线性调频信号的表达式为
\[ s(t) = \operatorname{rect}(\frac{t}{T_p})\exp(j2\pi f_c t + j\pi k t^2 + j\phi_0) \]
其傅里叶变换为
\[ \begin{align} S(f) &= \int{s(t)\exp(-j2\pi ft)dt} \\ &= \int_{-\frac{T_p}{2}}^{\frac{T_p}{2}}{ \exp(j2\pi f_c t + j\pi k t^2 + j\phi_0 - j2\pi ft)dt } \\ &= \exp(-j\frac{\pi}{k}(f_c - f)^2 + j\phi_0) \int_{\frac{f_c - f}{k}-\frac{T_p}{2}}^{\frac{f_c - f}{k}+\frac{T_p}{2}}{ \exp(j\pi k t^2)dt } \end{align} \]
