Common window functions in Signal Processing - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Hann window values

What is the output array when applying a Hann window of length 5?

Signal Processing

import numpy as np
window = np.hanning(5)
print(window)

A [0. 0.25 1. 0.25 0. ]

B [0. 0.345 0.9 0.345 0. ]

C [0. 0.6545 1. 0.6545 0. ]

D [0. 0.5 1. 0.5 0. ]

💡 Hint

Recall the Hann window formula: w(n) = 0.5 * (1 - cos(2*pi*n/(N-1)))

The Hann window for length 5 produces values [0., 0.5, 1., 0.5, 0.].

🧠 Conceptual

intermediate

Purpose of window functions in signal processing

What is the main purpose of applying a window function to a signal before performing a Fourier transform?

A To remove noise from the signal completely

B To reduce spectral leakage by tapering the signal edges

C To convert the signal from time domain to frequency domain

D To increase the signal amplitude uniformly

💡 Hint

Think about what happens at the edges of a signal segment.

Window functions reduce spectral leakage by smoothing the edges of the signal segment before Fourier transform.

❓ data_output

advanced

Length of Blackman window output

What is the length of the output array when generating a Blackman window with parameter M=8?

Signal Processing

import numpy as np
window = np.blackman(8)
print(len(window))

A 9

B 7

C 8

D 10

💡 Hint

The window length equals the parameter M.

The Blackman window function returns an array of length equal to the input parameter M.

🔧 Debug

advanced

Identify error in window function code

What error will this code produce? import numpy as np window = np.hanning(-5) print(window)

Signal Processing

import numpy as np
window = np.hanning(-5)
print(window)

A ValueError: window length must be non-negative

B TypeError: unsupported operand type(s) for -: 'int' and 'str'

C SyntaxError: invalid syntax

D No error, outputs an empty array

💡 Hint

Check the parameter passed to np.hanning.

Negative window length is invalid and raises a ValueError.

🚀 Application

expert

Choosing window function for frequency resolution

You want to analyze a signal with closely spaced frequency components. Which window function is best to use to achieve the highest frequency resolution?

A Rectangular window

B Hamming window

C Blackman window

D Bartlett window

💡 Hint

Consider the trade-off between main lobe width and side lobe levels.

The rectangular window has the narrowest main lobe, giving the best frequency resolution but higher spectral leakage.