Magnitude and phase spectrum in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to compute the magnitude spectrum of a signal using its Fourier Transform.

Signal Processing

magnitude = abs([1])

Drag options to blanks, or click blank then click option'

Anp.fft.ifft(signal)

Bnp.angle(signal)

Cnp.real(signal)

Dnp.fft.fft(signal)

Attempts:

3 left

💡 Hint

Common Mistakes

Using inverse FFT instead of FFT

Taking real part instead of absolute value

The magnitude spectrum is the absolute value of the Fourier Transform of the signal.

2fill in blank

medium

Complete the code to compute the phase spectrum of a signal using its Fourier Transform.

Signal Processing

phase = [1](np.fft.fft(signal))

Drag options to blanks, or click blank then click option'

Aangle

Breal

Cimag

Dabs

Attempts:

3 left

💡 Hint

Common Mistakes

Using absolute value instead of angle

Using real or imaginary parts directly

The phase spectrum is the angle of the Fourier Transform of the signal.

3fill in blank

hard

Fix the error in the code to correctly compute the magnitude spectrum.

Signal Processing

magnitude = np.abs(np.fft.[1](signal))

Drag options to blanks, or click blank then click option'

Aifftshift

Bifft

Cfft

Dfftshift

Attempts:

3 left

💡 Hint

Common Mistakes

Using ifft instead of fft

Using fftshift or ifftshift incorrectly

The magnitude spectrum requires the forward FFT, not the inverse FFT or shifts.

4fill in blank

hard

Fill both blanks to create a dictionary with magnitude and phase spectra of the signal.

Signal Processing

spectrum = {'magnitude': [1], 'phase': [2]

Drag options to blanks, or click blank then click option'

Anp.abs(np.fft.fft(signal))

Bnp.angle(np.fft.fft(signal))

Cnp.real(signal)

Dnp.imag(signal)

Attempts:

3 left

💡 Hint

Common Mistakes

Using real or imaginary parts instead of magnitude and phase

The magnitude is the absolute value of the FFT, and the phase is the angle of the FFT.

5fill in blank

hard

Fill the blanks to compute magnitude and phase spectra and plot them using matplotlib.

Signal Processing

import matplotlib.pyplot as plt

import numpy as np

fft_result = np.fft.fft(signal)
magnitude = [1]
phase = [2]

plt.figure(figsize=(10,4))
plt.subplot(1,2,1)
plt.plot(magnitude)
plt.title('Magnitude Spectrum')
plt.subplot(1,2,2)
plt.plot(phase)
plt.title('Phase Spectrum')
plt.show()

Drag options to blanks, or click blank then click option'

Anp.abs(fft_result)

Bnp.angle(fft_result)

Cnp.real(fft_result)

Dnp.imag(fft_result)

Attempts:

3 left

💡 Hint

Common Mistakes

Plotting real or imaginary parts instead of magnitude and phase

Magnitude is the absolute value of the FFT result, phase is the angle of the FFT result.

Practice

1. What does the magnitude spectrum represent in signal processing?

easy

A. The strength or amplitude of different frequency components

B. The timing or phase shift of frequency components

C. The original time-domain signal values

D. The noise level in the signal

Solution

1. Step 1: Understand magnitude spectrum meaning

   The magnitude spectrum shows how strong or intense each frequency is in a signal.

2. Step 2: Differentiate from phase spectrum

   The phase spectrum shows timing, not strength, so it is not the magnitude.

3. Final Answer:

   The strength or amplitude of different frequency components -> Option A

4. Quick Check:

   Magnitude spectrum = strength [OK]

Hint: Magnitude = strength of frequencies, phase = timing [OK]

Common Mistakes:

• Confusing magnitude with phase
• Thinking magnitude shows time values
• Mixing magnitude with noise level

2. Which Python function is used to get the phase spectrum from a Fourier Transform result stored in variable F?

easy

A. np.abs(F)

B. np.angle(F)

C. np.fft(F)

D. np.real(F)

Solution

1. Step 1: Recall phase extraction function

   In Python's NumPy, np.angle() returns the phase angles of complex numbers.

2. Step 2: Differentiate from magnitude and other functions

   np.abs() returns magnitude, np.fft() is not a valid function, and np.real() returns real parts only.

