initial commit

test_scaling.py

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+"""test what the scaling factore of numpy's fft is"""
+import numpy as np
+from customfunc.app import PlotApp
+
+
+def setup_axes(n: int, lims=(-10, 10)) -> tuple[np.ndarray, float, np.ndarray, float]:
+    x, dx = np.linspace(*lims, n, retstep=True)
+    f = np.fft.fftfreq(n, dx)
+    return x, dx, f, f[1] - f[0]
+
+
+def abs2(z):
+    return z.real ** 2 + z.imag ** 2
+
+
+def g(x, w):
+    return np.exp(-w * x ** 2)
+
+
+def main():
+
+    with PlotApp(exp_param=np.linspace(1, 50), n=np.arange(32, 1024)) as app:
+
+        app.set_antialiasing(True)
+        fax = app["Frequency"]
+
+        @app.update
+        def draw(exp_param, n):
+            x, dx, f, df = setup_axes(n)
+            ind = np.argsort(f)
+            time_amp = 1
+
+            freq_amp = np.sqrt(np.pi / exp_param) * time_amp / dx
+            freq_w = np.pi ** 2 / exp_param
+
+            signal = g(x, exp_param) * time_amp
+
+            transformed = np.fft.fft(np.fft.fftshift(signal))
+            fax.set_line_data("transformed", f[ind], transformed[ind].real)
+
+            modeled = g(f, freq_w) * freq_amp
+            fax.set_line_data("expected", f[ind], modeled[ind])
+
+
+if __name__ == "__main__":
+    main()