京都大学 情報学研究科 知能情報学専攻 2020年8月実施 専門科目 S-5

Author

realball

Description

The Fourier spectrum of a continuous-time signal is given by , where denotes the imaginary unit. Let denote discrete Fourier transform of a finite-length discrete signal of length , . Answer the following questions.

Q.1

Suppose that is an even function, that is The Fourier spectrum of is given by

Answer . Calculation procedure must also be included in the answer.

Q.2

Let be the circular shifted version of by ,

The discrete Fourier transform of is given by .

Answer . Calculation procedure must also be included in the answer.

Q.3

Let be a finite-length discrete signal of length ,

The discrete Fourier transform of is given by

Answer and . Calculation procedure must also be included in the answer.

Q.4

The transform of ,

is known as a discrete cosine tranform (DCT-II), and is used in data compression such as JPEG.

Explain an advantage of the discrete cosine transform compared to the discrete Fourier transform in terms of data compression.

Kai

Q.1

Thus, blank (A) is .

Q.2

Q.3

Q.4

Better concentrate energy