Frequency array generation (fftfreq) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of fftfreq with default d=1.0

What is the output of the following code snippet?

SciPy

from scipy.fft import fftfreq
freqs = fftfreq(6)
print(freqs)

A [0. 0.2 0.4 0.6 0.8 1. ]

B [ 0. 0.16666667 0.33333333 0.5 -0.33333333 -0.16666667]

C [ 0. 0.16666667 0.33333333 -0.5 -0.33333333 -0.16666667]

D [ 0. 0.16666667 0.33333333 -0.33333333 -0.16666667 -0.5 ]

💡 Hint

Remember that fftfreq returns frequencies in cycles per unit sample spacing, with negative frequencies after the Nyquist frequency.

fftfreq(n) returns an array of length n with frequencies starting at 0, increasing to the positive Nyquist frequency, then negative frequencies in increasing order. For n=6 and default d=1.0, the output matches option C.

❓ data_output

intermediate

Frequency array with custom sample spacing

Given sample spacing d=0.5 and n=4, what is the output of fftfreq?

SciPy

from scipy.fft import fftfreq
freqs = fftfreq(4, d=0.5)
print(freqs)

A [ 0. 0.25 -1. -0.5]

B [ 0. 0.25 -0.5 -0.25]

C [ 0. 0.5 -0.5 -0.25]

D [ 0. 0.5 -1. -0.5]

💡 Hint

Frequency values scale inversely with sample spacing d.

With n=4 and d=0.5, fftfreq returns frequencies [0, 1/(4*0.5), -1/(2*0.5), -1/(4*0.5)] = [0, 0.5, -1, -0.5].

🧠 Conceptual

advanced

Understanding negative frequencies in fftfreq output

Why does fftfreq return negative frequency values in its output array?

A Negative frequencies represent the direction of rotation in complex exponentials and are necessary for representing real signals in the frequency domain.

B Negative frequencies are errors and should be ignored when analyzing FFT results.

C Negative frequencies indicate frequencies below zero Hertz, which physically do not exist.

D Negative frequencies are placeholders for missing data points in the FFT output.

💡 Hint

Think about how complex sinusoids represent signals in both positive and negative directions.

In Fourier analysis, negative frequencies correspond to complex conjugate components and represent direction of rotation in the complex plane. They are essential for reconstructing real-valued signals.

🔧 Debug

advanced

Identify the error in fftfreq usage

What error will the following code produce?

SciPy

from scipy.fft import fftfreq
freqs = fftfreq(-5)
print(freqs)

A TypeError: fftfreq() missing required positional argument

B ValueError: n must be non-negative

C SyntaxError: invalid syntax

D No error, outputs an empty array

💡 Hint

Check the parameter constraints for fftfreq's n argument.

The fftfreq function requires n to be a non-negative integer. Passing a negative value raises a ValueError.

🚀 Application

expert

Using fftfreq to find the dominant frequency index

Given a signal sampled at 100 Hz with 8 samples, which index corresponds to the dominant frequency 12.5 Hz using fftfreq?

SciPy

from scipy.fft import fftfreq
sample_rate = 100
n = 8
freqs = fftfreq(n, d=1/sample_rate)
print(freqs)

A Index 1

B Index 3

C Index 2

D Index 4

💡 Hint

Calculate frequency bins as k * sample_rate / n for k in [0..n-1], considering fftfreq output order.

With n=8 and sample_rate=100 Hz, fftfreq returns frequencies: [0, 12.5, 25, 37.5, -50, -37.5, -25, -12.5]. The frequency 12.5 Hz is at index 1.