matlab用符号函数法求解方程at2 + b*t + c=0

可以使用 Matlab 中的符号计算工具箱来求解该方程。具体步骤如下：

1. 定义符号变量

使用 `syms` 命令定义符号变量，这里我们定义符号变量 t，a，b，c：

syms t a b c

2. 构建方程

使用上述定义的符号变量构建方程：

eqn = a*t^2 + b*t + c == 0;

3. 解方程

使用 `solve` 命令求解方程，得到解析解：

sol = solve(eqn, t);

此时，`sol` 的值将为一个符号表达式，包含方程的解析解。

完整代码示例：

syms t a b c
eqn = a*t^2 + b*t + c == 0;
sol = solve(eqn, t);

需要注意的是，符号计算工具箱求解的解析解可能会比较复杂，需要根据具体情况进行简化和化简。

相关问题

改写这段代码 function [At,Ph,A2]=EnvelopPhase(X,f0,fs) HX=imag(hilbert(X)); t=0:1/fs:((length(X)-1)/fs); Ac=X.cos(2*pi*f0*t)+HX.sin(2*pi*f0*t); As=HX.cos(2*pi*f0*t)-X.sin(2*pi*f0*t); Ph=atan2(As,Ac); A2=Ac.^2+As.^2; At=sqrt(A2); end function X=Narrowbandsignal(N,f0,delt,fs,M) N1=N-M; xt=randn(1,N1); f1=f0*2/fs; df=delt/fs; ht = fir1(M, [f1-df, f1+df], 'bandpass'); X=conv(xt,ht); X=X(1:N); end N=10000; f0=10000; delt=400; fs=22000; M=50; al=2; a2=4; a3=8; sitl=pi/6; sit2=pi/4; sit3=pi/3; X=Narrowbandsignal(N,f0,delt,fs,M); X=X/sqrt(var(X)); t=0:1/fs:((N-1)/fs); X1=X+al*cos(2*pi*f0*t+sitl); X2=X+a2*cos(2*pi*f0*t+sit2); X3=X+a3*cos(2*pi*f0*t+sit3); [Atl,Ph1,A21]=EnvelopPhase(X1, f0, fs); [At2,Ph2,A22]=EnvelopPhase(X2, f0, fs); [At3,Ph3,A23]=EnvelopPhase(X3, f0, fs); LA=0:0.4:12; [GA1, ~] = histcounts(Atl, LA); [GA2, ~] = histcounts(At2, LA); [GA3, ~] = histcounts(At3, LA); figure; plot(LA,GA1,':',LA,GA2,'-',LA,GA3,'--'); title('包络的分布直方图'); LP=-pi/2:0.05:pi/2; [GP1, ~] = histcounts((Ph1-sitl), LP); [GP2, ~] = histcounts((Ph2-sit2), LP); [GP3, ~] = histcounts((Ph3-sit3), LP); figure; plot(LP,GP1,':',LP,GP2,'-',LP,GP3,'--'); title('相位的分布直方图'); LA2=0:1:120; [GA21, ~] = histcounts(A21,LA2); [GA22, ~] = histcounts(A22,LA2); [GA23, ~] = histcounts(A23,LA2); figure; plot(LA2,GA21,':', LA2,GA22,'-',LA2,GA23,'--'); title('包络平方值的分布直方图');

已经将代码进行了改写，修改后的代码如下：

function [At,Ph,A2] = EnvelopPhase(X,f0,fs)
    HX = imag(hilbert(X));
    t = 0:1/fs:((length(X)-1)/fs);
    Ac = X .* cos(2*pi*f0*t) + HX .* sin(2*pi*f0*t);
    As = HX .* cos(2*pi*f0*t) - X .* sin(2*pi*f0*t);
    Ph = atan2(As,Ac);
    A2 = Ac.^2 + As.^2;
    At = sqrt(A2);
end

function X = Narrowbandsignal(N,f0,delt,fs,M)
    N1 = N - M;
    xt = randn(1,N1);
    f1 = f0 * 2 / fs;
    df = delt / fs;
    ht = fir1(M, [f1-df, f1+df], 'bandpass');
    X = conv(xt, ht);
    X = X(1:N);
end

N = 10000;
f0 = 10000;
delt = 400;
fs = 22000;
M = 50;
al = 2;
a2 = 4;
a3 = 8;
sitl = pi/6;
sit2 = pi/4;
sit3 = pi/3;

X = Narrowbandsignal(N,f0,delt,fs,M);
X = X / sqrt(var(X));
t = 0:1/fs:((N-1)/fs);
X1 = X + al*cos(2*pi*f0*t+sitl);
X2 = X + a2*cos(2*pi*f0*t+sit2);
X3 = X + a3*cos(2*pi*f0*t+sit3);

[Atl,Ph1,A21] = EnvelopPhase(X1, f0, fs);
[At2,Ph2,A22] = EnvelopPhase(X2, f0, fs);
[At3,Ph3,A23] = EnvelopPhase(X3, f0, fs);

LA = 0:0.4:12;
[GA1, ~] = histcounts(Atl, LA);
[GA2, ~] = histcounts(At2, LA);
[GA3, ~] = histcounts(At3, LA);

figure;
plot(LA,GA1,':',LA,GA2,'-',LA,GA3,'--');
title('包络的分布直方图');

LP = -pi/2:0.05:pi/2;
[GP1, ~] = histcounts((Ph1-sitl), LP);
[GP2, ~] = histcounts((Ph2-sit2), LP);
[GP3, ~] = histcounts((Ph3-sit3), LP);

figure;
plot(LP,GP1,':',LP,GP2,'-',LP,GP3,'--');
title('相位的分布直方图');

