範例：局部餘弦轉換

函數 > 轉換與濾波器 > 範例：局部餘弦轉換

範例：局部餘弦轉換

1. 透過串連含有四個不同頻率的四條正弦曲線，來定義測試信號。

<region id="ID0EGEJDB" top="96.000000000000014" left="38.400000000000006" height="25.6" width="58.13000000000001" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="145"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve">n</id> <real>512</real> </define> </math> </region>
<region id="ID0EHFJDB" top="134.40000000000003" left="38.400000000000006" height="27.791200000000003" width="53.580000000000005" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="147"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">f<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span> </id> <real>32</real> </define> </math> </region>	<region id="ID0E3FJDB" top="134.40000000000003" left="134.40000000000003" height="49.391200000000005" width="58.433333333333337" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="149"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ω<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span> </id> <apply> <div /> <real>1</real> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">f<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span> </id> </apply> </define> </math> </region>
<region id="ID0EWGJDB" top="172.8" left="38.400000000000006" height="47.2" width="89.13" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="151"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve">i</id> <range> <real>0</real> <apply> <minus /> <apply> <div /> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">n</id> <real>4</real> </apply> <real>1</real> </apply> </range> </define> </math> </region>	<region id="ID0ELHJDB" top="172.8" left="192.00000000000003" height="36.800000000000004" width="155.33" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="153"> <define xmlns="http://schemas.mathsoft.com/math50"> <apply> <indexer /> <id labels="VARIABLE" xml:space="preserve">y</id> <id labels="*" xml:space="preserve">i</id> </apply> <apply> <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">cos</id> <apply> <mult /> <apply> <mult /> <apply> <mult /> <apply> <mult /> <real>2</real> <id labels="CONSTANT" xml:space="preserve" label-is-contextual="true">π</id> </apply> <id xml:space="preserve">i</id> </apply> <real>1</real> </apply> <id labels="VARIABLE" xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ω<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span> </id> </apply> </apply> </define> </math> </region>
<region id="ID0EFIJDB" top="230.40000000000003" left="38.400000000000006" height="47.2" width="96.36333333333333" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="155"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve">j</id> <range> <apply> <div /> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">n</id> <real>4</real> </apply> <apply> <minus /> <apply> <div /> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">n</id> <real>2</real> </apply> <real>1</real> </apply> </range> </define> </math> </region>	<region id="ID0E1IJDB" top="230.40000000000003" left="192.00000000000003" height="36.800000000000004" width="157.2" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="157"> <define xmlns="http://schemas.mathsoft.com/math50"> <apply> <indexer /> <id labels="VARIABLE" xml:space="preserve">y</id> <id labels="*" xml:space="preserve">j</id> </apply> <apply> <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">cos</id> <apply> <mult /> <apply> <mult /> <apply> <mult /> <apply> <mult /> <real>2</real> <id labels="CONSTANT" xml:space="preserve" label-is-contextual="true">π</id> </apply> <id xml:space="preserve">j</id> </apply> <real>5</real> </apply> <id labels="VARIABLE" xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ω<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span> </id> </apply> </apply> </define> </math> </region>
<region id="ID0EUJJDB" top="288.00000000000006" left="38.400000000000006" height="47.2" width="115.34" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="159"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve">k</id> <range> <apply> <div /> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">n</id> <real>2</real> </apply> <apply> <minus /> <apply> <div /> <apply> <mult /> <real>3</real> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">n</id> </apply> <real>4</real> </apply> <real>1</real> </apply> </range> </define> </math> </region>	<region id="ID0EJKJDB" top="288.00000000000006" left="192.00000000000003" height="36.800000000000004" width="168.64" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="161"> <define xmlns="http://schemas.mathsoft.com/math50"> <apply> <indexer /> <id labels="VARIABLE" xml:space="preserve">y</id> <id labels="*" xml:space="preserve">k</id> </apply> <apply> <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">cos</id> <apply> <mult /> <apply> <mult /> <apply> <mult /> <apply> <mult /> <real>2</real> <id labels="CONSTANT" xml:space="preserve" label-is-contextual="true">π</id> </apply> <id xml:space="preserve">k</id> </apply> <real>10</real> </apply> <id labels="VARIABLE" xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ω<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span> </id> </apply> </apply> </define> </math> </region>
<region id="ID0ECLJDB" top="345.6" left="38.400000000000006" height="47.2" width="106.81333333333335" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="163"> <define xmlns="http://schemas.mathsoft.com/math50"> <id labels="VARIABLE" xml:space="preserve">l</id> <range> <apply> <mult /> <real>3</real> <apply> <div /> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">n</id> <real>4</real> </apply> </apply> <apply> <minus /> <id labels="VARIABLE" xml:space="preserve" label-is-contextual="true">n</id> <real>1</real> </apply> </range> </define> </math> </region>	<region id="ID0EWLJDB" top="345.6" left="192.00000000000003" height="36.800000000000004" width="162.54" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="165"> <define xmlns="http://schemas.mathsoft.com/math50"> <apply> <indexer /> <id labels="VARIABLE" xml:space="preserve">y</id> <id labels="*" xml:space="preserve">l</id> </apply> <apply> <id labels="FUNCTION" xml:space="preserve" label-is-contextual="true">cos</id> <apply> <mult /> <apply> <mult /> <apply> <mult /> <apply> <mult /> <real>2</real> <id labels="CONSTANT" xml:space="preserve" label-is-contextual="true">π</id> </apply> <id xml:space="preserve">l</id> </apply> <real>15</real> </apply> <id labels="VARIABLE" xml:space="preserve"> <Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation">ω<Subscript xmlns="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">0</Subscript></Span> </id> </apply> </apply> </define> </math> </region>

