京都大学 情報学研究科 知能情報学専攻 2022年8月実施 専門科目 S-5

Author

realball

Description

Suppose that the Fourier transform of a function and the Fourier integral representation of the Dirac delta function are given by the following formulae, where and are real numbers, and . Answer the following questions.

Q.1

Compute the Fourier transform of the function given below, where is a real number.

(1)

(2)

Q.2

Compute the Fourier transform of function by following the steps below.

(1) Derive the following equation concerning convolution operation.

(2) Find function whose convolution with the above satisfies , and explain how the convolution gives .

(3) Compute .

Kai

Q.1

(1)

applying the Euler formula,

(2)

Hence

Q.2

(1)

(2)

(3)