This is an automated email from the ASF dual-hosted git repository. erans pushed a commit to branch master in repository https://gitbox.apache.org/repos/asf/commons-math.git
commit 962d6b6543865ce9dba217b0223441a244d48a1a Author: Gilles Sadowski <gillese...@gmail.com> AuthorDate: Sun Jul 18 12:50:33 2021 +0200 Use MathJaX (Javadoc). --- .../commons/math4/transform/FastFourierTransform.java | 17 ++++++----------- 1 file changed, 6 insertions(+), 11 deletions(-) diff --git a/commons-math-transform/src/main/java/org/apache/commons/math4/transform/FastFourierTransform.java b/commons-math-transform/src/main/java/org/apache/commons/math4/transform/FastFourierTransform.java index 1dbad58..182b1c1 100644 --- a/commons-math-transform/src/main/java/org/apache/commons/math4/transform/FastFourierTransform.java +++ b/commons-math-transform/src/main/java/org/apache/commons/math4/transform/FastFourierTransform.java @@ -402,12 +402,10 @@ public class FastFourierTransform implements ComplexTransform { * to use the <em>standard</em> normalization convention. This normalization * convention is defined as follows * <ul> - * <li>forward transform: y<sub>n</sub> = ∑<sub>k=0</sub><sup>N-1</sup> - * x<sub>k</sub> exp(-2πi n k / N),</li> - * <li>inverse transform: x<sub>k</sub> = N<sup>-1</sup> - * ∑<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> exp(2πi n k / N),</li> + * <li>forward transform: \( y_n = \sum_{k = 0}^{N - 1} x_k e^{-2 \pi i n k / N} \),</li> + * <li>inverse transform: \( x_k = \frac{1}{N} \sum_{n = 0}^{N - 1} y_n e^{2 \pi i n k / N} \),</li> * </ul> - * where N is the size of the data sample. + * where \( N \) is the size of the data sample. */ STD, @@ -416,13 +414,10 @@ public class FastFourierTransform implements ComplexTransform { * to use the <em>unitary</em> normalization convention. This normalization * convention is defined as follows * <ul> - * <li>forward transform: y<sub>n</sub> = (1 / √N) - * ∑<sub>k=0</sub><sup>N-1</sup> x<sub>k</sub> - * exp(-2πi n k / N),</li> - * <li>inverse transform: x<sub>k</sub> = (1 / √N) - * ∑<sub>n=0</sub><sup>N-1</sup> y<sub>n</sub> exp(2πi n k / N),</li> + * <li>forward transform: \( y_n = \frac{1}{\sqrt{N}} \sum_{k = 0}^{N - 1} x_k e^{-2 \pi i n k / N} \),</li> + * <li>inverse transform: \( x_k = \frac{1}{\sqrt{N}} \sum_{n = 0}^{N - 1} y_n e^{2 \pi i n k / N} \),</li> * </ul> - * which makes the transform unitary. N is the size of the data sample. + * where \( N \) is the size of the data sample. */ UNIT; }