Inverse FFT for reconstruction in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to compute the inverse FFT of the frequency data.

Signal Processing

import numpy as np
freq_data = np.array([1+0j, 0-1j, -1+0j, 0+1j])
time_data = np.fft.[1](freq_data)
print(time_data)

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

Aifft

Birfft

Crfft

Dfft

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'fft' instead of 'ifft' which performs forward FFT.

Using 'rfft' or 'irfft' which are for real-valued signals only.

The inverse FFT function in numpy is ifft. It converts frequency domain data back to time domain.

2fill in blank

medium

Complete the code to get the real part of the inverse FFT result.

Signal Processing

import numpy as np
freq_data = np.array([2+0j, 0-2j, -2+0j, 0+2j])
time_data = np.fft.ifft(freq_data)
real_time_data = time_data.[1]
print(real_time_data)

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

Aimag

Breal

Cconj

Dabs

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'imag' which gives the imaginary part.

Using 'abs' which gives magnitude, not the real part.

The real part of a complex array is accessed with .real.

3fill in blank

hard

Fix the error in the code to correctly reconstruct the time signal from frequency data.

Signal Processing

import numpy as np
freq_data = np.array([1+0j, 1-1j, 1+0j, 1+1j])
time_data = np.fft.ifft([1])
print(time_data)

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

Anp.fft.fft(freq_data)

Btime_data

Cfreq_data

Dnp.fft.irfft(freq_data)

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the time domain data or the result of FFT instead of frequency data.

Using irfft incorrectly for complex frequency data.

The inverse FFT function ifft needs the frequency domain data as input, which is freq_data.

4fill in blank

hard

Fill both blanks to create a dictionary of time samples and their magnitudes from inverse FFT.

Signal Processing

import numpy as np
freq_data = np.array([3+0j, 0-3j, -3+0j, 0+3j])
time_data = np.fft.ifft(freq_data)
magnitude_dict = {i: abs(time_data[1]) for i in range(len(time_data)) if abs(time_data[2]) > 0}
print(magnitude_dict)

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

A[i]

B(i)

C[0]

D(0)

Attempts:

3 left

💡 Hint

Common Mistakes

Using parentheses which is for function calls, not indexing.

Using fixed index like 0 instead of variable i.

To access elements of time_data, use square brackets with the index [i].

5fill in blank

hard

Fill all three blanks to create a dictionary with indices, real parts, and a filter for positive real values.

Signal Processing

import numpy as np
freq_data = np.array([4+0j, 0-4j, -4+0j, 0+4j])
time_data = np.fft.ifft(freq_data)
filtered_dict = {i: time_data[1] for i in range(len(time_data)) if time_data[2] > 0 and i != [3]
print(filtered_dict)

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

A[i].real

B[i]

C0

D[0]

Attempts:

3 left

💡 Hint

Common Mistakes

Using just [i] without .real for the filter condition.

Using string '0' or [0] instead of integer 0 for index exclusion.

Access the real part of each element with [i].real. The filter checks if the real part is positive and excludes index 0.

Practice

1. What is the main purpose of using the Inverse FFT (IFFT) in signal processing?

easy

A. To convert frequency domain data back to time domain

B. To convert time domain data to frequency domain

C. To filter out noise from a signal

D. To amplify the signal strength

Solution

1. Step 1: Understand FFT and IFFT roles

   FFT converts time data to frequency data, while IFFT reverses this process.

2. Step 2: Identify IFFT purpose

   IFFT takes frequency domain data and reconstructs the original time domain signal.

3. Final Answer:

   To convert frequency domain data back to time domain -> Option A

4. Quick Check:

   Inverse FFT = frequency to time [OK]

Hint: IFFT always reverses FFT to get original time signal [OK]

Common Mistakes:

• Confusing FFT with IFFT
• Thinking IFFT filters noise
• Assuming IFFT amplifies signals

2. Which of the following is the correct Python syntax to compute the inverse FFT of a numpy array freq_data?

easy

A. time_data = np.inverse_fft(freq_data)

B. time_data = np.ifft(freq_data)

C. time_data = np.fft.fft(freq_data)

D. time_data = np.fft.ifft(freq_data)

Solution

1. Step 1: Recall numpy FFT module usage

   Inverse FFT is accessed via np.fft.ifft() in numpy.

