qsp-fft¶
Quaternionic and spectral transform utilities for frequency-domain analysis.
What it is¶
qsp-fft provides transform tools for quaternionic and structured signals. It extends classical FFT-based spectral analysis to quaternion-valued inputs and offers utilities for frequency-domain processing within the QSP framework.
Why it exists¶
Classical FFT libraries operate on real or complex-valued data. Many signals in the QSP domain are quaternion-valued — for example, a three-axis sensor signal embedded in quaternion form. qsp-fft provides transforms suited to these inputs, without requiring the user to manually decompose and recompose quaternion components.
Key responsibilities¶
- Forward and inverse quaternionic Fourier transforms
- Spectral analysis utilities for quaternion-valued signals
- Windowing, zero-padding, and frequency-bin utilities compatible with QSP types
- Interoperability with NumPy FFT conventions where applicable
Typical users¶
- Signal processing engineers analyzing frequency content of multi-axis or polarized signals
- Researchers working with quaternionic spectral representations
- Engineers building pipelines that include both spatial and frequency domain stages
Example use cases¶
- Computing the quaternionic FFT of a sensor data stream
- Analyzing spectral content of a polarized signal
- Building a frequency-domain filter using quaternionic transforms
Relationship to other QSP packages¶
qsp-fft depends on qsp-core for quaternion types and signal containers. Its outputs are compatible with qsp-filter for frequency-domain filtering workflows. It has no dependency on qsp-modulation or qsp-orientation.
Status¶
Core transform functionality is the primary focus. Future expansion may include additional transform types (e.g., quaternionic wavelet transforms) and optimized backends for large signal arrays.