modulating = Am * sawtooth(2*pi*fm*t,0.5); modulated = carrier .* (1 + modulating);

这段代码是进行模拟调制的过程，其中：

- `Am` 代表调制信号的振幅。
- `sawtooth` 是锯齿波函数，它的频率为 `fm`。
- `t` 是时间变量。
- `2*pi*fm*t` 是锯齿波的角频率，乘以 `2*pi` 是为了将频率转换为角频率。
- `0.5` 是锯齿波的对称因子，代表了锯齿波的波峰和波谷之间的比例关系。
- `carrier` 是载波信号。
- `.*` 表示逐元素相乘，即将调制信号和载波信号的每个元素相乘。
- `(1 + modulating)` 代表调制后的信号，其中 `1` 是为了保证信号的直流分量不变，`modulating` 是调制信号，两者相加得到调制后的信号。

相关问题

class FocalLoss(nn.Module): # Wraps focal loss around existing loss_fcn(), i.e. criteria = FocalLoss(nn.BCEWithLogitsLoss(), gamma=1.5) def __init__(self, loss_fcn, gamma=1.5, alpha=0.25): super(FocalLoss, self).__init__() self.loss_fcn = loss_fcn # must be nn.BCEWithLogitsLoss() self.gamma = gamma self.alpha = alpha self.reduction = loss_fcn.reduction self.loss_fcn.reduction = 'none' # required to apply FL to each element def forward(self, pred, true): loss = self.loss_fcn(pred, true) # p_t = torch.exp(-loss) # loss *= self.alpha * (1.000001 - p_t) ** self.gamma # non-zero power for gradient stability # TF implementation https://github.com/tensorflow/addons/blob/v0.7.1/tensorflow_addons/losses/focal_loss.py pred_prob = torch.sigmoid(pred) # prob from logits p_t = true * pred_prob + (1 - true) * (1 - pred_prob) alpha_factor = true * self.alpha + (1 - true) * (1 - self.alpha) modulating_factor = (1.0 - p_t) ** self.gamma loss *= alpha_factor * modulating_factor if self.reduction == 'mean': return loss.mean() elif self.reduction == 'sum': return loss.sum() else: # 'none' return loss

这个代码实现了一个 Focal Loss 损失函数，它是对二分类问题中的交叉熵损失函数的一种改进。它主要通过增加一个可调的超参数 $\gamma$，来调整难易样本的权重，从而解决类别不平衡问题。在代码中，它被实现为一个 PyTorch 模块，它的 forward 方法接受两个张量，即预测值和真实值，并返回计算出来的损失值。在实现中，它首先对传入的 loss_fcn 进行了封装，将其 reduction 属性设为 'none'，然后在 forward 方法中使用封装后的 loss_fcn 计算出二分类交叉熵损失，接着使用预测值和真实值计算出概率值，根据概率值和超参数 $\gamma$ 计算出一个调制因子，最后将原始损失值乘以调制因子和一个可调的超参数 $\alpha$，从而得到最终的 Focal Loss 损失。

t=0:0.0001:0.1;x_FM= cos(fc*t+kf*quadgk(@(s)Fm(s),0,w));

As an AI language model, I cannot run this code, but I can explain it to you.

This code defines a time vector t from 0 to 0.1 with a step size of 0.0001. The next line generates a frequency modulated signal x_FM using the cosine function with a carrier frequency fc and a frequency deviation kf multiplied by the integral of a function Fm(s) from 0 to w, where w is a constant. The function Fm(s) represents the message signal that is being modulated onto the carrier frequency. The quadgk function is used to numerically integrate the function Fm(s) over the range [0, w]. The resulting signal x_FM is a frequency modulated signal that varies in frequency according to the message signal Fm(s), which is modulating the carrier frequency.