京都大学情報学研究科知能情報学専攻 2018年8月実施専門科目 T-2

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The Fourier spectrum of a continuous-time signal is given by

where denotes the imaginary unit and denotes Fourier transform. Let

be the inverse Fourier transform.

Find the continuous-time signal corresponding to the Fourier spectrum , where denotes a rectangular function of width and is given by

Let be a comb function whose time period is ,

Show that

where is a function that satisfies

and

You may use for any real number .

Let be a continuous-time signal sampled from with a sampling period . Describe with and .