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1721--h-m-tri-la-gi [2018/11/07 17:09] (current)
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 +<​HTML><​br><​div id="​mw-content-text"​ lang="​vi"​ dir="​ltr"><​div class="​mw-parser-output"><​div class="​thumb tright"><​div class="​thumbinner"​ style="​width:​222px;"><​img alt=""​ src="​http://​upload.wikimedia.org/​wikipedia/​commons/​thumb/​c/​c8/​Triangular_function.svg/​220px-Triangular_function.svg.png"​ width="​220"​ height="​154"​ class="​thumbimage"​ srcset="//​upload.wikimedia.org/​wikipedia/​commons/​thumb/​c/​c8/​Triangular_function.svg/​330px-Triangular_function.svg.png 1.5x, //​upload.wikimedia.org/​wikipedia/​commons/​thumb/​c/​c8/​Triangular_function.svg/​440px-Triangular_function.svg.png 2x" data-file-width="​695"​ data-file-height="​485"/> ​ </​div></​div>​
 +<​p><​b>​Hàm tri</​b>​ hay còn gọi là <​b>​hàm tam giác</​b>​ là một hàm số toán học được định nghĩa như sau:
 +</p>
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle {begin{aligned}operatorname {tri} (t)=land (t)quad &​amp;​{overset {underset {mathrm {def} }{}}{=}} max(1-|t|,​0)\&​amp;​={begin{cases}1-|t|,&​amp;​|t|&​lt;​1\0,&​amp;​{mbox{khác}}end{cases}}end{aligned}}}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mrow class="​MJX-TeXAtom-ORD"><​mtable columnalign="​right left right left right left right left right left right left" rowspacing="​3pt"​ columnspacing="​0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="​true"><​mtr><​mtd><​mi>​tri</​mi><​mo>​⁡<​!-- &#8289; --></​mo><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo>​=</​mo><​mo>​∧<​!-- &and; --></​mo><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mspace width="​1em"/></​mtd><​mtd><​mi/><​mrow class="​MJX-TeXAtom-ORD"><​mover><​mo>​=</​mo><​munder><​mrow/><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​normal">​d</​mi><​mi mathvariant="​normal">​e</​mi><​mi mathvariant="​normal">​f</​mi></​mrow></​munder></​mover></​mrow><​mtext>​ </​mtext><​mo movablelimits="​true"​ form="​prefix">​max</​mo><​mo stretchy="​false">​(</​mo><​mn>​1</​mn><​mo>​−<​!-- &minus; --></​mo><​mrow class="​MJX-TeXAtom-ORD"><​mo stretchy="​false">​|</​mo></​mrow><​mi>​t</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mo stretchy="​false">​|</​mo></​mrow><​mo>,</​mo><​mn>​0</​mn><​mo stretchy="​false">​)</​mo></​mtd></​mtr><​mtr><​mtd/><​mtd><​mi/><​mo>​=</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mrow><​mo>​{</​mo><​mtable columnalign="​left left" rowspacing="​.2em"​ columnspacing="​1em"​ displaystyle="​false"><​mtr><​mtd><​mn>​1</​mn><​mo>​−<​!-- &minus; --></​mo><​mrow class="​MJX-TeXAtom-ORD"><​mo stretchy="​false">​|</​mo></​mrow><​mi>​t</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mo stretchy="​false">​|</​mo></​mrow><​mo>,</​mo></​mtd><​mtd><​mrow class="​MJX-TeXAtom-ORD"><​mo stretchy="​false">​|</​mo></​mrow><​mi>​t</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mo stretchy="​false">​|</​mo></​mrow><​mo>&​lt;</​mo><​mn>​1</​mn></​mtd></​mtr><​mtr><​mtd><​mn>​0</​mn><​mo>,</​mo></​mtd><​mtd><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​false"​ scriptlevel="​0"><​mtext>​khác</​mtext></​mstyle></​mrow></​mtd></​mtr></​mtable><​mo fence="​true"​ stretchy="​true"​ symmetric="​true"/></​mrow></​mrow></​mtd></​mtr></​mtable></​mrow></​mstyle></​mrow>​{displaystyle {begin{aligned}operatorname {tri} (t)=land (t)quad &​amp;​{overset {underset {mathrm {def} }{}}{=}} max(1-|t|,​0)\&​amp;​={begin{cases}1-|t|,&​amp;​|t|&​lt;​1\0,&​amp;​{mbox{khác}}end{cases}}end{aligned}}}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​214c298fdac7153ac3770892cfc07415ba888f50"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -4.671ex; width:​36.577ex;​ height:​10.509ex;"​ alt="​{displaystyle {begin{aligned}operatorname {tri} (t)=land (t)quad &​amp;​{overset {underset {mathrm {def} }{}}{=}} max(1-|t|,​0)\&​amp;​={begin{cases}1-|t|,&​amp;​|t|&​lt;​1\0,&​amp;​{mbox{khác}}end{cases}}end{aligned}}}"/></​span></​dd></​dl><​p>​Hoặc tương đương với <a href="​http://​vi.wikipedia.org/​wiki/​T%C3%ADch_ch%E1%BA%ADp"​ title="​Tích chập">​tích chập của 2 hàm rect đơn vị giống nhau:
 +</p>
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle {begin{aligned}operatorname {tri} (t)=operatorname {rect} (t)*operatorname {rect} (t)quad &​amp;​{overset {underset {mathrm {def} }{}}{=}}int _{-infty }^{infty }mathrm {rect} (tau )cdot mathrm {rect} (t-tau ) dtau \&​amp;​=int _{-infty }^{infty }mathrm {rect} (tau )cdot mathrm {rect} (tau -t) dtau .end{aligned}}}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mrow class="​MJX-TeXAtom-ORD"><​mtable columnalign="​right left right left right left right left right left right left" rowspacing="​3pt"​ columnspacing="​0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="​true"><​mtr><​mtd><​mi>​tri</​mi><​mo>​⁡<​!-- &#8289; --></​mo><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo>​=</​mo><​mi>​rect</​mi><​mo>​⁡<​!-- &#8289; --></​mo><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo>​∗<​!-- &​lowast;​ --></​mo><​mi>​rect</​mi><​mo>​⁡<​!-- &#8289; --></​mo><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mspace width="​1em"/></​mtd><​mtd><​mi/><​mrow class="​MJX-TeXAtom-ORD"><​mover><​mo>​=</​mo><​munder><​mrow/><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​normal">​d</​mi><​mi mathvariant="​normal">​e</​mi><​mi mathvariant="​normal">​f</​mi></​mrow></​munder></​mover></​mrow><​msubsup><​mo>​∫<​!-- &int; --></​mo><​mrow class="​MJX-TeXAtom-ORD"><​mo>​−<​!-- &minus; --></​mo><​mi mathvariant="​normal">​∞<​!-- &infin; --></​mi></​mrow><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​normal">​∞<​!-- &infin; --></​mi></​mrow></​msubsup><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​normal">​r</​mi><​mi mathvariant="​normal">​e</​mi><​mi mathvariant="​normal">​c</​mi><​mi mathvariant="​normal">​t</​mi></​mrow><​mo stretchy="​false">​(</​mo><​mi>​τ<​!-- &tau; --></​mi><​mo stretchy="​false">​)</​mo><​mo>​⋅<​!-- &sdot; --></​mo><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​normal">​r</​mi><​mi mathvariant="​normal">​e</​mi><​mi mathvariant="​normal">​c</​mi><​mi mathvariant="​normal">​t</​mi></​mrow><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​τ<​!-- &tau; --></​mi><​mo stretchy="​false">​)</​mo><​mtext>​ </​mtext><​mi>​d</​mi><​mi>​τ<​!-- &tau; --></​mi></​mtd></​mtr><​mtr><​mtd/><​mtd><​mi/><​mo>​=</​mo><​msubsup><​mo>​∫<​!-- &int; --></​mo><​mrow class="​MJX-TeXAtom-ORD"><​mo>​−<​!-- &minus; --></​mo><​mi mathvariant="​normal">​∞<​!-- &infin; --></​mi></​mrow><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​normal">​∞<​!