Algoritma kompresi JPEG menggunakan Transformasi Fourier Diskret, yang didefinisikan menggunakan basis \(\bcal\) dengan vektor-vektor basis
\begin{equation*}
\begin{aligned}
\vvec_0 = \left[\begin{array}{c}
\cos\left(\frac{(2\cdot0+1)\cdot0\pi}{16}\right) \\
\cos\left(\frac{(2\cdot1+1)\cdot0\pi}{16}\right) \\
\cos\left(\frac{(2\cdot2+1)\cdot0\pi}{16}\right) \\
\vdots \\
\cos\left(\frac{(2\cdot7+1)\cdot0\pi}{16}\right) \\
\end{array}\right], \amp
\vvec_1 = \left[\begin{array}{c}
\cos\left(\frac{(2\cdot0+1)\cdot1\pi}{16}\right) \\
\cos\left(\frac{(2\cdot1+1)\cdot1\pi}{16}\right) \\
\cos\left(\frac{(2\cdot2+1)\cdot1\pi}{16}\right) \\
\vdots \\
\cos\left(\frac{(2\cdot7+1)\cdot1\pi}{16}\right) \\
\end{array}\right], \\ \\
\ldots,
\vvec_6 = \left[\begin{array}{c}
\cos\left(\frac{(2\cdot0+1)\cdot6\pi}{16}\right) \\
\cos\left(\frac{(2\cdot1+1)\cdot6\pi}{16}\right) \\
\cos\left(\frac{(2\cdot2+1)\cdot6\pi}{16}\right) \\
\vdots \\
\cos\left(\frac{(2\cdot7+1)\cdot6\pi}{16}\right) \\
\end{array}\right], \amp
\vvec_7 = \left[\begin{array}{c}
\cos\left(\frac{(2\cdot0+1)\cdot7\pi}{16}\right) \\
\cos\left(\frac{(2\cdot1+1)\cdot7\pi}{16}\right) \\
\cos\left(\frac{(2\cdot2+1)\cdot7\pi}{16}\right) \\
\vdots \\
\cos\left(\frac{(2\cdot7+1)\cdot7\pi}{16}\right) \\
\end{array}\right]\text{.} \\
\end{aligned}
\end{equation*}