3. Final Answer:

   np.angle(F) -> Option B

4. Quick Check:

   Phase spectrum = np.angle() [OK]

Hint: Use np.angle() for phase, np.abs() for magnitude [OK]

Common Mistakes:

• Using np.abs() instead of np.angle() for phase
• Trying to use np.fft() which is invalid
• Confusing real part with phase

3. Given the code:

import numpy as np
x = np.array([1, 0, -1, 0])
F = np.fft.fft(x)
magnitude = np.abs(F)
phase = np.angle(F)
print(np.round(magnitude, 2))
print(np.round(phase, 2))

What is the printed magnitude and phase arrays?

medium

A. [4.00 0.00 0.00 0.00]
[0.00 0.00 0.00 0.00]

B. [0.00 2.00 0.00 2.00]
[0.00 0.00 0.00 0.00]

C. [2.00 2.00 2.00 2.00]
[ 0.00 -1.57 3.14 1.57]

D. [2.00 0.00 2.00 0.00]
[0.00 1.57 3.14 -1.57]

Solution

1. Step 1: Compute FFT of x

   The FFT of [1, 0, -1, 0] is [0+0j, 2+0j, 0+0j, 2+0j].

2. Step 2: Calculate magnitude and phase arrays

   Magnitude is [2.00 2.00 2.00 2.00]. Phase angles are [0.00 -1.57 3.14 1.57].

3. Final Answer:

   [2.00 2.00 2.00 2.00] [ 0.00 -1.57 3.14 1.57] -> Option C

4. Quick Check:

   Magnitude = [2 2 2 2], Phase = approx [-pi/2, pi, pi/2] [OK]

Hint: FFT magnitude is abs(), phase is angle() in radians [OK]

Common Mistakes:

• Confusing magnitude with real part
• Not rounding phase correctly
• Mixing up signs of phase angles

4. The following code attempts to compute magnitude and phase but has an error:

import numpy as np
x = np.array([1, 2, 3, 4])
F = np.fft.fft(x)
magnitude = np.angle(F)
phase = np.abs(F)
print(magnitude)
print(phase)

What is the error?

medium

A. No error; code runs correctly

B. np.fft.fft() is used incorrectly; should be np.fft.ifft()

C. The input array x must be complex numbers

D. Magnitude and phase are swapped; np.angle() should be for phase, np.abs() for magnitude

Solution

1. Step 1: Check function usage for magnitude and phase

   Magnitude is the absolute value, so np.abs() should be used for magnitude, not np.angle(). Phase is angle, so np.angle() is for phase.

2. Step 2: Identify swapped assignments

   The code assigns magnitude = np.angle(F) and phase = np.abs(F), which is reversed.

3. Final Answer:

   Magnitude and phase are swapped; np.angle() should be for phase, np.abs() for magnitude -> Option D

4. Quick Check:

   Magnitude = abs(), Phase = angle() [OK]

Hint: Remember: abs() for magnitude, angle() for phase [OK]

Common Mistakes:

• Swapping magnitude and phase functions
• Thinking FFT input must be complex
• Confusing FFT and IFFT usage

5. You have a noisy signal and want to keep only frequencies with magnitude above 5. Which steps correctly apply this filter using FFT results stored in F?

hard

A. Calculate magnitude = np.abs(F), create mask = magnitude > 5, then set F_filtered = F * mask

B. Calculate phase = np.angle(F), create mask = phase > 5, then set F_filtered = F * mask

C. Calculate magnitude = np.abs(F), create mask = magnitude < 5, then set F_filtered = F * mask

D. Calculate magnitude = np.abs(F), create mask = magnitude > 5, then set F_filtered = np.abs(F) * mask

Solution

1. Step 1: Compute magnitude and create mask

   Calculate magnitude with np.abs(F). Create a boolean mask where magnitude > 5 to keep strong frequencies.

2. Step 2: Apply mask to original FFT data

   Multiply the complex FFT array F by the mask to zero out weak frequencies, preserving phase and magnitude of strong ones.

3. Final Answer:

   Calculate magnitude = np.abs(F), create mask = magnitude > 5, then set F_filtered = F * mask -> Option A

4. Quick Check:

   Filter by magnitude > 5, multiply mask with F [OK]

Hint: Filter frequencies by magnitude mask, multiply mask with FFT [OK]

Common Mistakes:

• Filtering by phase instead of magnitude
• Using magnitude < 5 to keep frequencies
• Multiplying mask with magnitude only, losing phase info