東京大学 情報理工学系研究科 電子情報学専攻 2017年8月実施 専門 第5問

Author

Josuke

Description

Answer the following questions about discrete signal processing. Here, is the sampling interval.

(1) Show the definition of the -transform for the discrete signal series , which is defined for . Here, is a complex variable.

(2) Derive the transfer function in the -domain(the Laplace transform domain) of the circuit in Fig.1.

(3) The relationship between the Laplace transform and the -transform is described as . Derive the following approximation.

You can use the following equation if necessary.

(4) Convert to the transfer function in the -domain by using the approximation derived in (3). Here, we assume .

(5) Show a schematic of a discrete signal circuit that corresponds to in (4).

(6) By taking the same procedure, show a schematic of a discrete signal circuit for the circuit shown in Fig.2.

Kai

(1)

(2)

(3)

(4)

(5)

(6)