尺度
[c,l]=wavedec(s,jN,wname);
snr1=20*log10(norm(x)/norm(s-x));

Ps=sum((x).^2);%signal power
Pn=sum((x-signal).^2);%noise power
snr2=10*log10(Ps/Pn);

p1=1/length(x)*norm(x)^2;
p2=1/length(x)*norm(x-signal)^2;
snr3=10*log10(p1/p2)


附2：matlab中 wnoise（）函数的说明：
X = wnoise(FUN,N) returns values of the test signal given by FUN, on a 2N grid of [0,1].
[X,XN] = wnoise(FUN,N,SQRT_SNR) returns a test vector X as above, rescaled such that std(X) = SQRT_SNR. The returned vector XN contains the same test vector corrupted by additive Gaussian white noise N(0,1). Then, XN has a signal-to-noise ratio of SNR = (SQRT_SNR)2.