Fourier transform playground

Generate an image by adding arbitrary 2D sine waves and observe how the fourier transform’s real and imaginary components are affected by the changes. Threading is used to smoothly animate the waves.

Tags: interactivity, gui

fourier transform playground
from time import sleep, time

import numpy as np
from magicgui import magic_factory
from scipy.fft import fft2, fftshift

import napari
from napari.qt.threading import thread_worker

FPS = 20

# meshgrid used to calculate the 2D sine waves
x = np.arange(IMAGE_SIZE) - IMAGE_SIZE / 2
X, Y = np.meshgrid(x, x)

def wave_2d(frequency, angle, phase_shift):
    """Generate a 2D sine wave based on angle, frequency and phase shift."""
    angle = np.deg2rad(angle)
    phase_shift = np.deg2rad(phase_shift)
    wave = 2 * np.pi * (X * np.cos(angle) + Y * np.sin(angle)) * frequency
    return np.sin(wave + phase_shift)

# set up viewer with grid-mode enabled
viewer = napari.Viewer()
viewer.grid.enabled = True

def update_layer(name, data, **kwargs):
    """Update a layer in the viewer with new data.

    If data is None, then the layer is removed.
    If the layer is not present, it's added to the viewer.
    if data is None:
        if name in viewer.layers:
    elif name not in viewer.layers:
        viewer.add_image(data, name=name, interpolation2d='spline36', **kwargs)
        viewer.layers[name].data = data

def combine_and_set_data(wave_args):
    """Merge 2D waves, calculate the FT and update the viewer.

    The wave phases are offset by the current time multiplied by an
    arbitrary speed value; this generates an animated wave if called repeatedly.
    if not wave_args:
        # this happens on yielding from the thread, no need to update anything

    t = time()
    waves = {
        wave_id: wave_2d(frequency, angle, phase_shift + t * speed * 100) if frequency else None
        for wave_id, (frequency, angle, phase_shift, speed) in wave_args.items()

    to_add = [d for d in waves.values() if d is not None]
    if to_add:
        mean = np.mean(to_add, axis=0)
        ft = fftshift(fft2(mean))
        power_spectrum = abs(ft)
        phase = np.angle(ft) * power_spectrum
        power_spectrum = np.log10(power_spectrum + 10)
        mean = power_spectrum = phase = None

    # for visualisation, it's clearer to use:
    # phase * ps instead of phase
    # and log10(ps + 1) instead of ps
    update_layer('phase * power_spectrum', phase, colormap=('blue', 'black', 'red'))
    update_layer('log10(power_spectrum + 1)', power_spectrum)
    update_layer('mean', mean)

    for name, data in waves.items():
        update_layer(f'wave {name}', data)

@thread_worker(connect={"yielded": combine_and_set_data})
def update_viewer():
    # keep track of each wave in a dictionary by id, this way we can modify/remove
    # existing waves or add new ones
    wave_args = {}
    new_params = None
    while True:
        sleep(1 / FPS)
        # see
        # this receives new_params from thread.send() and yields {} for the `yielded` callback
        new_params = yield wave_args
        if new_params is not None:
            # note that these come from thread.send() in moving_wave()!
            wave_id, *args = new_params
            wave_args[wave_id] = args
        yield wave_args

# start the thread responsible for updating the viewer
thread = update_viewer()

    frequency={'widget_type': 'FloatSlider', 'min': 0, 'max': 1, 'step': 0.01},
    angle={'widget_type': 'Slider', 'min': 0, 'max': 180},
    phase_shift={'widget_type': 'Slider', 'min': 0, 'max': 180},
    speed={'widget_type': 'FloatSlider', 'min': -10, 'max': 10, 'step': 0.1},
def moving_wave(
    wave_id: int = 0,
    frequency: float = 0.2,
    angle: int = 0,
    phase_shift: int = 0,
    speed: float = 1,
    """Send new parameters to the listening thread to update the 2D waves.

    The `run` checkbox can be disabled to stop sending values to the thread
    while changing parameters.
    if run:
        thread.send((wave_id, frequency, angle, phase_shift, speed))

wdg = moving_wave()

# add the widget to the window and run it once
viewer.window.add_dock_widget(wdg, area='bottom')


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