Power spectral density in SciPy - Mini Project: Build & Apply

Calculate Power Spectral Density using SciPy

📖 Scenario: You have recorded a simple signal from a sensor measuring vibrations. You want to analyze the signal to find out how its power is distributed across different frequencies. This helps in understanding the main frequency components of the signal.

🎯 Goal: Build a Python program that calculates the power spectral density (PSD) of a given signal using SciPy's signal.welch function.

📋 What You'll Learn

Create a signal as a list of numbers representing sensor data.

Set the sampling frequency of the signal.

Use SciPy's signal.welch function to calculate the PSD.

Print the frequency array and the corresponding PSD values.

💡 Why This Matters

🌍 Real World

Power spectral density analysis is used in engineering and science to find dominant frequencies in signals like vibrations, sound, or electrical signals.

💼 Career

Understanding PSD helps in roles like signal processing engineer, data analyst, and research scientist to analyze and interpret sensor data.

1

Create the signal data

Create a list called signal_data with these exact values: 0, 1, 0, -1, 0, 1, 0, -1 representing the sensor measurements.

SciPy

# Create the signal_data list with the given values
# Your code here

Hint

Use square brackets to create a list and separate values with commas.

2

Set the sampling frequency

Create a variable called sampling_freq and set it to 4, representing 4 samples per second.

SciPy

signal_data = [0, 1, 0, -1, 0, 1, 0, -1]
# Set the sampling frequency to 4
# Your code here

Hint

Assign the number 4 to the variable sampling_freq.

3

Calculate the power spectral density

Import signal from scipy. Then use signal.welch with signal_data and sampling_freq to calculate the frequency array freqs and power spectral density array psd.

SciPy

signal_data = [0, 1, 0, -1, 0, 1, 0, -1]
sampling_freq = 4
# Import signal from scipy and calculate freqs and psd using signal.welch
# Your code here

Hint

Use from scipy import signal to import. Then call signal.welch(signal_data, fs=sampling_freq) and unpack the result into freqs and psd.

4

Print the frequency and PSD arrays

Print the variables freqs and psd on separate lines to display the frequency values and their corresponding power spectral density values.

SciPy

from scipy import signal

signal_data = [0, 1, 0, -1, 0, 1, 0, -1]
sampling_freq = 4

freqs, psd = signal.welch(signal_data, fs=sampling_freq)
# Print freqs and psd
# Your code here

Hint

Use two print statements: one for freqs and one for psd.

Practice

1. What does the power spectral density (PSD) represent in signal analysis?

easy

A. The phase shift of a signal at various points

B. The total energy of a signal over time

C. How the power of a signal is distributed over different frequencies

D. The amplitude of a signal at a single point in time

Solution

1. Step 1: Understand the definition of PSD

   Power spectral density shows how the power of a signal is spread across frequencies, not just total energy or amplitude at one time.

2. Step 2: Compare options with PSD meaning

   Only How the power of a signal is distributed over different frequencies correctly describes PSD as power distribution over frequencies.

3. Final Answer:

   How the power of a signal is distributed over different frequencies -> Option C

4. Quick Check:

   PSD = power distribution over frequency [OK]

Hint: PSD shows power spread by frequency, not time or phase [OK]

Common Mistakes:

• Confusing PSD with total signal energy
• Thinking PSD shows amplitude at one time
• Mixing PSD with phase information

2. Which of the following is the correct way to import the Welch method for PSD calculation from scipy?

easy

A. from scipy.signal import welch

B. import scipy.welch

C. from scipy import welch

D. import scipy.signal.welch as welch

Solution

1. Step 1: Recall scipy.signal module structure

   The Welch method is inside scipy.signal, so we import it from there.

2. Step 2: Check import syntax correctness

   Only 'from scipy.signal import welch' is valid Python syntax for this function.

3. Final Answer:

   from scipy.signal import welch -> Option A

4. Quick Check:

   Correct import = from scipy.signal import welch [OK]

Hint: Welch is in scipy.signal, import directly from there [OK]

Common Mistakes:

• Trying to import welch directly from scipy
• Using incorrect import syntax
• Assuming welch is a standalone module

3. What will be the output type of the following code snippet?

from scipy.signal import welch
import numpy as np
fs = 100
x = np.sin(2 * np.pi * 10 * np.arange(1000) / fs)
freqs, psd = welch(x, fs)
print(type(freqs), type(psd))

medium

A. (, )

B. (, )

C. (, )

D. (, )

Solution

1. Step 1: Understand welch output types

   The welch function returns two numpy arrays: frequencies and power spectral density values.

2. Step 2: Check printed types

   Printing type(freqs) and type(psd) will show numpy.ndarray for both.

3. Final Answer:

   (<class 'numpy.ndarray'>, <class 'numpy.ndarray'>) -> Option D

4. Quick Check:

   welch returns arrays = numpy.ndarray [OK]

Hint: Welch returns frequency and PSD as numpy arrays [OK]

Common Mistakes:

• Expecting lists instead of numpy arrays
• Thinking output is a tuple of floats
• Confusing output with single float values

4. Identify the error in this code snippet that calculates PSD:

from scipy.signal import welch
import numpy as np
fs = 50
x = np.random.randn(500)
freqs, psd = welch(x)
print(freqs)

medium

A. The print statement should be print(psd) instead

B. Missing sampling frequency (fs) argument in welch call

C. Random data cannot be used with welch

D. Import statement for welch is incorrect

Solution

1. Step 1: Check welch function call parameters

   The welch function needs the sampling frequency (fs) to correctly compute frequencies.

2. Step 2: Identify missing argument

   Here, fs=50 is defined but not passed to welch, causing incorrect frequency calculation.

3. Final Answer:

   Missing sampling frequency (fs) argument in welch call -> Option B

4. Quick Check:

   Pass fs to welch to get correct frequencies [OK]

Hint: Always pass fs to welch for correct frequency output [OK]

Common Mistakes:

• Forgetting to pass fs argument
• Assuming random data is invalid input
• Confusing print output with error

5. You have a noisy signal sampled at 200 Hz. You want to find the dominant frequency component using scipy's Welch method. Which parameter adjustment helps improve frequency resolution in the PSD estimate?

hard

A. Increase the segment length (nperseg) to use longer data chunks

B. Decrease the sampling frequency (fs) to reduce data size

C. Use a smaller window type to reduce computation

D. Set detrend to False to keep original signal shape

Solution

1. Step 1: Understand frequency resolution in Welch method

   Frequency resolution improves with longer segments (nperseg) because it provides finer frequency bins.

2. Step 2: Evaluate options for improving resolution

   Increasing nperseg increases segment length, improving resolution. Decreasing fs reduces max frequency but not resolution. Window type affects leakage, not resolution. Detrend affects baseline, not resolution.

3. Final Answer:

   Increase the segment length (nperseg) to use longer data chunks -> Option A

4. Quick Check:

   Longer nperseg = better frequency resolution [OK]

Hint: Longer segments (nperseg) give finer frequency detail [OK]

Common Mistakes:

• Reducing sampling frequency to improve resolution
• Confusing window type with resolution effect
• Ignoring segment length impact on frequency bins