Under the transform convention , a Gaussian stays Gaussian. Its spatial width is proportional to , while its frequency width is proportional to .采用变换约定 时，高斯函数 的变换仍是高斯函数。空间宽度正比于 ，频率宽度则正比于 。
Green shows the spatial profile and gold the frequency profile, with both peaks normalized to one to compare widths. A wider profile on one side means a narrower profile on the other.绿色表示空间分布，金色表示频率分布；两者峰值均归一化为一，以便比较宽度。一侧变宽，另一侧就变窄。