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<ml:imag>-4</ml:imag> </ml:complex> <ml:complex> <ml:real>1.2246063538223775E-16</ml:real> <ml:imag>-1.1102230246251565E-16</ml:imag> </ml:complex> <ml:real>5.436731793928562E-16</ml:real> <ml:real>2.3348293784475338E-16</ml:real> <ml:real>3.2162857446782489E-16</ml:real> <ml:complex> <ml:real>1.224606353822377E-16</ml:real> <ml:imag>1.1102230246251565E-16</ml:imag> </ml:complex> <ml:complex> <ml:real>-1.6767728698574569E-15</ml:real> <ml:imag>4</ml:imag> </ml:complex> </ml:matrix> </result> </ml:eval> </ml:define> </math> <rendering item-idref="37"/> </region> <region region-id="356" left="6" top="2027.25" width="18.75" height="15.75" align-x="6" align-y="2040" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="14">4.1</f> </p> </text> </region> <region region-id="367" left="6" top="2048.25" width="387" height="24" align-x="6" align-y="2058" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Da jeg lavede Decemation in time fik jeg matrixen Dec, så det ses at slut resultatet er det samme, for både decemation in time og decemation in frequency. </p> </text> </region> <region region-id="383" left="6" top="2102.25" width="84" height="12" align-x="6" align-y="2112" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Decemation in time</p> </text> </region> <region region-id="382" left="192" top="2102.25" width="107.25" height="12" align-x="192" align-y="2112" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Decemation in frequency</p> </text> </region> <region region-id="380" left="6" top="2124" width="72" height="167.25" align-x="6" align-y="2124" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <metafile mapping-mode="8" x-extent="70.49763" y-extent="165.7417" item-idref="38"/> </picture> <rendering item-idref="39"/> </region> <region region-id="381" left="216" top="2126.25" width="51" height="158.25" align-x="225" align-y="2208" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">x</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="8" cols="1"> <ml:real>1.1438332919722072E-17</ml:real> <ml:complex> <ml:real>3.2162857446782489E-16</ml:real> <ml:imag>-4</ml:imag> </ml:complex> <ml:complex> <ml:real>1.2246063538223775E-16</ml:real> <ml:imag>-1.1102230246251565E-16</ml:imag> </ml:complex> <ml:real>5.436731793928562E-16</ml:real> <ml:real>2.3348293784475338E-16</ml:real> <ml:real>3.2162857446782489E-16</ml:real> <ml:complex> <ml:real>1.224606353822377E-16</ml:real> <ml:imag>1.1102230246251565E-16</ml:imag> </ml:complex> <ml:complex> <ml:real>-1.6767728698574569E-15</ml:real> <ml:imag>4</ml:imag> </ml:complex> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="40"/> </region> <region region-id="384" left="6" top="2303.25" width="18.75" height="15.75" align-x="6" align-y="2316" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="14">4.2</f> </p> </text> </region> <region region-id="386" left="6" top="2330.25" width="68.25" height="12" align-x="22.5" align-y="2340" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Hanning vindue:</p> </text> </region> <region region-id="389" left="12" top="2355" width="30" height="12.75" align-x="27" align-y="2364" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">M</ml:id> <ml:id xml:space="preserve">N</ml:id> </ml:define> </math> <rendering item-idref="41"/> </region> <region region-id="400" left="6" top="2374.5" width="155.25" height="35.25" align-x="57.75" align-y="2394" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:function> <ml:id xml:space="preserve">hanning</ml:id> <ml:boundVars> <ml:id xml:space="preserve">n</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:mult style="auto-select"/> <ml:real>2</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:minus/> <ml:id xml:space="preserve">M</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="42"/> </region> <region region-id="413" left="6" top="2412" width="393.75" height="144.75" align-x="6" align-y="2412" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="43"/> <rendering item-idref="44"/> </region> <region region-id="424" left="12" top="2690.25" width="106.5" height="12" align-x="21" align-y="2700" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">laver vinduet til en matrix</p> </text> </region> <region region-id="425" left="12" top="2709" width="96.75" height="18" align-x="55.5" align-y="2718" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">hanning</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:id xml:space="preserve">hanning</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="45"/> </region> <region region-id="422" left="186" top="2690.25" width="96" height="158.25" align-x="224.25" align-y="2772" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">hanning</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="8" cols="1"> <ml:real>0</ml:real> <ml:real>0.1882550990706332</ml:real> <ml:real>0.61126046697815717</ml:real> <ml:real>0.95048443395120952</ml:real> <ml:real>0.95048443395120952</ml:real> <ml:real>0.61126046697815728</ml:real> <ml:real>0.18825509907063331</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="46"/> </region> <region