LA2 = 0:1:120;
[GA21, ~] = histcounts(A21,LA2);
[GA22, ~] = histcounts(A22,LA2);
[GA23, ~] = histcounts(A23,LA2);

figure;
plot(LA2,GA21,':', LA2,GA22,'-',LA2,GA23,'--');
title('包络平方值的分布直方图');

不使用function改写这段代码 function [At,Ph,A2]=EnvelopPhase(X,f0,fs) HX=imag(hilbert(X)); [M,N]=size(X); t=0:1/fs:((N-1)/fs); Ac=X.*cos(2*pi*f0*t)+HX.*sin(2*pi*f0*t); As=HX.*cos(2*pi*f0*t)-X.*sin(2*pi*f0*t); Ph=atan(As./Ac); A2=Ac.*Ac+As.*As; At=sqrt(A2); function X=Narrowbandsignal(N,f0,delt,fs,M) N1=N-M; xt=random(1,N1); f1=f0*2/fs; df=delt/fs; ht=fir1(M,[f1-df f1+df]); X=conv(xt,ht); X=X/max(abs(X)); return N=10000;f0=10000;delt=400;fs=22000;M=50; al=2;a2=4;a3=8; sitl=pi/6;sit2=pi/4;sit3=pi/3 X=Narrowbandsignal(N,f0,delt,fs,M); X=X/sqrt(var(X)); t=0:1/fs:((N-1)/fs); X1=X+alcos(2*pi*f0*t+sitl); X2=X+a2cos(2*pi*f0*t+sit2); X3=X+a3cos(2*pi*f0*t+sit3); [Atl,Ph1,A21]=EnvelopPhase(X1, f0, fs); [At2,Ph2,A22]=EnvelopPhase(X2, f0, fs); [At3,Ph3,A23]=EnvelopPhase(X3, f0, fs); LA=0:0.4:12; GA1=histogram(Atl, LA); GA2=histogram(At2, LA); GA3=histogram(At3, LA); plot(LA,GA1,':',LA,GA2,'-',LA,GA3,'–'); title('包络的分布直方图'); figure; LP=-pi/2:0.05:pi/2; GP1=histogram((Ph1-sitl),LP); GP2=histogram((Ph2-sit2),LP); GP3=histogram((Ph3-sit3),LP); plot(LP,GP1,':',LP,GP2,'-',LP,GP3,'–'); title('相位的分布直方图'); figure; LA2=0:1:120; GA21=histogram(A21,LA2); GA22=histogram(A22,LA2); GA23=histogram(A23,LA2); plot(LA2,GA21,':', LA2,GA22,'-',LA2,GA23,'–'); title('包络平方值的分布直方图');

以下不使用 `function` 的改写代码：

N = 10000;
f0 = 10000;
delt = 400;
fs = 22000;
M = 50;
al = 2;
a2 = 4;
a3 = 8;
sitl = pi/6;
sit2 = pi/4;
sit3 = pi/3;

% 生成窄带信号
N1 = N-M;
xt = rand(1, N1);
f1 = f0*2/fs;
df = delt/fs;
ht = fir1(M, [f1-df f1+df]);
X = conv(xt, ht);
X = X/max(abs(X));
t = 0:1/fs:((N-1)/fs);

% 生成三个幅度不同的信号
X1 = X + al*cos(2*pi*f0*t+sitl);
X2 = X + a2*cos(2*pi*f0*t+sit2);
X3 = X + a3*cos(2*pi*f0*t+sit3);

% 计算三个信号的包络和相位
HX1 = imag(hilbert(X1));
Ac1 = X1.*cos(2*pi*f0*t) + HX1.*sin(2*pi*f0*t);
As1 = HX1.*cos(2*pi*f0*t) - X1.*sin(2*pi*f0*t);
Ph1 = atan2(As1, Ac1);
A21 = Ac1.*Ac1 + As1.*As1;
Atl = sqrt(A21);

HX2 = imag(hilbert(X2));
Ac2 = X2.*cos(2*pi*f0*t) + HX2.*sin(2*pi*f0*t);
As2 = HX2.*cos(2*pi*f0*t) - X2.*sin(2*pi*f0*t);
Ph2 = atan2(As2, Ac2);
A22 = Ac2.*Ac2 + As2.*As2;
At2 = sqrt(A22);

HX3 = imag(hilbert(X3));
Ac3 = X3.*cos(2*pi*f0*t) + HX3.*sin(2*pi*f0*t);
As3 = HX3.*cos(2*pi*f0*t) - X3.*sin(2*pi*f0*t);
Ph3 = atan2(As3, Ac3);
A23 = Ac3.*Ac3 + As3.*As3;
At3 = sqrt(A23);

% 画图
LA = 0:0.4:12;
GA1 = histogram(Atl, LA);
GA2 = histogram(At2, LA);
GA3 = histogram(At3, LA);
plot(LA, GA1, ':', LA, GA2, '-', LA, GA3, '–');
title('包络的分布直方图');
figure;

LP = -pi/2:0.05:pi/2;
GP1 = histogram((Ph1-sitl), LP);
GP2 = histogram((Ph2-sit2), LP);
GP3 = histogram((Ph3-sit3), LP);
plot(LP, GP1, ':', LP, GP2, '-', LP, GP3, '–');
title('相位的分布直方图');
figure;

LA2 = 0:1:120;
GA21 = histogram(A21, LA2);
GA22 = histogram(A22, LA2);
GA23 = histogram(A23, LA2);
plot(LA2, GA21, ':', LA2, GA22, '-', LA2, GA23, '–');
title('包络平方值的分布直方图');

注意，这里直接使用了幅度和相位的计算公式，没有对其进行封装成函数。同时，为了避免变量名重复，对原先函数中的 `N` 进行了修改，改为 `N1`。