频域卷积定理 急迫万分，求高手立刻解答！

频域卷积定理（最新阐述）

在信号处理领域，频域卷积定理是一个至关重要的原理，它揭示了时间域与频域之间的一种深刻联系。简而言之，该定理指出：两个信号在时域上的卷积等于它们在频域上的乘积，反之亦然（在适当条件下，并考虑到适当的变换，如傅里叶变换）。

用数学语言来表达，假设有两个信号x(t)和h(t)，它们的傅里叶变换分别为X(ω)和H(ω)。那么，根据频域卷积定理，我们有：

时域卷积：x(t) h(t) 的傅里叶变换是 X(ω)H(ω)。

频域乘积：X(ω)H(ω) 的逆傅里叶变换是 x(t) h(t)。

In English:

Convolution Theorem in the Frequency Domain (Updated Explanation)

In the field of signal processing, the convolution theorem in the frequency domain is a fundamental principle that uncovers a profound connection between the time domain and the frequency domain. Simply put, the theorem states that the convolution of two signals in the time domain is equivalent to their product in the frequency domain, and vice versa (under appropriate conditions and considering appropriate transformations, such as the Fourier transform).

Mathematically, suppose we have two signals x(t) and h(t), with their Fourier transforms denoted as X(ω) and H(ω), respectively. Then, according to the convolution theorem in the frequency domain, we have:

Time-domain convolution: The Fourier transform of x(t) h(t) is X(ω)H(ω).

Frequency-domain product: The inverse Fourier transform of X(ω)H(ω) is x(t) h(t).

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