- All Implemented Interfaces:
Serializable
,Comparable<FFT.Mode>
- Enclosing class:
- FFT
FFT normalization mode.
There are multiple conventions regarding how Fourier transforms are defined. For an FFT, these affect how a transform is normalized.
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Enum Constant Summary
Enum ConstantsEnum ConstantDescriptionThe transform is defined by $X_k = \sum_{n=0}^{N-1} x_ne^{-2\pi kni/N}$, and the inverse transform is defined by $x_n = \frac1N \sum_{k=0}^{N-1} X_ke^{2\pi kni/N}$, where the indices have values in the range [0, N-1).The transform is defined by $X_k = \frac1N \sum_{n=0}^{N-1} x_ne^{-2\pi kni/N}$, and the inverse transform is defined by $x_n = \sum_{k=0}^{N-1} X_ke^{2\pi kni/N}$, where the indices have values in the range [0, N-1).The transform is defined by $X_k = \frac1{\sqrt{N}}\sum_{n=0}^{N-1} x_ne^{-2\pi kni/N}$, and the inverse transform is defined by $x_n = \frac1{\sqrt{N}}\sum_{k=0}^{N-1} X_ke^{2\pi kni/N}$, where the indices have values in the range [0, N-1). -
Method Summary
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Enum Constant Details
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NORMAL
The transform is defined by $X_k = \sum_{n=0}^{N-1} x_ne^{-2\pi kni/N}$, and the inverse transform is defined by $x_n = \frac1N \sum_{k=0}^{N-1} X_ke^{2\pi kni/N}$, where the indices have values in the range [0, N-1). This is particularly useful when using an FFT to compute a convolution or cross correlation. -
SYMMETRIC
The transform is defined by $X_k = \frac1{\sqrt{N}}\sum_{n=0}^{N-1} x_ne^{-2\pi kni/N}$, and the inverse transform is defined by $x_n = \frac1{\sqrt{N}}\sum_{k=0}^{N-1} X_ke^{2\pi kni/N}$, where the indices have values in the range [0, N-1). This is useful when one wants the norm of a vector and its transform to be identical, as is typically the case in physics applications. -
REVERSED
The transform is defined by $X_k = \frac1N \sum_{n=0}^{N-1} x_ne^{-2\pi kni/N}$, and the inverse transform is defined by $x_n = \sum_{k=0}^{N-1} X_ke^{2\pi kni/N}$, where the indices have values in the range [0, N-1). This is useful for statistics applications due to the definition of the characteristic function.
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Method Details
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values
Returns an array containing the constants of this enum type, in the order they are declared.- Returns:
- an array containing the constants of this enum type, in the order they are declared
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valueOf
Returns the enum constant of this type with the specified name. The string must match exactly an identifier used to declare an enum constant in this type. (Extraneous whitespace characters are not permitted.)- Parameters:
name
- the name of the enum constant to be returned.- Returns:
- the enum constant with the specified name
- Throws:
IllegalArgumentException
- if this enum type has no constant with the specified nameNullPointerException
- if the argument is null
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