region-id="427" left="6" top="2864.25" width="144.75" height="12" align-x="6" align-y="2874" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">ganger haning vinduet på Indputet</p> </text> </region> <region region-id="431" left="6" top="2895" width="87" height="21" align-x="32.25" align-y="2904" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="0.h">x</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="0">x</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve">hanning</ml:id> <ml:id xml:space="preserve">n</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="47"/> </region> <region region-id="433" left="168" top="2894.25" width="84" height="158.25" align-x="189" align-y="2976" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="0.h">x</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="8" cols="1"> <ml:real>0</ml:real> <ml:real>0.13311645714579004</ml:real> <ml:real>0.61126046697815717</ml:real> <ml:real>0.67209398865915748</ml:real> <ml:real>1.163969277025917E-16</ml:real> <ml:real>-0.43222642127151067</ml:real> <ml:real>-0.18825509907063331</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="48"/> </region> <region region-id="456" left="6" top="3062.25" width="324" height="12" align-x="6" align-y="3072" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">køre decemation in frequence igen med inputtet gange med hanning viduet:</p> </text> </region> <region region-id="436" left="18" top="3095.25" width="39" height="15.75" align-x="25.5" align-y="3108" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f size="14">Trin 1:</f> </p> </text> </region> <region region-id="492" left="78" top="3132" width="111.75" height="162" align-x="78" align-y="3132" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{D3E34B21-9D75-101A-8C3D-00AA001A1652}" type="embedded" item-idref="49"/> <rendering item-idref="50"/> </region> <region region-id="487" left="6" top="3128.25" width="84" height="158.25" align-x="27" align-y="3210" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="0.h">x</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="8" cols="1"> <ml:real>0</ml:real> <ml:real>0.13311645714579004</ml:real> <ml:real>0.61126046697815717</ml:real> <ml:real>0.67209398865915748</ml:real> <ml:real>1.163969277025917E-16</ml:real> <ml:real>-0.43222642127151067</ml:real> <ml:real>-0.18825509907063331</ml:real> <ml:real>0</ml:real> </ml:matrix> </result> </ml:eval> </math> <rendering item-idref="51"/> </region> <region region-id="491" left="186" top="3095.25" width="260.25" height="236.25" align-x="207.75" align-y="3216" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve" subscript="1.h">x</ml:id> <ml:eval placeholderMultiplicationStyle="default"> <ml:matrix rows="8" cols="1"> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="0.h">x</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="0.h">x</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="0.h">x</ml:id> 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subscript="0.h">x</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="8">W</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult/> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="0.h">x</ml:id> <ml:real>7</ml:real> </ml:apply> <ml:parens> <ml:real>-1</ml:real> </ml:parens> </ml:apply> <ml:apply> <ml:indexer/> <ml:id xml:space="preserve" subscript="0.h">x</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="8">W</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:matrix> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:matrix rows="8" cols="1"> <ml:real>1.163969277025917E-16</ml:real> <ml:real>-0.29910996412572066</ml:real> <ml:real>0.42300536790752385</ml:real> <ml:real>0.67209398865915748</ml:real> 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use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Det ses, at når Hanning viduet er blevet ganget på, bliver stolpen ved 1 og spejlet ved 7 reduceret. 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Så i denne situration er det ikke nogen god idé at bruge vinduet. </p> </text> </region> <region region-id="617" left="6" top="4691.25" width="22.5" height="15.75" align-x="14.25" align-y="4704" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f size="14">4.3 </f> </p> </text> </region> <region region-id="626" left="42" top="4722" width="360" height="188.25" align-x="42" align-y="4722" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <ole clsid="{D3E34B21-9D75-101A-8C3D-00AA001A1652}" type="embedded" item-idref="72"/> <rendering item-idref="73"/> </region> <region region-id="628" left="12" top="4928.25" width="455.25" height="60" align-x="12" align-y="4938" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">På billedet ses det at der bliver multipliseret 12 gange, da fortegnskiftet (-1) kan laves uden at multiplicere</p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">hvis det havde været DTF skulle der laves 64 multiplikationer ifølge tabel 8.1 på side 522 i proakis 4.</p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" 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