文档介绍:小波分析实验报告
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实验一小波函数的Fourier变换和Fourier逆变换
实验目的
用Matlab实现函数的Fourier变换和Fourier逆变换
实验内容
用Matlab实现下列函数的Fourier变换和Fourier逆变换
>> syms x i w0;
>> f=exp(-x^2/2)*exp(i*w0*x);
>> F=fourier(f,x)
F =
(2^(1/2)*pi^(1/2))/exp((x + i*w0*sqrt(-1))^2/2)
>> f=ifourier(F)
f =
exp((i^2*w0^2)/2 - (t - i*w0)^2/2)
>> syms x;
>> f=(1-x^2)*exp(-x^2/2);
>> F=fourier(f)
F =
(2^(1/2)*pi^(1/2)*w^2)/exp(w^2/2)
>> f=ifourier(F)
f =
(2^(1/2)*((2^(1/2)*pi^(1/2))/exp(x^2/2) - (2^(1/2)*pi^(1/2)*x^2)/exp(x^2/2)))/(2*pi^(1/2))
>> syms x;
f=exp(-x^2/2)-exp(-x^2/8)/2;
>> F=fourier(f)
F =
(2^(1/2)*pi^(1/2))/exp(w^2/2) - (2^(1/2)*pi^(1/2))/exp(2*w^2)
>> f=ifourier(F)
f =
((2*pi)/exp(x^2/2) - pi/exp(x^2/8))/(2*pi)
>> syms x;
>> g1=1/(2*pi^(1/2))*exp(-x^2/4);
>> F1=fourier(g1)
F1 =
(5081767996463981*pi^(1/2))/(9007199254740992*exp(w^2))
>> g1=ifourier(F1)
g1 =
5081767996463981/(18014398509481984*exp(x^2/4))
>> syms x;
>> g2=1/(pi^(1/2))*exp(-x^2);
>> F2=fourier(g2)
F2 =
(5081767996463981*pi^(1/2))/(9007199254740992*exp(w^2/4))
>> g2=ifourier(F2)
g2 =
5081767996463981/(9007199254740992*exp(x^2))
a=1/16时
>> syms x;
>> g3=2/(pi^(1/2))*exp(-4*x^2);
>> F3=fourier(g3)
F3 =
(5081767996463981*pi^(1/2))/(9007199254740992*exp(w^2/16))
>> g3=ifourier(F3)
g3 =
5081767996463981/(4503599627370496*exp(4*x^2))
2. 画出小波函数的图形
实验内容:用Matlab画出下列函数图形
>> x=-6::6;
>> w0=6;
>> y=exp(-1/2.*x.^2+w0*i.*x);
>> plot(x,y);
>> x=-6::6;
>> y=(1-x.^2).*exp(-x.^2/2);
>> plot(x,y);
>> x=-6::6;
>> y=exp(-x.^2/2)-(exp(-x.^2/8))/2;
>> plot(x,y);
>> x=-5::5;
>> g1=1/(2*pi^(1/2))*exp(-x.^2/4);
>> g2=1/(pi^(1/2))*exp(-x.^2);
>> g3=2/(pi^(1/2))*exp(-4*x.^2);
>> plot(x,g1,x,g2,x,g3);
,并画出图形
>> t=1::5;
>> f=sin(2*pi*t)+sin(4