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Linear operations performed in one domain (time or frequency) have corresponding operations in the other domain, which are sometimes easier to perform. The operation of differentiation in the time domain corresponds to multiplication by the frequency,[remark 1] so some differential equations are easier to analyze in the frequency domain. Also, convolution in the time domain corresponds to ordinary multiplication in the frequency domain (see Convolution theorem). After performing the desired operations, transformation of the result can be made back to the time domain. Harmonic analysis is the systematic study of the relationship between the frequency and time domains, including the kinds of functions or operations that are "simpler" in one or the other, and has deep connections to many areas of modern mathematics.

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1つのドメイン（時間または周波数）で実行される線形操作は、他のドメインでも対応する操作を持ちます。時間領域での微分の演算は周波数による乗算に相当します[注意1]。そのため、微分方程式の中には周波数領域で解析しやすいものがあります。また、conv

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Linear operations performed in one domain (time or frequency) have corresponding operations in the other domain. The operation of differentiation in the time domain is equivalent to multiplication by frequency [Note 1]. Therefore, some differential equations are easy to analyze in the frequency domain. Also, conv

INTO JAPANESE

一方の領域（時間または周波数）で実行される線形演算は、他方の領域でも対応する演算を持ちます。時間領域での微分演算は、周波数による乗算に相当します[注1]。したがって、いくつかの微分方程式は周波数領域で分析するのが簡単です。また、conv

BACK INTO ENGLISH

Linear operations performed in one domain (time or frequency) have corresponding operations in the other domain. Differentiation in the time domain is equivalent to multiplication by frequency [1]. Therefore, some differential equations are easy to analyze in the frequency domain. Also, conv

INTO JAPANESE

一方の領域（時間または周波数）で実行される線形演算は、他方の領域でも対応する演算を持ちます。時間領域での微分は周波数による乗算と等価です[1]。したがって、いくつかの微分方程式は周波数領域で分析するのが簡単です。また、conv

BACK INTO ENGLISH

Linear operations performed in one domain (time or frequency) have corresponding operations in the other domain. Differentiation in the time domain is equivalent to multiplication by frequency [1]. Therefore, some differential equations are easy to analyze in the frequency domain. Also, conv