Merge branch 'main' of github.com:chris-langfield/hexfft

Author: chris-langfield

README.md

@@ -1,8 +1,58 @@
-## hexfft
+![Screenshot 2024-05-21 at 1 00 10 PM](https://github.com/chris-langfield/hexfft/assets/34426450/b4eff5e9-2375-4d2c-a77e-5009efb34495)
+
+# hexfft
 
 A Python package aiming to provide an easy and efficient interface to various implementations of the [Hexagonal Fast Fourier Transform](https://en.wikipedia.org/wiki/Hexagonal_fast_Fourier_transform).
 
-### Install
+## Get started
+
+#### Plot hexagonally sampled 2D signals
+```python
+from hexfft import HexArray
+from hexfft.plot import hexshow
+import numpy as np
+
+data = np.random.normal(size=(8, 6))
+h = HexArray(data)
+hexshow(h)
+```
+![Screenshot 2024-05-21 at 1 06 04 PM](https://github.com/chris-langfield/hexfft/assets/34426450/92d11a97-8b64-4d3f-9ac9-c612aa4b5437)
+
+#### Perform FFT for rectangularly or hexagonally periodic signals
+
+```python
+from hexfft import fft, ifft
+
+X = fft(h)
+X_hx = fft(h, periodicity="rect") # or "hex"
+```
+
+#### Operate on a 3D stack
+
+```python
+from hexfft import FFT
+
+shape = (32, 32)
+
+fftobj = FFT(shape, periodicity="hex") # or "rect"
+x = np.random.normal(size=(10, 32, 32))
+X = fftobj.forward(x)
+xx = fftobj.inverse(X)
+
+...
+```
+
+#### Example notebooks
+
+[1 - `HexArray` and visualization](https://github.com/chris-langfield/hexfft/blob/main/examples/HexArray.ipynb)
+
+[2 - FFT with rectangular periodicity](https://github.com/chris-langfield/hexfft/blob/main/examples/RectangularPeriodicity.ipynb)
+
+[3 - FFT with hexagonal periodicity](https://github.com/chris-langfield/hexfft/blob/main/examples/HexagonalPeriodicity.ipynb)
+
+[4 - Basic filtering example](https://github.com/chris-langfield/hexfft/blob/main/examples/BasicFiltering.ipynb)
+
+## Install
 
 ```
 pip install hexfft
@@ -19,7 +69,8 @@ cd hexfft
 pytest tests/
 ```
 
+## Further reading
 ---------------------------------------
 > R. M. Mersereau, "The processing of hexagonally sampled two-dimensional signals," in Proceedings of the IEEE, vol. 67, no. 6, pp. 930-949, June 1979, doi: 10.1109/PROC.1979.11356
 
-> Ehrhardt, J. C. (1993). Hexagonal fast Fourier transform with rectangular output. In IEEE Transactions on Signal Processing (Vol. 41, Issue 3, pp. 1469–1472). Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/78.205759 
+> J. C. Ehrhardt, “Hexagonal fast Fourier transform with rectangular output,” IEEE Transactions on Signal Processing, vol. 41, no. 3. Institute of Electrical and Electronics Engineers (IEEE), pp. 1469–1472, Mar. 1993. doi: 10.1109/78.205759.