-- &infin; --></​mi></​mrow></​msubsup><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​normal">​r</​mi><​mi mathvariant="​normal">​e</​mi><​mi mathvariant="​normal">​c</​mi><​mi mathvariant="​normal">​t</​mi></​mrow><​mo stretchy="​false">​(</​mo><​mi>​τ<​!-- &tau; --></​mi><​mo stretchy="​false">​)</​mo><​mo>​⋅<​!-- &sdot; --></​mo><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​normal">​r</​mi><​mi mathvariant="​normal">​e</​mi><​mi mathvariant="​normal">​c</​mi><​mi mathvariant="​normal">​t</​mi></​mrow><​mo stretchy="​false">​(</​mo><​mi>​τ<​!-- &tau; --></​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mtext>​ </​mtext><​mi>​d</​mi><​mi>​τ<​!-- &tau; --></​mi><​mo>​.</​mo></​mtd></​mtr></​mtable></​mrow></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle {begin{aligned}operatorname {tri} (t)=operatorname {rect} (t)*operatorname {rect} (t)quad &​amp;​{overset {underset {mathrm {def} }{}}{=}}int _{-infty }^{infty }mathrm {rect} (tau )cdot mathrm {rect} (t-tau ) dtau \&​amp;​=int _{-infty }^{infty }mathrm {rect} (tau )cdot mathrm {rect} (tau -t) dtau .end{aligned}}}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​ded288eb3d29c5be53d4eda6879ccb40837d78cc"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -5.505ex; width:​57.26ex;​ height:​12.176ex;"​ alt="​{displaystyle {begin{aligned}operatorname {tri} (t)=operatorname {rect} (t)*operatorname {rect} (t)quad &​amp;​{overset {underset {mathrm {def} }{}}{=}}int _{-infty }^{infty }mathrm {rect} (tau )cdot mathrm {rect} (t-tau ) dtau \&​amp;​=int _{-infty }^{infty }mathrm {rect} (tau )cdot mathrm {rect} (tau -t) dtau .end{aligned}}}"/></​span></​dd></​dl> ​
 +<div class="​center"><​div class="​thumb tnone"><​div class="​thumbinner"​ style="​width:​470px;"><​img alt=""​ src="​http://​upload.wikimedia.org/​wikipedia/​commons/​6/​6a/​Convolution_of_box_signal_with_itself2.gif"​ width="​468"​ height="​147"​ class="​thumbimage"​ data-file-width="​468"​ data-file-height="​147"/> ​ <div class="​thumbcaption">​Tích chập của 2 hàm rect là 1 hàm tri.</​div></​div></​div></​div>​
  
 +<​p>​Hàm tri cũng có thể được biểu diễn bởi hàm rect và hàm trị tuyệt đối:
 +</p>
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle operatorname {tri} (t)=operatorname {rect} (t/​2)left(1-left|tright|right)}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mi>​tri</​mi><​mo>​⁡<​!-- &#8289; --></​mo><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo>​=</​mo><​mi>​rect</​mi><​mo>​⁡<​!-- &#8289; --></​mo><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mo>/</​mo></​mrow><​mn>​2</​mn><​mo stretchy="​false">​)</​mo><​mrow><​mo>​(</​mo><​mrow><​mn>​1</​mn><​mo>​−<​!-- &minus; --></​mo><​mrow><​mo>​|</​mo><​mi>​t</​mi><​mo>​|</​mo></​mrow></​mrow><​mo>​)</​mo></​mrow></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle operatorname {tri} (t)=operatorname {rect} (t/​2)left(1-left|tright|right)}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​2d4e309badf39aa133ac26463f42c97b5a5256ef"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​25.398ex;​ height:​2.843ex;"​ alt="​{displaystyle operatorname {tri} (t)=operatorname {rect} (t/​2)left(1-left|tright|right)}"/></​span></​dd></​dl><​p>​Hàm số này được sử dụng nhiều trong xử lý tín hiệu và kỹ thuật truyền thông.
