Example of zero-padding technique for the Discrete Fourier Transform (DFT): DFT <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 X(k)}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>X</mi><mo stretchy="false">(</mo><mi>k</mi><mo stretchy="false">)</mo></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle X(k)}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bba570685e082df7e6ff2d7f1c86cbb990aa6743" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:5.001ex; height:2.843ex;" alt="{\displaystyle X(k)}"></span> of the gate sequence <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 x\left(n\right)={\begin{cases}1&amp;0\leq n\leq N-1\\0&amp;n\geq N\end{cases}}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>x</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow><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></mtd><mtd><mn>0</mn><mo>≤<!-- ≤ --></mo><mi>n</mi><mo>≤<!-- ≤ --></mo><mi>N</mi><mo>−<!-- − --></mo><mn>1</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mi>n</mi><mo>≥<!-- ≥ --></mo><mi>N</mi></mtd></mtr></mtable><mo fence="true" stretchy="true" symmetric="true"></mo></mrow></mrow></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle x\left(n\right)={\begin{cases}1&amp;0\leq n\leq N-1\\0&amp;n\geq N\end{cases}}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/506c3252a1a895d18f515eba5d5b7695b1f367cb" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -2.505ex; width:28.819ex; height:6.176ex;" alt="{\displaystyle x\left(n\right)={\begin{cases}1&amp;0\leq n\leq N-1\\0&amp;n\geq N\end{cases}}}"></span> with <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 N_{1}=2N}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>N</mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub><mo>=</mo><mn>2</mn><mi>N</mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle N_{1}=2N}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/17596aa0465b40e590b83e0c61e83e5eec61d08f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.671ex; width:9.245ex; height:2.509ex;" alt="{\displaystyle N_{1}=2N}"></span>.
<a href="//commons.wikimedia.org/wiki/User:Luca_Ghio" title="User:Luca Ghio">Luca Ghio</a>
<span class="int-own-work" lang="en">Own work</span>