Spectrogram generation in SciPy - Step-by-Step Execution

Concept Flow - Spectrogram generation

Load audio signal

↓

Set parameters: window size, overlap, FFT points

↓

Split signal into overlapping windows

↓

Apply window function to each segment

↓

Compute FFT for each window

↓

Calculate magnitude squared (power) for each FFT

↓

Arrange power values over time and frequency

↓

Display or return spectrogram matrix

The process starts with an audio signal, splits it into overlapping windows, applies FFT to each, then computes power to form a time-frequency spectrogram.

Execution Sample

SciPy

import numpy as np
from scipy.signal import spectrogram

fs = 1000
x = np.sin(2*np.pi*50*np.linspace(0,1,fs,endpoint=False))
f, t, Sxx = spectrogram(x, fs)
print(Sxx.shape)

This code generates a spectrogram of a 50 Hz sine wave sampled at 1000 Hz and prints the shape of the spectrogram matrix.

Execution Table

Step	Action	Input/Variable	Output/Result
1	Generate time vector	fs=1000	t = array of 1000 points from 0 to 1 sec
2	Create sine wave signal	t	x = sine wave at 50 Hz, length 1000
3	Call spectrogram()	x, fs=1000	Compute windows, FFTs, power spectrum
4	Split signal into windows	x	Segments of length 256 with overlap
5	Apply window function	Each segment	Windowed segments
6	Compute FFT	Windowed segments	FFT results per segment
7	Calculate power spectrum	FFT results	Power values per frequency bin and time
8	Return f, t, Sxx	Power matrix	f: freq bins, t: time bins, Sxx: power matrix
9	Print Sxx.shape	Sxx	(129, 4) - 129 freq bins, 4 time bins
10	End	-	-

💡 Spectrogram computed and shape printed; execution ends.

Variable Tracker

Variable	Start	After Step 2	After Step 3	Final
fs	1000	1000	1000	1000
t	undefined	array(1000 points 0-1s)	array(1000 points 0-1s)	array(1000 points 0-1s)
x	undefined	sine wave 50Hz length 1000	sine wave 50Hz length 1000	sine wave 50Hz length 1000
f	undefined	undefined	array(129 freq bins)	array(129 freq bins)
t (time bins)	undefined	undefined	array(4 time bins)	array(4 time bins)
Sxx	undefined	undefined	2D power matrix shape (129,4)	2D power matrix shape (129,4)

Key Moments - 3 Insights

Why does the spectrogram output have fewer time bins than the original signal length?

Because the signal is split into overlapping windows of fixed size (e.g., 256 samples), the number of time bins equals how many windows fit, not the total samples. See execution_table step 4 and 8.

What does each value in the spectrogram matrix represent?

Each value is the power (magnitude squared) of a frequency component at a specific time window. This is shown in execution_table step 7.

Why do we apply a window function before FFT?

To reduce edge effects and spectral leakage in each segment. This is done in step 5 of execution_table.

Visual Quiz - 3 Questions

Look at the execution_table at step 9, what is the shape of the spectrogram matrix Sxx?

A (256, 256)

B (1000, 1000)

C (129, 4)

D (50, 100)

💡 Hint

Refer to execution_table row 9 where Sxx.shape is printed.

At which step in the execution_table is the FFT computed for each window?

A Step 4

B Step 6

C Step 7

D Step 5

💡 Hint

Look for the step mentioning FFT computation in execution_table.

If the window size is increased, how would the number of time bins in the spectrogram change?

A Decrease

B Increase

C Stay the same

D Become zero

💡 Hint

Refer to key_moments about how window size affects time bins.

Concept Snapshot

Spectrogram generation:
- Input: signal and sampling rate
- Split signal into overlapping windows
- Apply window function
- Compute FFT per window
- Calculate power spectrum
- Output: frequency bins, time bins, power matrix
- Shows how frequency content changes over time

Full Transcript

Spectrogram generation starts by loading an audio signal sampled at a known rate. The signal is split into overlapping windows, each window is multiplied by a window function to reduce edge effects. Then, FFT is computed on each window to get frequency components. The magnitude squared of these FFTs forms the power spectrum for each time window. The result is a matrix showing how power varies by frequency and time. This matrix can be visualized as a spectrogram image. The example code generates a 50 Hz sine wave, computes its spectrogram, and prints the shape of the resulting power matrix, showing 129 frequency bins and 4 time bins.