 +</p>
 +
 +<​p>​Với các giá trị <span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle aneq 0,​}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mi>​a</​mi><​mo>​≠<​!-- &ne; --></​mo><​mn>​0</​mn><​mspace width="​thinmathspace"/></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle aneq 0,​}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​afa35d06866e48768602d3b73a20555a5c384625"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -0.838ex; width:​5.878ex;​ height:​2.676ex;"​ alt="​{displaystyle aneq 0,​}"/></​span>​ <​b>:</​b>​
 +</p>
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle {begin{aligned}operatorname {tri} (t/​a)&​amp;​=int _{-infty }^{infty }mathrm {rect} (tau )cdot mathrm {rect} (tau -t/a) dtau \&​amp;​={begin{cases}1-|t/​a|,&​amp;​|t|&​lt;​|a|\0,&​amp;​{mbox{khác}}.end{cases}}end{aligned}}}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mrow class="​MJX-TeXAtom-ORD"><​mtable columnalign="​right left right left right left right left right left right left" rowspacing="​3pt"​ columnspacing="​0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="​true"><​mtr><​mtd><​mi>​tri</​mi><​mo>​⁡<​!-- &#8289; --></​mo><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mo>/</​mo></​mrow><​mi>​a</​mi><​mo stretchy="​false">​)</​mo></​mtd><​mtd><​mi/><​mo>​=</​mo><​msubsup><​mo>​∫<​!-- &int; --></​mo><​mrow class="​MJX-TeXAtom-ORD"><​mo>​−<​!-- &minus; --></​mo><​mi mathvariant="​normal">​∞<​!-- &infin; --></​mi></​mrow><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​normal">​∞<​!-- &infin; --></​mi></​mrow></​msubsup><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​normal">​r</​mi><​mi mathvariant="​normal">​e</​mi><​mi mathvariant="​normal">​c</​mi><​mi mathvariant="​normal">​t</​mi></​mrow><​mo stretchy="​false">​(</​mo><​mi>​τ<​!-- &tau; --></​mi><​mo stretchy="​false">​)</​mo><​mo>​⋅<​!-- &sdot; --></​mo><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​normal">​r</​mi><​mi mathvariant="​normal">​e</​mi><​mi mathvariant="​normal">​c</​mi><​mi mathvariant="​normal">​t</​mi></​mrow><​mo stretchy="​false">​(</​mo><​mi>​τ<​!-- &tau; --></​mi><​mo>​−<​!-- &minus; --></​mo><​mi>​t</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mo>/</​mo></​mrow><​mi>​a</​mi><​mo stretchy="​false">​)</​mo><​mtext>​ </​mtext><​mi>​d</​mi><​mi>​τ<​!-- &tau; --></​mi></​mtd></​mtr><​mtr><​mtd/><​mtd><​mi/><​mo>​=</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mrow><​mo>​{</​mo><​mtable columnalign="​left left" rowspacing="​.2em"​ columnspacing="​1em"​ displaystyle="​false"><​mtr><​mtd><​mn>​1</​mn><​mo>​−<​!