# 1.5.12.9. Spectrogram, power spectral density¶

Demo spectrogram and power spectral density on a frequency chirp.

```import numpy as np
import matplotlib.pyplot as plt
```

## Generate a chirp signal¶

```# Seed the random number generator
np.random.seed(0)

time_step = 0.01
time_vec = np.arange(0, 70, time_step)

# A signal with a small frequency chirp
sig = np.sin(0.5 * np.pi * time_vec * (1 + 0.1 * time_vec))

plt.figure(figsize=(8, 5))
plt.plot(time_vec, sig)
``` ```[<matplotlib.lines.Line2D object at 0x7f95239d64d0>]
```

## Compute and plot the spectrogram¶

The spectrum of the signal on consecutive time windows

```import scipy as sp

freqs, times, spectrogram = sp.signal.spectrogram(sig)

plt.figure(figsize=(5, 4))
plt.imshow(spectrogram, aspect="auto", cmap="hot_r", origin="lower")
plt.title("Spectrogram")
plt.ylabel("Frequency band")
plt.xlabel("Time window")
plt.tight_layout()
``` ## Compute and plot the power spectral density (PSD)¶

The power of the signal per frequency band

```freqs, psd = sp.signal.welch(sig)

plt.figure(figsize=(5, 4))
plt.semilogx(freqs, psd)
plt.title("PSD: power spectral density")
plt.xlabel("Frequency")
plt.ylabel("Power")
plt.tight_layout()
``` ```plt.show()
```

Total running time of the script: (0 minutes 0.392 seconds)

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