Inverse FFT (ifft) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Inverse FFT on a Simple Array

What is the output of the following code that uses scipy.fft.ifft on a simple frequency domain array?

SciPy

from scipy.fft import ifft
import numpy as np
freq_data = np.array([4+0j, 0+0j, 0+0j, 0+0j])
time_data = ifft(freq_data)
print(np.round(time_data, decimals=2))

A [0.+0.j 0.+0.j 0.+0.j 0.+0.j]

B [4.+0.j 0.+0.j 0.+0.j 0.+0.j]

C [1.+0.j 0.+0.j 0.+0.j 0.+0.j]

D [1.+0.j 1.+0.j 1.+0.j 1.+0.j]

💡 Hint

Recall that the inverse FFT converts frequency data back to time domain. The input array has only the zero frequency component.

The input frequency array has a value 4 at zero frequency and zeros elsewhere. The inverse FFT divides this by the length (4), resulting in all time domain values equal to 1.

❓ data_output

intermediate

Length of Output from ifft

Given a frequency domain array of length 8, what is the length of the output array after applying scipy.fft.ifft?

SciPy

from scipy.fft import ifft
import numpy as np
freq_data = np.arange(8) + 1j * np.zeros(8)
time_data = ifft(freq_data)
print(len(time_data))

A 8

B 7

C 16

D 4

💡 Hint

The inverse FFT output length matches the input frequency array length.

The ifft function returns an array of the same length as the input frequency domain array.

🧠 Conceptual

advanced

Effect of Scaling in Inverse FFT

Which statement correctly describes the scaling behavior of scipy.fft.ifft compared to scipy.fft.fft?

A The ifft output is the fft input squared element-wise.

B The ifft output is the fft input divided by the length of the array.

C The ifft output is the fft input unchanged in scale.

D The ifft output is the fft input multiplied by the length of the array.

💡 Hint

Think about how the inverse FFT reverses the FFT operation including normalization.

The inverse FFT divides the sum by the length of the array, effectively scaling down the output compared to the FFT input.

🔧 Debug

advanced

Identify the Error in ifft Usage

What error will this code raise when run?

from scipy.fft import ifft
import numpy as np
freq_data = [1, 2, 3]
time_data = ifft(freq_data, n=5)
print(time_data)

A No error; outputs an array of length 5 with zero-padding

B TypeError: ifft() got an unexpected keyword argument 'n'

C ValueError: n must be a positive integer and >= input length

D IndexError: list index out of range

💡 Hint

Consult the documentation or function signature for scipy.fft.ifft; it supports the n argument.

No error is raised. The scipy.fft.ifft function accepts the n parameter, which pads the input array with zeros to the specified length before performing the inverse FFT.

🚀 Application

expert

Reconstructing a Signal from Frequency Components

You have frequency domain data representing a signal sampled at 8 points: [4+0j, 1-1j, 0+0j, 1+1j, 0+0j, 1-1j, 0+0j, 1+1j]. Using scipy.fft.ifft, what is the real part of the time domain signal rounded to two decimals?

SciPy

from scipy.fft import ifft
import numpy as np
freq_data = np.array([4+0j, 1-1j, 0+0j, 1+1j, 0+0j, 1-1j, 0+0j, 1+1j])
time_data = ifft(freq_data)
real_time = np.round(time_data.real, 2)
print(real_time)

A [4. 1. 0. 1. 0. 1. 0. 1.]

B [0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5]

C [1. 0.5 1. 0.5 0. 0.5 1. 0.5]

D [1. 1. 1. 1. 1. 1. 1. 1.]

💡 Hint

The inverse FFT reconstructs the time signal; the imaginary parts should be near zero due to symmetry.

The given frequency components produce a time domain signal with the pattern shown in option C.