-- &minus; --></​mo><​mrow class="​MJX-TeXAtom-ORD"><​mo stretchy="​false">​|</​mo></​mrow><​mi>​t</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mo>/</​mo></​mrow><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mo stretchy="​false">​|</​mo></​mrow><​mo>,</​mo></​mtd><​mtd><​mrow class="​MJX-TeXAtom-ORD"><​mo stretchy="​false">​|</​mo></​mrow><​mi>​t</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mo stretchy="​false">​|</​mo></​mrow><​mo>&​lt;</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mo stretchy="​false">​|</​mo></​mrow><​mi>​a</​mi><​mrow class="​MJX-TeXAtom-ORD"><​mo stretchy="​false">​|</​mo></​mrow></​mtd></​mtr><​mtr><​mtd><​mn>​0</​mn><​mo>,</​mo></​mtd><​mtd><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​false"​ scriptlevel="​0"><​mtext>​khác</​mtext></​mstyle></​mrow><​mo>​.</​mo></​mtd></​mtr></​mtable><​mo fence="​true"​ stretchy="​true"​ symmetric="​true"/></​mrow></​mrow></​mtd></​mtr></​mtable></​mrow></​mstyle></​mrow><​annotation encoding="​application/​x-tex">​{displaystyle {begin{aligned}operatorname {tri} (t/​a)&​amp;​=int _{-infty }^{infty }mathrm {rect} (tau )cdot mathrm {rect} (tau -t/a) dtau \&​amp;​={begin{cases}1-|t/​a|,&​amp;​|t|&​lt;​|a|\0,&​amp;​{mbox{khác}}.end{cases}}end{aligned}}}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​90a46e60991118fd065cfb37a8d74069eb41efa2"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -5.671ex; width:​40.722ex;​ height:​12.509ex;"​ alt="​{displaystyle {begin{aligned}operatorname {tri} (t/​a)&​amp;​=int _{-infty }^{infty }mathrm {rect} (tau )cdot mathrm {rect} (tau -t/a) dtau \&​amp;​={begin{cases}1-|t/​a|,&​amp;​|t|&​lt;​|a|\0,&​amp;​{mbox{khác}}.end{cases}}end{aligned}}}"/></​span></​dd></​dl>​
 +<​p>​Biển đổi Fourier dễ dàng bằng cách sử dụng công thức tích chập của 2 hàm rect:
 +</p>
 +<​dl><​dd><​span class="​mwe-math-element"><​span class="​mwe-math-mathml-inline mwe-math-mathml-a11y"​ style="​display:​ none;"><​math xmlns="​http://​www.w3.org/​1998/​Math/​MathML"​ alttext="​{displaystyle {begin{aligned}{mathcal {F}}{operatorname {tri} (t)}&​amp;​={mathcal {F}}{operatorname {rect} (t)*operatorname {rect} (t)}\&​amp;​={mathcal {F}}{operatorname {rect} (t)}cdot {mathcal {F}}{operatorname {rect} (t)}\&​amp;​={mathcal {F}}{operatorname {rect} (t)}^{2}\&​amp;​=mathrm {si} ^{2}(f).end{aligned}}}"><​semantics><​mrow class="​MJX-TeXAtom-ORD"><​mstyle displaystyle="​true"​ scriptlevel="​0"><​mrow class="​MJX-TeXAtom-ORD"><​mtable columnalign="​right left right left right left right left right left right left" rowspacing="​3pt"​ columnspacing="​0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="​true"><​mtr><​mtd><​mrow class="​MJX-TeXAtom-ORD"><​mrow class="​MJX-TeXAtom-ORD"><​mi class="​MJX-tex-caligraphic"​ mathvariant="​script">​F</​mi></​mrow></​mrow><​mo fence="​false"​ stretchy="​false">​{</​mo><​mi>​tri</​mi><​mo>​⁡<​!-- &#8289; --></​mo><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo fence="​false"​ stretchy="​false">​}</​mo></​mtd><​mtd><​mi/><​mo>​=</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mrow class="​MJX-TeXAtom-ORD"><​mi class="​MJX-tex-caligraphic"​ mathvariant="​script">​F</​mi></​mrow></​mrow><​mo fence="​false"​ stretchy="​false">​{</​mo><​mi>​rect</​mi><​mo>​⁡<​!-- &#8289; --></​mo><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo>​∗<​!-- &​lowast;​ --></​mo><​mi>​rect</​mi><​mo>​⁡<​!