2. 繪製測試信號。

3. 使用函數 cpt 計算 2 階的順向局部餘弦轉換。

傳回的矩陣包含 3 階的局部餘弦轉換。

0 階區塊：	<region id="ID0ENSJDB" top="921.60000000000014" left="307.20000000000005" height="36.800000000000004" width="40.436666666666667" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="183"> <apply xmlns="http://schemas.mathsoft.com/math50"> <indexer /> <id xml:space="preserve">W</id> <sequence> <real>0</real> <real>0</real> </sequence> </apply> </math> </region>
1 階區塊：	<region id="ID0ESTJDB" top="960.00000000000011" left="230.40000000000003" height="36.800000000000004" width="40.436666666666667" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="185"> <apply xmlns="http://schemas.mathsoft.com/math50"> <indexer /> <id xml:space="preserve">W</id> <sequence> <real>1</real> <real>0</real> </sequence> </apply> </math> </region>		<region id="ID0EIUJDB" top="960.00000000000011" left="384.00000000000006" height="36.800000000000004" width="40.436666666666667" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="187"> <apply xmlns="http://schemas.mathsoft.com/math50"> <indexer /> <id xml:space="preserve">W</id> <sequence> <real>1</real> <real>1</real> </sequence> </apply> </math> </region>
2 階區塊：	<region id="ID0ELVJDB" top="998.40000000000009" left="192.00000000000003" height="36.800000000000004" width="40.436666666666667" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="189"> <apply xmlns="http://schemas.mathsoft.com/math50"> <indexer /> <id xml:space="preserve">W</id> <sequence> <real>2</real> <real>0</real> </sequence> </apply> </math> </region>	<region id="ID0E6VJDB" top="998.40000000000009" left="268.80000000000007" height="36.800000000000004" width="40.436666666666667" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="191"> <apply xmlns="http://schemas.mathsoft.com/math50"> <indexer /> <id xml:space="preserve">W</id> <sequence> <real>2</real> <real>1</real> </sequence> </apply> </math> </region>	<region id="ID0ETWJDB" top="998.40000000000009" left="345.6" height="36.800000000000004" width="40.436666666666667" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="193"> <apply xmlns="http://schemas.mathsoft.com/math50"> <indexer /> <id xml:space="preserve">W</id> <sequence> <real>2</real> <real>2</real> </sequence> </apply> </math> </region>	<region id="ID0EHXJDB" top="998.40000000000009" left="422.40000000000009" height="36.800000000000004" width="40.436666666666667" xmlns="http://schemas.mathsoft.com/worksheet50"> <math resultRef="195"> <apply xmlns="http://schemas.mathsoft.com/math50"> <indexer /> <id xml:space="preserve">W</id> <sequence> <real>2</real> <real>3</real> </sequence> </apply> </math> </region>

4. 繪製包含單一斜度數據區塊之 DCT 的 0 階轉換。

此轉換包含 4 個尖峰，對應至 4 條正弦曲線的頻率。

5. 繪製包含 2 個 DCT 的 1 階轉換，其中一個代表數據的前半部，另一個代表後半部。

此轉換在 n/2 數據點的兩個 DCT 中，各有 2 個尖峰。·如按下垂直標記所示，前兩個尖峰位於前兩條正弦曲線頻率的一半，而後兩個尖峰位於 (n/2) + 後兩條正弦曲線頻率的中間。藍色標記顯示兩個 DCT 的邊界。

6. 繪製包含 4 個 DCT 的 2 階轉換，每個 DCT 各佔數據的四分之一。

此轉換在 n/4 數據點的四個 DCT 中，各有 1 個尖峰。如按下垂直標記所示，第一個尖峰位於第一條正弦曲線頻率的四分之一處，第二個尖峰位於 n/4 + 第二條正弦曲線頻率的四分之一處，第三個尖峰位於 2n/4 + 第三條正弦曲線頻率的四分之一處，而第四個尖峰位於 3n/4 + 第四條正弦曲線頻率的四分之一處。藍色標記顯示四個 DCT 的邊界。

相關主題

局部餘弦轉換

這是否有幫助?