Signal Processing

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

All methods on this page are instance methods on NDArray.

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.