Spectrogram generation in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of spectrogram shape

What is the shape of the spectrogram array generated by this code snippet?

SciPy

import numpy as np
from scipy.signal import spectrogram
fs = 1000
x = np.sin(2 * np.pi * 50 * np.linspace(0, 1, fs))
f, t, Sxx = spectrogram(x, fs)
print(Sxx.shape)

A (129, 10)

B (128, 10)

C (130, 10)

D (129, 9)

💡 Hint

Think about how the spectrogram divides the signal and the default window size.

The default window length is 256 samples, so the frequency bins are 129 (NFFT/2 + 1). The time bins depend on the overlap and signal length, resulting in 10 segments.

❓ data_output

intermediate

Spectrogram frequency bins values

Given this code, what is the first frequency bin value printed?

SciPy

import numpy as np
from scipy.signal import spectrogram
fs = 500
x = np.random.randn(fs)
f, t, Sxx = spectrogram(x, fs, nperseg=100)
print(round(f[0], 2))

A 0.0

B 5.0

C 2.5

D 50.0

💡 Hint

Frequency bins start from zero frequency (DC component).

The first frequency bin is always 0.0 Hz representing the DC component of the signal.

❓ visualization

advanced

Spectrogram visualization output

What will the color intensity represent in the spectrogram plot generated by this code?

SciPy

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import spectrogram
fs = 1000
t = np.linspace(0, 1, fs)
x = np.sin(2 * np.pi * 100 * t) + np.sin(2 * np.pi * 200 * t)
f, t, Sxx = spectrogram(x, fs)
plt.pcolormesh(t, f, 10 * np.log10(Sxx))
plt.ylabel('Frequency [Hz]')
plt.xlabel('Time [sec]')
plt.title('Spectrogram')
plt.colorbar(label='Intensity [dB]')
plt.show()

A Amplitude of the signal at each frequency and time

B Raw signal values over time

C Phase angle of the signal at each frequency and time

D Power spectral density in decibels at each frequency and time

💡 Hint

The plot uses 10 * log10 of Sxx values.

The spectrogram shows power spectral density (PSD) which is the power of each frequency component over time. The 10 * log10 converts it to decibels (dB) for better visualization.

🔧 Debug

advanced

Identify error in spectrogram call

What error will this code produce and why?

SciPy

import numpy as np
from scipy.signal import spectrogram
fs = 1000
x = np.sin(2 * np.pi * 50 * np.linspace(0, 1, fs))
f, t, Sxx = spectrogram(x, fs, nperseg=2000)
print(Sxx.shape)

A IndexError: index out of range

B TypeError: spectrogram() got an unexpected keyword argument 'nperseg'

C ValueError: nperseg must not be greater than input length

D No error, prints shape (1001, 1)

💡 Hint

Check the length of the input signal vs nperseg parameter.

The input signal length is 1000 samples but nperseg is set to 2000, which is invalid and causes a ValueError.

🚀 Application

expert

Detecting frequency components from spectrogram data

Given a spectrogram output Sxx and frequency array f, which code snippet correctly identifies the dominant frequency at each time slice?

SciPy

import numpy as np
from scipy.signal import spectrogram
fs = 1000
t = np.linspace(0, 1, fs)
x = np.sin(2 * np.pi * 150 * t) + np.sin(2 * np.pi * 300 * t)
f, t, Sxx = spectrogram(x, fs)
# Identify dominant frequency code here

A dominant_freqs = np.max(Sxx, axis=1)

B dominant_freqs = f[np.argmax(Sxx, axis=0)]

C dominant_freqs = t[np.argmax(Sxx, axis=1)]

D dominant_freqs = f[np.argmax(Sxx, axis=1)]

💡 Hint

Find the frequency index with max power for each time column.

Sxx shape is (frequency_bins, time_bins). To find dominant frequency per time, find max along frequency axis (axis=0) for each time slice, then map indices to frequencies.