Update README.md

Signed-off-by: David Rotermund <54365609+davrot@users.noreply.github.com>

pywavelet/README.md

@@ -145,6 +145,21 @@ import numpy as np
 import matplotlib.pyplot as plt
 import pywt
 
+# Calculate the wavelet scales we requested
+def calculate_wavelet_scale(
+    number_of_frequences: int,
+    frequency_range_min: float,
+    frequency_range_max: float,
+    dt: float,
+) -> np.ndarray:
+    s_spacing: np.ndarray = (1.0 / (number_of_frequences - 1)) * np.log2(
+        frequency_range_max / frequency_range_min
+    )
+    scale: np.ndarray = np.power(2, np.arange(0, number_of_frequences) * s_spacing)
+    frequency_axis_request: np.ndarray = frequency_range_min * np.flip(scale)
+    return 1.0 / (frequency_axis_request * dt)
+
+
 f_test: float = 50  # Hz
 number_of_test_samples: int = 1000
 
@@ -160,15 +175,16 @@ dt: float = 1.0 / 1000  # sec
 t_test: np.ndarray = np.arange(0, number_of_test_samples) * dt
 test_data: np.ndarray = np.sin(2 * np.pi * f_test * t_test)
 
-# Calculate the wavelet scales we requested
-s_spacing: np.ndarray = (1.0 / (number_of_frequences - 1)) * np.log2(
-    frequency_range_max / frequency_range_min
+wave_scales = calculate_wavelet_scale(
+    number_of_frequences=number_of_frequences,
+    frequency_range_min=frequency_range_min,
+    frequency_range_max=frequency_range_max,
+    dt=dt,
 )
-scale: np.ndarray = np.power(2, np.arange(0, number_of_frequences) * s_spacing)
-frequency_axis_request: np.ndarray = frequency_range_min * np.flip(scale)
-wave_scales: np.ndarray = 1.0 / (frequency_axis_request * dt)
 
-complex_spectrum, frequency_axis = pywt.cwt(test_data, wave_scales, mother, dt)
+complex_spectrum, frequency_axis = pywt.cwt(
+    data=test_data, scales=wave_scales, wavelet=mother, sampling_period=dt
+)
 
 plt.imshow(abs(complex_spectrum) ** 2, cmap="hot", aspect="auto")
 plt.colorbar()
@@ -182,4 +198,111 @@ plt.show()
 ```
 ![figure 5](image5.png)
 
+**Done** ?!?!
+
+### Fixing the problems -- the axis of the plot 
+
+The axis look horrible! Let us fix that. 
+
+```python
+import numpy as np
+import matplotlib.pyplot as plt
+import pywt
+
+
+# Calculate the wavelet scales we requested
+def calculate_wavelet_scale(
+    number_of_frequences: int,
+    frequency_range_min: float,
+    frequency_range_max: float,
+    dt: float,
+) -> np.ndarray:
+    s_spacing: np.ndarray = (1.0 / (number_of_frequences - 1)) * np.log2(
+        frequency_range_max / frequency_range_min
+    )
+    scale: np.ndarray = np.power(2, np.arange(0, number_of_frequences) * s_spacing)
+    frequency_axis_request: np.ndarray = frequency_range_min * np.flip(scale)
+    return 1.0 / (frequency_axis_request * dt)
+
+
+def get_y_ticks(
+    reduction_to_ticks: int, frequency_axis: np.ndarray, round: int
+) -> tuple[np.ndarray, np.ndarray]:
+    output_ticks = np.arange(
+        0,
+        frequency_axis.shape[0],
+        int(np.floor(frequency_axis.shape[0] / reduction_to_ticks)),
+    )
+    if round < 0:
+        output_freq = frequency_axis[output_ticks]
+    else:
+        output_freq = np.round(frequency_axis[output_ticks], round)
+    return output_ticks, output_freq
+
+
+def get_x_ticks(
+    reduction_to_ticks: int, dt: float, number_of_timesteps: int, round: int
+) -> tuple[np.ndarray, np.ndarray]:
+    time_axis = dt * np.arange(0, number_of_timesteps)
+    output_ticks = np.arange(
+        0, time_axis.shape[0], int(np.floor(time_axis.shape[0] / reduction_to_ticks))
+    )
+    if round < 0:
+        output_time_axis = time_axis[output_ticks]
+    else:
+        output_time_axis = np.round(time_axis[output_ticks], round)
+    return output_ticks, output_time_axis
+
+
+f_test: float = 50  # Hz
+number_of_test_samples: int = 1000
+
+# The wavelet we want to use
+mother = pywt.ContinuousWavelet("cmor1.5-1.0")
+
+# Parameters for the wavelet transform
+number_of_frequences: int = 25  # frequency bands
+frequency_range_min: float = 15  # Hz
+frequency_range_max: float = 200  # Hz
+dt: float = 1.0 / 1000  # sec
+
+t_test: np.ndarray = np.arange(0, number_of_test_samples) * dt
+test_data: np.ndarray = np.sin(2 * np.pi * f_test * t_test)
+
+wave_scales = calculate_wavelet_scale(
+    number_of_frequences=number_of_frequences,
+    frequency_range_min=frequency_range_min,
+    frequency_range_max=frequency_range_max,
+    dt=dt,
+)
+
+complex_spectrum, frequency_axis = pywt.cwt(
+    data=test_data, scales=wave_scales, wavelet=mother, sampling_period=dt
+)
+
+plt.imshow(abs(complex_spectrum) ** 2, cmap="hot", aspect="auto")
+plt.colorbar()
+
+y_ticks, y_labels = get_y_ticks(
+    reduction_to_ticks=10, frequency_axis=frequency_axis, round=1
+)
+
+x_ticks, x_labels = get_x_ticks(
+    reduction_to_ticks=10, dt=dt, number_of_timesteps=complex_spectrum.shape[1], round=2
+)
+
+plt.yticks(y_ticks, y_labels)
+plt.xticks(x_ticks, x_labels)
+
+plt.xlabel("Time [sec]")
+plt.ylabel("Frequency [Hz]")
+plt.show()
+```
+![figure 6](image6.png)
+
+This looks already better...
+
+
+
+