matlab采用HMC得到时频谱图代码

这里提供一个MATLAB示例代码，用于利用HMC方法得到信号的时频谱图：

% 定义信号
N = 1024;
t = linspace(0, 1, N);
f = 20;
signal = sin(2 * pi * f * t);

% 分帧并进行FFT
frame_size = 64;
step = 32;
frames = zeros(frame_size, N);
for i = 1:step:N-frame_size+1
    frame = signal(i:i+frame_size-1);
    frames(:,i) = abs(fft(frame));
end

% 定义概率分布函数
sigma = 0.1;
log_prob = @(x) -sum(sum((x - frames).^2)) / (2 * sigma^2);

% 定义HMC采样函数
epsilon = 0.01;
L = 10;
n_samples = 1000;
x0 = frames + randn(size(frames)) * sigma;
samples = hmc_sampler(log_prob, x0, n_samples, epsilon, L);

% 取最后一部分采样结果并计算平均值
samples = samples(end-499:end,:);
mean = mean(samples, 1);

% 绘制时频谱图
imagesc(mean')
colorbar

其中，`hmc_sampler`函数可以参考以下代码实现：

function samples = hmc_sampler(log_prob, x0, n_samples, epsilon, L)
    samples = zeros(n_samples+1, size(x0,1), size(x0,2));
    samples(1,:,:) = x0;
    x = x0;
    for i = 1:n_samples
        p = randn(size(x));
        H = 0.5 * sum(sum(p.^2)) - log_prob(x);
        x_new = x;
        p_new = p;
        for j = 1:L
            grad = gradient(log_prob(x_new));
            p_new = p_new - 0.5 * epsilon * grad;
            x_new = x_new + epsilon * p_new;
            grad = gradient(log_prob(x_new));
            p_new = p_new - 0.5 * epsilon * grad;
        end
        H_new = 0.5 * sum(sum(p_new.^2)) - log_prob(x_new);
        alpha = min(1, exp(H - H_new));
        if rand() < alpha
            x = x_new;
        end
        samples(i+1,:,:) = x;
    end
end

需要注意的是，这只是一个简单的示例代码，实际应用中需要根据具体情况进行调整和优化。