2. Step 2: Check each option

   time_data = np.fft.ifft(freq_data) uses correct function and module. Others are incorrect or do not exist.

3. Final Answer:

   time_data = np.fft.ifft(freq_data) -> Option D

4. Quick Check:

   Use np.fft.ifft() for inverse FFT [OK]

Hint: Use np.fft.ifft() to get time data from frequency data [OK]

Common Mistakes:

• Using np.ifft() without fft module
• Using fft instead of ifft
• Using non-existent functions like inverse_fft

3. Given the code below, what will be the output of print(time_data.real)?

import numpy as np
freq_data = np.array([4+0j, 1-1j, 0+0j, 1+1j])
time_data = np.fft.ifft(freq_data)
print(time_data.real)

medium

A. [0.5 1.5 0.5 1.5]

B. [1.0 0.0 1.0 0.0]

C. [1.5 1.5 0.5 0.5]

D. [4.0 1.0 0.0 1.0]

Solution

1. Step 1: Apply inverse FFT formula on freq_data

   Using numpy's ifft on freq_data returns complex time domain values.

2. Step 2: Extract real parts of the result

   The real parts of the output are [0.5 1.5 0.5 1.5].

3. Final Answer:

   [0.5 1.5 0.5 1.5] -> Option A

4. Quick Check:

   Real part of ifft(freq_data) = [0.5 1.5 0.5 1.5] [OK]

Hint: Real part of IFFT output gives reconstructed time signal [OK]

Common Mistakes:

• Printing full complex output instead of real part
• Confusing FFT output with IFFT output
• Misreading array order

4. Identify the error in the following code snippet that attempts to reconstruct a signal using inverse FFT:

import numpy as np
freq_data = [10, 0, 0, 0]
time_data = np.fft.ifft(freq_data.real)
print(time_data)

medium

A. np.fft.ifft cannot process real parts only

B. freq_data is a list, should be a numpy array

C. Using freq_data.real is incorrect because freq_data is not complex

D. No error, code runs correctly

Solution

1. Step 1: Check data type and usage of .real

   freq_data is a list of real numbers, so .real attribute is invalid here.

2. Step 2: Understand .real usage

   .real is for complex numbers; using it on a list causes error or unexpected behavior.

3. Final Answer:

   Using freq_data.real is incorrect because freq_data is not complex -> Option C

4. Quick Check:

   Only complex arrays have .real attribute [OK]

Hint: Use .real only on complex numpy arrays [OK]

Common Mistakes:

• Assuming lists have .real attribute
• Ignoring data type requirements for ifft
• Thinking freq_data must be complex always

5. You have frequency domain data from a noisy signal. After applying inverse FFT, you notice small imaginary parts in the time domain output. What is the best way to reconstruct the original real signal?

hard

A. Discard the imaginary parts and keep the rest as complex

B. Take only the real part of the inverse FFT output

C. Apply FFT again to remove imaginary parts

D. Increase the frequency resolution before inverse FFT

Solution

1. Step 1: Understand inverse FFT output nature

   Inverse FFT of real signals may have tiny imaginary parts due to numerical errors.

2. Step 2: Choose correct reconstruction method

   Taking the real part removes these small imaginary errors and recovers the original signal.

3. Final Answer:

   Take only the real part of the inverse FFT output -> Option B

4. Quick Check:

   Real part extraction fixes small imaginary noise [OK]

Hint: Use .real to clean small imaginary parts after IFFT [OK]

Common Mistakes:

• Ignoring imaginary parts causing confusion
• Trying to remove imaginary parts by reapplying FFT
• Thinking frequency resolution affects imaginary noise