# How to Use FFT Operations in MLX for Signal Processing

> Unlock powerful signal processing with MLX FFT operations. Learn to implement complex and real-valued transforms efficiently across CPU, CUDA, and Metal backends.

- Repository: [ml-explore/mlx](https://github.com/ml-explore/mlx)
- Tags: how-to-guide
- Published: 2026-06-18

---

**MLX provides high-performance Fast Fourier Transform (FFT) operations through the `mlx.fft` module, implementing complex and real-valued transforms with unified CPU, CUDA, and Metal backend support.**

The ml-explore/mlx repository delivers Apple's machine learning framework with first-class signal processing capabilities built directly into its tensor computation graph. Understanding how to leverage FFT operations in MLX enables efficient spectral analysis and convolution operations across diverse hardware targets including Apple Silicon, NVIDIA GPUs, and standard CPUs.

## Core FFT Architecture

The FFT implementation in MLX follows a layered architecture that separates high-level API definitions from hardware-specific optimizations.

### C++ Implementation Headers

The public C++ interface resides in [`mlx/fft.h`](https://github.com/ml-explore/mlx/blob/main/mlx/fft.h), which declares the core FFT functions including `fft`, `ifft`, `rfft`, and `irfft`. These templates handle multi-dimensional arrays and support batch processing across arbitrary axes. The generic implementation logic lives in [`mlx/fft.cpp`](https://github.com/ml-explore/mlx/blob/main/mlx/fft.cpp), providing CPU fallback algorithms and orchestrating calls to specialized backends.

### Python Bindings

The Python interface is generated in [`python/src/fft.cpp`](https://github.com/ml-explore/mlx/blob/main/python/src/fft.cpp), which exposes the C++ functionality through pybind11 wrappers. This binding registers functions under the `mlx.fft` namespace, allowing direct manipulation of `mx.array` objects. The documentation source in `docs/src/python/fft.rst` defines the argument signatures, including the optional `norm` parameter that mirrors NumPy's normalization behavior.

## Available FFT Functions

MLX supports both complex and real-valued Fourier transforms with standard conventions:

- **Complex transforms**: `fft.fft()` and `fft.ifft()` operate on complex64 arrays, performing forward and inverse transforms respectively.
- **Real transforms**: `fft.rfft()` computes the one-sided spectrum for real-valued inputs, while `fft.irfft()` reconstructs real signals from the frequency domain.
- **Normalization**: All functions accept a `norm` parameter supporting `"backward"`, `"ortho"`, or `"forward"` scaling conventions.

## Backend Implementations

The actual computational kernels are hardware-specific and located in the backend directories:

- **CPU**: [`mlx/fft.cpp`](https://github.com/ml-explore/mlx/blob/main/mlx/fft.cpp) contains the general-purpose CPU implementation using standard algorithms.
- **CUDA**: `mlx/backend/cuda/fft.cu` implements NVIDIA GPU acceleration with dedicated CUDA kernels.
- **Metal**: [`mlx/backend/metal/fft.cpp`](https://github.com/ml-explore/mlx/blob/main/mlx/backend/metal/fft.cpp) provides Apple Silicon optimization through Metal compute shaders.

Each backend handles plan creation, memory layout transformations, and scaling operations automatically based on the target device.

## Practical Code Examples

### Simple 1-D Complex FFT

```python
import mlx.core as mx
import mlx.fft as fft

signal = mx.array([0.0, 1.0, 0.0, -1.0], dtype=mx.complex64)
spectrum = fft.fft(signal)
reconstructed = fft.ifft(spectrum)

print("Original :", signal)
print("Spectrum :", spectrum)
print("Recovered:", reconstructed)

```

### Real-Valued FFT

```python
real_signal = mx.array([0.0, 1.0, 0.0, -1.0], dtype=mx.float32)
real_spectrum = fft.rfft(real_signal)
time_signal = fft.irfft(real_spectrum)

print("Real spectrum:", real_spectrum)

```

### Batched Multi-Signal Processing

```python
batch = mx.random.normal(shape=(8, 1024), dtype=mx.complex64)
batch_fft = fft.fft(batch, dim=-1)

```

### Normalization Options

```python
normed_fft = fft.fft(signal, norm="ortho")
normed_ifft = fft.ifft(normed_fft, norm="ortho")

```

## Testing and Numerical Accuracy

Correctness verification spans both C++ and Python test suites. The C++ unit tests in [`tests/fft_tests.cpp`](https://github.com/ml-explore/mlx/blob/main/tests/fft_tests.cpp) validate core algorithmic accuracy, while [`python/tests/test_fft.py`](https://github.com/ml-explore/mlx/blob/main/python/tests/test_fft.py) compares MLX output against NumPy's reference implementations across various shapes and data types. This dual-layer testing ensures numerical fidelity across all hardware backends.

## Summary

- **MLX** implements FFT operations in [`mlx/fft.h`](https://github.com/ml-explore/mlx/blob/main/mlx/fft.h) and [`mlx/fft.cpp`](https://github.com/ml-explore/mlx/blob/main/mlx/fft.cpp) with bindings in [`python/src/fft.cpp`](https://github.com/ml-explore/mlx/blob/main/python/src/fft.cpp).
- **Four primary functions** are available: `fft`, `ifft`, `rfft`, and `irfft`, supporting complex64 and float32 data types.
- **Hardware acceleration** is provided through backend-specific implementations in `mlx/backend/cuda/fft.cu` and [`mlx/backend/metal/fft.cpp`](https://github.com/ml-explore/mlx/blob/main/mlx/backend/metal/fft.cpp).
- **Batch processing** operates along specified dimensions using the `dim` parameter.
- **Normalization** follows NumPy conventions via the `norm` argument.

## Frequently Asked Questions

### What FFT functions are available in MLX?

MLX provides `fft.fft()`, `fft.ifft()`, `fft.rfft()`, and `fft.irfft()` for complex and real-valued transforms respectively. These are implemented in [`mlx/fft.h`](https://github.com/ml-explore/mlx/blob/main/mlx/fft.h) and exposed to Python through `mlx.fft`.

### How does MLX FFT compare to NumPy?

MLX FFT matches NumPy's API conventions including the `norm` parameter and axis handling. The test suite in [`python/tests/test_fft.py`](https://github.com/ml-explore/mlx/blob/main/python/tests/test_fft.py) explicitly validates numerical equivalence against NumPy references.

### Does MLX support GPU acceleration for FFT?

Yes. MLX automatically utilizes GPU acceleration through Metal on Apple Silicon ([`mlx/backend/metal/fft.cpp`](https://github.com/ml-explore/mlx/blob/main/mlx/backend/metal/fft.cpp)) and CUDA on NVIDIA hardware (`mlx/backend/cuda/fft.cu`), falling back to CPU implementation ([`mlx/fft.cpp`](https://github.com/ml-explore/mlx/blob/main/mlx/fft.cpp)) when necessary.

### What data types does MLX FFT support?

MLX FFT primarily supports `float32` for real-valued inputs and `complex64` for complex signals. The functions handle batch dimensions automatically and preserve data types through forward and inverse transforms.