Spectrogram visualization in Signal Processing - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the shape of the spectrogram matrix?

Given a signal sampled at 1024 Hz with 1 second duration, a window size of 256 samples, and an overlap of 128 samples, what is the shape of the spectrogram matrix produced by the following code?

Signal Processing

import numpy as np
from scipy.signal import spectrogram
fs = 1024
signal = np.sin(2 * np.pi * 50 * np.linspace(0, 1, fs, endpoint=False))
f, t, Sxx = spectrogram(signal, fs=fs, window='hann', nperseg=256, noverlap=128)
print(Sxx.shape)

A (256, 8)

B (128, 8)

C (129, 8)

D (129, 7)

💡 Hint

Remember the number of frequency bins is nperseg//2 + 1, and the number of time segments depends on overlap.

The number of frequency bins is 256/2 + 1 = 129. The number of time segments is calculated as floor((1024 - 256) / (256 - 128)) + 1 = floor(768 / 128) + 1 = 6 + 1 = 7. So the shape is (129, 7).

❓ data_output

intermediate

Identify the dominant frequency from the spectrogram data

Using the spectrogram data from the code below, which frequency has the highest average power over time?

Signal Processing

import numpy as np
from scipy.signal import spectrogram
fs = 500
t = np.linspace(0, 2, 2*fs, endpoint=False)
signal = np.sin(2 * np.pi * 60 * t) + 0.5 * np.sin(2 * np.pi * 120 * t)
f, _, Sxx = spectrogram(signal, fs=fs, nperseg=128)
avg_power = Sxx.mean(axis=1)
max_freq = f[np.argmax(avg_power)]
print(round(max_freq))

A 60

B 120

C 90

D 30

💡 Hint

Look for the frequency with the highest mean power across all time segments.

The signal has two frequencies: 60 Hz and 120 Hz. The 60 Hz component has higher amplitude, so its average power is higher, making 60 Hz the dominant frequency.

❓ visualization

advanced

Which plot shows the correct spectrogram visualization?

You run the following code to plot a spectrogram of a signal. Which option shows the correct plot output?

Signal Processing

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import spectrogram
fs = 1000
t = np.linspace(0, 1, fs, endpoint=False)
signal = np.sin(2 * np.pi * 100 * t)
f, t_spec, Sxx = spectrogram(signal, fs=fs, nperseg=256)
plt.pcolormesh(t_spec, f, 10 * np.log10(Sxx), shading='gouraud')
plt.ylabel('Frequency [Hz]')
plt.xlabel('Time [sec]')
plt.title('Spectrogram')
plt.colorbar(label='Intensity [dB]')
plt.show()

A A plot with frequency on y-axis from 0 to 1000 Hz, time on x-axis from 0 to 1 sec, and no visible lines.

B A plot with time on y-axis and frequency on x-axis, showing a vertical line at 100 Hz.

C A plot with frequency on y-axis from 0 to 500 Hz, time on x-axis from 0 to 1 sec, and a bright horizontal line at 100 Hz.

D A plot with frequency on x-axis and time on y-axis, showing a bright horizontal line at 100 Hz.

💡 Hint

Remember the spectrogram frequency axis goes from 0 to Nyquist frequency (fs/2).

The spectrogram frequency axis ranges from 0 to 500 Hz (half the sampling rate). The signal frequency is 100 Hz, so a bright horizontal line appears at 100 Hz over time.

🔧 Debug

advanced

Why does this spectrogram plot show no signal?

The code below produces a spectrogram plot, but the plot is completely dark with no visible signal. What is the most likely cause?

Signal Processing

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import spectrogram
fs = 1000
t = np.linspace(0, 1, fs, endpoint=False)
signal = np.sin(2 * np.pi * 50 * t)
f, t_spec, Sxx = spectrogram(signal, fs=fs, nperseg=1024)
plt.pcolormesh(t_spec, f, 10 * np.log10(Sxx), shading='gouraud')
plt.show()

A The sampling frequency fs is too low to capture 50 Hz signal.

B The window size nperseg is larger than the signal length, causing no segments to be computed.

C The signal is zero, so no power is shown.

D The plotting function plt.pcolormesh is used incorrectly without axis labels.

💡 Hint

Check the relationship between signal length and nperseg parameter.

The signal length is 1000 samples, but nperseg=1024 > 1000. This causes the array of start indices np.arange(0, 1000 - 1024 + 1, ...) to be empty (upper limit negative), so no segments are computed and Sxx is empty, resulting in a blank plot.

🚀 Application

expert

How to detect time-varying frequency components using spectrogram?

You have a signal composed of two sine waves: one at 50 Hz active during the first half of the signal, and another at 150 Hz active during the second half. Which approach using spectrogram visualization best reveals these time-varying frequency components?

A Use a short window size (e.g., 64 samples) with overlap to get good time resolution and plot the spectrogram.

B Use a very long window size (e.g., 1024 samples) without overlap to get best frequency resolution.

C Use no windowing and plot the raw FFT of the entire signal.

D Use a window size equal to the entire signal length to maximize frequency resolution.

💡 Hint

Short windows improve time resolution but reduce frequency resolution.

To detect changes in frequency over time, good time resolution is needed. Short windows with overlap provide this, allowing the spectrogram to show when frequencies appear and disappear.