# Connexions

You are here: Home » Content » Multirate Filtering: Theory Exercise (日本語 - Japanese)

### Lenses

What is a lens?

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

#### Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
• Rice Digital Scholarship

This module is included in aLens by: Digital Scholarship at Rice UniversityAs a part of collection: "DSP Laboratory with TI TMS320C54x (International Demo)"

Click the "Rice Digital Scholarship" link to see all content affiliated with them.

Click the tag icon to display tags associated with this content.

### Recently Viewed

This feature requires Javascript to be enabled.

### Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

# Multirate Filtering: Theory Exercise (日本語 - Japanese)

Summary: この演習課題を通じて、ダウンサンプルおよびアップサンプルという操作が信号のスペクトルにどのような影響を与えるかを調査・理解することができます。

## マルチレート理論の演習課題

入力信号として、図 1に示すスペクトル Xω X ω を有するサンプル値信号を考えよう。ただし、 Xω X ω は、入力信号のDTFT(discrete time Fourier transform)であるとします。

U=D=3 U D 3 と仮定し、図 2 (帯域制限用フィルタ無し)のマルチレートシステムを通過した各部の信号のDTFT結果 Wω W ω および Yω Y ω を示して下さい。 このとき、ダウンサンプルおよびアップサンプル前後の信号のスペクトルの関係式（式 1および式 2）を用いて下さい。なお、正規化角周波数 ω ωをアナログ周波数表現に変換する場合、信号のレートが異なると正規化する際に用いるサンプリング周波数が異なることに注意する必要があります。したがって、図 1における Xω X ω ω ω と以下の式における Wω W ω ω ω では、同じ記号を用いているにもかかわらず、正規化表現の際に仮定しているサンプリング周波数が異なっており、後者のサンプリング周波数は前者の 1D 1 D 倍です。

Wω=1D k =0D1Xω2πkD W ω 1 D k 0 D 1 X ω 2 k D
(1)
Yω=WUω Y ω W U ω
(2)

## Content actions

PDF | EPUB (?)

### What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

#### Definition of a lens

##### Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

##### What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

##### Who can create a lens?

Any individual member, a community, or a respected organization.

##### What are tags?

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks