Signal Processing

Discrete transforms for frequency-domain analysis (FFT, real FFT, and DCT).

All methods on this page are instance methods on NDArray.

Global functions

FFT and DCT entry points are also exposed as functions under PhpMlKit\NDArray\Fft (for example, fft($a, …) calls $a->fft(…)). See Global functions — FFT and DCT.

Normalization

Transforms accept a Normalization enum (backward, ortho, forward, none). Default: Normalization::Backward.

Unnormalized transforms (Normalization::None)

Normalization::None returns the raw backend scaling. This is useful for low-level work, but it means round-trips like $x->fft(norm: Normalization::None)->ifft(norm: Normalization::None) will generally return a scaled version of x (not x itself).

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fft()

public function fft(?int $n = null, int $axis = -1, Normalization $norm = Normalization::Backward): NDArray

Complex discrete Fourier transform along one axis. Real inputs are promoted to a complex dtype.

Parameters

Parameter	Type	Description
$n	int|null	Transform length along axis. If null, uses the current axis length.
$axis	int	Axis index (negative indices allowed). Default: -1 (last axis).
$norm	Normalization	Normalization mode. Default: Normalization::Backward.

Returns

• NDArray - Complex array (Complex64 or Complex128).

Examples

use PhpMlKit\NDArray\NDArray;
use PhpMlKit\NDArray\Normalization;

$x = NDArray::array([0.0, 1.0, 2.0, 3.0]);
$X = $x->fft(norm: Normalization::Backward);

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ifft()

public function ifft(?int $n = null, int $axis = -1, Normalization $norm = Normalization::Backward): NDArray

Inverse complex FFT along one axis.

Parameters

Parameter	Type	Description
$n	int|null	Transform length along axis. If null, uses the current axis length.
$axis	int	Axis index (negative indices allowed). Default: -1.
$norm	Normalization	Normalization mode. Default: Normalization::Backward.

Returns

• NDArray - Complex array.

Examples

use PhpMlKit\NDArray\Normalization;

$x = NDArray::array([0.0, 1.0, 2.0, 3.0]);
$X = $x->fft(norm: Normalization::Backward);
$x2 = $X->ifft(norm: Normalization::Backward);

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fftn()

public function fftn(?array $axes = null, Normalization $norm = Normalization::Backward): NDArray

N-dimensional complex FFT. If axes is null or empty, transforms all axes in order.

Parameters

Parameter	Type	Description
$axes	array<int>|null	Axes to transform (negative indices allowed). Null/empty means all axes.
$norm	Normalization	Normalization mode. Default: Normalization::Backward.

Returns

• NDArray - Complex array.

Examples

use PhpMlKit\NDArray\Normalization;

$a = NDArray::array([[1.0, 0.0], [0.0, 0.0]]);
$F = $a->fftn(norm: Normalization::Backward);

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ifftn()

public function ifftn(?array $axes = null, Normalization $norm = Normalization::Backward): NDArray

N-dimensional inverse complex FFT.

Parameters

Parameter	Type	Description
$axes	array<int>|null	Axes to transform (negative indices allowed). Null/empty means all axes.
$norm	Normalization	Normalization mode. Default: Normalization::Backward.

Returns

• NDArray - Complex array.

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fft2()

public function fft2(Normalization $norm = Normalization::Backward): NDArray

2-D FFT on the last two axes. Requires ndim >= 2.

Parameters

Parameter	Type	Description
$norm	Normalization	Normalization mode. Default: Normalization::Backward.

Returns

• NDArray - Complex array.

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ifft2()

public function ifft2(Normalization $norm = Normalization::Backward): NDArray

2-D inverse FFT on the last two axes. Requires ndim >= 2.

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rfft()

public function rfft(?int $n = null, int $axis = -1, Normalization $norm = Normalization::Backward): NDArray

Real-input FFT along one axis. The output is complex and has length n//2 + 1 along the transformed axis.

Parameters

Parameter	Type	Description
$n	int|null	Real transform length along axis. If null, uses current axis length.
$axis	int	Axis index (negative indices allowed). Default: -1.
$norm	Normalization	Normalization mode. Default: Normalization::Backward.

Returns

• NDArray - Complex array.

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irfft()

public function irfft(?int $n = null, int $axis = -1, Normalization $norm = Normalization::Backward): NDArray

Inverse real FFT: complex Hermitian spectrum → real signal.

Parameters

Parameter	Type	Description
$n	int|null	Real output length along axis. If null, it is inferred from the spectrum length.
$axis	int	Axis index (negative indices allowed). Default: -1.
$norm	Normalization	Normalization mode. Default: Normalization::Backward.

Returns

• NDArray - Real array (Float32 or Float64).

Length inference

If you want an exact output length, pass $n. When omitted, irfft() infers a length from the frequency axis size.

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dct()

public function dct(int $type = 2, ?int $n = null, int $axis = -1, Normalization $norm = Normalization::Backward): NDArray

Discrete cosine transform (types I–IV) along one axis. This method only supports real inputs.

Parameters

Parameter	Type	Description
$type	int	DCT type: 1, 2, 3, or 4. Default: 2.
$n	int|null	Transform length along axis. If null, uses current axis length.
$axis	int	Axis index (negative indices allowed). Default: -1.
$norm	Normalization	Normalization mode. Default: Normalization::Backward.

Returns

• NDArray - Real array with the same float dtype as the input (Float32 or Float64).

Raises

• InvalidArgumentException - If $type is not in 1..4.
• DTypeException - If the input is complex.

Examples

use PhpMlKit\NDArray\Normalization;

$x = NDArray::array([1.0, 2.0, 3.0, 4.0]);
$y = $x->dct(2, norm: Normalization::Backward);

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idct()

public function idct(int $type = 2, ?int $n = null, int $axis = -1, Normalization $norm = Normalization::Backward): NDArray

Inverse DCT along one axis. For reconstructing norms (backward, ortho, forward), pairing with the same type and norm reconstructs the original signal:

$x2 = $x->dct(2, norm: Normalization::Ortho)->idct(2, norm: Normalization::Ortho);

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dctn()

public function dctn(?array $axes = null, int $type = 2, Normalization $norm = Normalization::Backward): NDArray

N-dimensional DCT. If axes is null or empty, transforms all axes in order.

Parameters

Parameter	Type	Description
$axes	array<int>|null	Axes to transform (negative indices allowed). Null/empty means all axes.
$type	int	DCT type (1..4). Default: 2.
$norm	Normalization	Normalization mode. Default: Normalization::Backward.

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idctn()

public function idctn(?array $axes = null, int $type = 2, Normalization $norm = Normalization::Backward): NDArray

N-dimensional inverse DCT.

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dct2() / idct2()

public function dct2(int $type = 2, Normalization $norm = Normalization::Backward): NDArray
public function idct2(int $type = 2, Normalization $norm = Normalization::Backward): NDArray

2-D DCT on the last two axes (and inverse). Requires ndim >= 2.