-- &#8289; --></​mo><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo fence="​false"​ stretchy="​false">​}</​mo></​mtd></​mtr><​mtr><​mtd/><​mtd><​mi/><​mo>​=</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mrow class="​MJX-TeXAtom-ORD"><​mi class="​MJX-tex-caligraphic"​ mathvariant="​script">​F</​mi></​mrow></​mrow><​mo fence="​false"​ stretchy="​false">​{</​mo><​mi>​rect</​mi><​mo>​⁡<​!-- &#8289; --></​mo><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo fence="​false"​ stretchy="​false">​}</​mo><​mo>​⋅<​!-- &sdot; --></​mo><​mrow class="​MJX-TeXAtom-ORD"><​mrow class="​MJX-TeXAtom-ORD"><​mi class="​MJX-tex-caligraphic"​ mathvariant="​script">​F</​mi></​mrow></​mrow><​mo fence="​false"​ stretchy="​false">​{</​mo><​mi>​rect</​mi><​mo>​⁡<​!-- &#8289; --></​mo><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​mo fence="​false"​ stretchy="​false">​}</​mo></​mtd></​mtr><​mtr><​mtd/><​mtd><​mi/><​mo>​=</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mrow class="​MJX-TeXAtom-ORD"><​mi class="​MJX-tex-caligraphic"​ mathvariant="​script">​F</​mi></​mrow></​mrow><​mo fence="​false"​ stretchy="​false">​{</​mo><​mi>​rect</​mi><​mo>​⁡<​!-- &#8289; --></​mo><​mo stretchy="​false">​(</​mo><​mi>​t</​mi><​mo stretchy="​false">​)</​mo><​msup><​mo fence="​false"​ stretchy="​false">​}</​mo><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup></​mtd></​mtr><​mtr><​mtd/><​mtd><​mi/><​mo>​=</​mo><​msup><​mrow class="​MJX-TeXAtom-ORD"><​mi mathvariant="​normal">​s</​mi><​mi mathvariant="​normal">​i</​mi></​mrow><​mrow class="​MJX-TeXAtom-ORD"><​mn>​2</​mn></​mrow></​msup><​mo stretchy="​false">​(</​mo><​mi>​f</​mi><​mo stretchy="​false">​)</​mo><​mo>​.</​mo></​mtd></​mtr></​mtable></​mrow></​mstyle></​mrow>​{displaystyle {begin{aligned}{mathcal {F}}{operatorname {tri} (t)}&​amp;​={mathcal {F}}{operatorname {rect} (t)*operatorname {rect} (t)}\&​amp;​={mathcal {F}}{operatorname {rect} (t)}cdot {mathcal {F}}{operatorname {rect} (t)}\&​amp;​={mathcal {F}}{operatorname {rect} (t)}^{2}\&​amp;​=mathrm {si} ^{2}(f).end{aligned}}}</​annotation></​semantics></​math></​span><​img src="​https://​wikimedia.org/​api/​rest_v1/​media/​math/​render/​svg/​b5ebdeb82769706326710626d28dbeec7eceb9e5"​ class="​mwe-math-fallback-image-inline"​ aria-hidden="​true"​ style="​vertical-align:​ -5.838ex; width:​36.455ex;​ height:​12.843ex;"​ alt="​{displaystyle {begin{aligned}{mathcal {F}}{operatorname {tri} (t)}&​amp;​={mathcal {F}}{operatorname {rect} (t)*operatorname {rect} (t)}\&​amp;​={mathcal {F}}{operatorname {rect} (t)}cdot {mathcal {F}}{operatorname {rect} (t)}\&​amp;​={mathcal {F}}{operatorname {rect} (t)}^{2}\&​amp;​=mathrm {si} ^{2}(f).end{aligned}}}"/></​span></​dd></​dl><​p>​với <​code>​si</​code>​ là <a href="​http://​vi.wikipedia.org/​wiki/​H%C3%A0m_sinc"​ title="​Hàm sinc">​hàm sinc không chuẩn.
 +</p>
 +
 +
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1721--h-m-tri-la-gi.txt · Last modified: 2018/11/07 17:09 (external edit)