Signal processing v0

docs/api_guide/tutorial_pynapple_spectrum.py

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+# -*- coding: utf-8 -*-
+"""
+Power spectral density
+======================
+
+See the [documentation](https://pynapple-org.github.io/pynapple/) of Pynapple for instructions on installing the package.
+
+"""
+
+# %%
+# !!! warning
+#     This tutorial uses matplotlib for displaying the figure
+#
+#     You can install all with `pip install matplotlib requests tqdm seaborn`
+#
+# Now, import the necessary libraries:
+#
+# mkdocs_gallery_thumbnail_number = 3
+
+import matplotlib.pyplot as plt
+import numpy as np
+import seaborn
+
+seaborn.set_theme()
+
+import pynapple as nap
+
+# %%
+# ***
+# Generating a signal
+# ------------------
+# Let's generate a dummy signal with 2Hz and 10Hz sinusoide with white noise.
+#
+
+F = [2, 10]
+
+Fs = 2000
+t = np.arange(0, 200, 1/Fs)
+sig = nap.Tsd(
+    t=t,
+    d=np.cos(t*2*np.pi*F[0])+np.cos(t*2*np.pi*F[1])+np.random.normal(0, 3, len(t)),
+    time_support = nap.IntervalSet(0, 200)
+    )
+
+# %%
+# Let's plot it
+plt.figure()
+plt.plot(sig.get(0, 0.4))
+plt.title("Signal")
+plt.xlabel("Time (s)")
+
+
+
+# %%
+# Computing power spectral density (PSD)
+# --------------------------------------
+#
+# To compute a PSD of a signal, you can use the function `nap.compute_power_spectral_density`. With `norm=True`, the output of the FFT is divided by the length of the signal.
+
+psd = nap.compute_power_spectral_density(sig, norm=True)
+
+# %%
+# Pynapple returns a pandas DataFrame.
+
+print(psd)
+
+# %%
+# It is then easy to plot it.
+
+plt.figure()
+plt.plot(np.abs(psd))
+plt.xlabel("Frequency (Hz)")
+plt.ylabel("Amplitude")
+
+
+# %%
+# Note that the output of the FFT is truncated to positive frequencies. To get positive and negative frequencies, you can set `full_range=True`.
+# By default, the function returns the frequencies up to the Nyquist frequency.
+# Let's zoom on the first 20 Hz.
+
+plt.figure()
+plt.plot(np.abs(psd))
+plt.xlabel("Frequency (Hz)")
+plt.ylabel("Amplitude")
+plt.xlim(0, 20)
+
+
+# %%
+# We find the two frequencies 2 and 10 Hz.
+#
+# By default, pynapple assumes a constant sampling rate and a single epoch. For example, computing the FFT over more than 1 epoch will raise an error.
+double_ep = nap.IntervalSet([0, 50], [20, 100])
+
+try:
+    nap.compute_power_spectral_density(sig, ep=double_ep)
+except ValueError as e:
+    print(e)
+
+
+# %%
+# Computing mean PSD
+# ------------------
+#
+# It is possible to compute an average PSD over multiple epochs with the function `nap.compute_mean_power_spectral_density`.
+# 
+# In this case, the argument `interval_size` determines the duration of each epochs upon which the FFT is computed.
+# If not epochs is passed, the function will split the `time_support`.
+# 
+# In this case, the FFT will be computed over epochs of 10 seconds.
+
+mean_psd = nap.compute_mean_power_spectral_density(sig, interval_size=20.0, norm=True)
+
+
+# %%
+# Let's compare `mean_psd` to `psd`. In both cases, the ouput is normalized.
+
+plt.figure()
+plt.plot(np.abs(psd), label='PSD')
+plt.plot(np.abs(mean_psd), label='Mean PSD (10s)')
+plt.xlabel("Frequency (Hz)")
+plt.ylabel("Amplitude")
+plt.legend()
+plt.xlim(0, 15)
+
+# %%
+# As we can see, `nap.compute_mean_power_spectral_density` was able to smooth out the noise.
+
+