Practice

1. What does the scipy.signal.spectrogram function primarily compute from a signal?

easy

A. The frequency content of the signal over time

B. The total energy of the signal

C. The average amplitude of the signal

D. The phase shift of the signal

Solution

1. Step 1: Understand the purpose of spectrogram

   A spectrogram shows how frequencies in a signal change over time, so it computes frequency content over time.

2. Step 2: Compare with other options

   Total energy, average amplitude, and phase shift are different signal properties, not what spectrogram calculates.

3. Final Answer:

   The frequency content of the signal over time -> Option A

4. Quick Check:

   Spectrogram = frequency over time [OK]

Hint: Spectrogram = frequency changes over time [OK]

Common Mistakes:

• Confusing spectrogram with total energy calculation
• Thinking it returns average amplitude only
• Assuming it gives phase information

2. Which of the following is the correct way to import the spectrogram function from scipy?

easy

A. from scipy import spectrogram

B. import scipy.spectrogram

C. from scipy.signal import spectrogram

D. import spectrogram from scipy.signal

Solution

1. Step 1: Recall correct import syntax for functions

   Functions inside submodules are imported using 'from module.submodule import function'.

2. Step 2: Check each option

   from scipy.signal import spectrogram matches this syntax exactly. Options B, C, and D are invalid Python import statements.

3. Final Answer:

   from scipy.signal import spectrogram -> Option C

4. Quick Check:

   Correct import syntax = from scipy.signal import spectrogram [OK]

Hint: Use 'from scipy.signal import spectrogram' [OK]

Common Mistakes:

• Using 'import scipy.spectrogram' which is invalid
• Trying 'from scipy import spectrogram' ignoring submodule
• Incorrect import order like 'import spectrogram from ...'

3. What will be the shape of the frequency array returned by f, t, Sxx = spectrogram(signal, fs=1000, nperseg=256) if signal length is 1024?

medium

A. (256,)

B. (129,)

C. (512,)

D. (1024,)

Solution

1. Step 1: Understand frequency bins from nperseg

   The frequency array length is nperseg/2 + 1 due to FFT symmetry, so 256/2 + 1 = 129.

2. Step 2: Confirm other options

   256 is the segment length, not frequency bins. 512 and 1024 are unrelated to frequency array size here.

3. Final Answer:

   (129,) -> Option B

4. Quick Check:

   Frequency bins = nperseg/2 + 1 = 129 [OK]

Hint: Frequency bins = nperseg/2 + 1 [OK]

Common Mistakes:

• Assuming frequency array length equals nperseg
• Confusing signal length with frequency bins
• Ignoring FFT symmetry in frequency output

4. Given this code snippet, what is the error?

from scipy.signal import spectrogram
signal = [1, 2, 3, 4, 5]
fs = 100
f, t, Sxx = spectrogram(signal, nperseg=256, fs=fs)

medium

A. nperseg is larger than signal length causing a warning or error

B. fs parameter is missing

C. spectrogram function is not imported correctly

D. signal must be a numpy array, not a list

Solution

1. Step 1: Check parameters and signal length

   Signal length is 5, but nperseg is 256, which is larger than signal length.

2. Step 2: Understand spectrogram behavior

   When nperseg > signal length, scipy issues a warning or error because segment size can't exceed signal length.

3. Final Answer:

   nperseg is larger than signal length causing a warning or error -> Option A

4. Quick Check:

   nperseg > signal length causes error [OK]

Hint: nperseg must be ≤ signal length [OK]

Common Mistakes:

• Ignoring nperseg size relative to signal length
• Thinking fs is missing when it is provided
• Assuming list input causes error (it works but numpy array preferred)

5. You want to generate a spectrogram for a noisy signal sampled at 2000 Hz. To improve time resolution, which parameter should you decrease in scipy.signal.spectrogram?

hard

A. window

B. fs

C. noverlap

D. nperseg

Solution

1. Step 1: Understand time vs frequency resolution trade-off

   Decreasing nperseg (segment length) improves time resolution but reduces frequency resolution.

2. Step 2: Check other parameters

   fs is sample rate, noverlap controls overlap, window shapes segments but doesn't directly improve time resolution.

3. Final Answer:

   nperseg -> Option D

4. Quick Check:

   Decrease nperseg for better time resolution [OK]

Hint: Lower nperseg for better time resolution [OK]

Common Mistakes:

• Trying to change fs which is fixed sample rate
• Confusing noverlap with time resolution
• Changing window type expecting time resolution change