---
title: "Define zero padding"
subject: "Digital Signal Analysis and Processing"
chapter: 7
key: "semester_7/digital_signal_analysis_and_processing:define-zero-padding"
source: https://www.bctengineer.com/q/semester_7/digital_signal_analysis_and_processing/define-zero-padding
site: BCT Engineering
---

# Define zero padding

Digital Signal Analysis and Processing · Chapter 7: Discrete Fourier Transform

- Asked in: 2074 Asoj, 1 marks; 2074 Chaitra, 1 marks; 2070 Chaitra, 1 marks (asked 3 times)
- Video: [07 - Zero-padding](https://www.youtube.com/watch?v=ukHTfD37THI) — IllinoisDSP
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/digital_signal_analysis_and_processing/define-zero-padding
- Whole chapter: https://www.bctengineer.com/md/semester_7/digital_signal_analysis_and_processing/chapter-7

## Question

What is zero padding? Define padding of zeros.

## Short answer

Zero padding appends zeros to a finite sequence to increase its length to N. It gives the DFT a denser frequency grid, makes N a power of two for FFT, and ensures circular convolution equals linear convolution when N ≥ L1+L2−1.

## Answer

**Zero padding** means appending zeros to the end of a finite sequence to increase its length, for example from L samples to N > L samples. It is used (1) to make the length a power of 2 for the FFT, (2) to give the DFT a finer frequency spacing (a denser sampling of the same DTFT) and (3) to make the circular convolution of two sequences equal their linear convolution (the padded length must be at least L₁ + L₂ − 1).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What is zero padding?
   A. Replacing samples with zeros
   B. Removing small samples
   C. Inserting zeros between samples
   D. Appending zeros to a finite sequence to increase its length
   Answer: D. Zeros are added at the end. (Key point: Definition)

2. What does zero padding do to the DFT?
   A. Samples the same DTFT more densely
   B. Changes the spectrum
   C. Adds noise
   D. Reduces resolution
   Answer: A. The DTFT is unchanged; only the sample spacing is finer. (Key point: Effect on DFT)

3. What length makes circular convolution equal linear convolution?
   A. N = L1
   B. N >= L1 + L2 - 1
   C. N = max(L1, L2)
   D. N = L1 x L2
   Answer: B. This avoids wrap-around. (Key point: Circular = linear)

## Related in Digital Signal Analysis and Processing

- [Map given poles and zeros, magnitude response](https://www.bctengineer.com/question.md?key=semester_7%2Fdigital_signal_analysis_and_processing%3Apole-zero-map-given-poles) — Digital Signal Analysis and Processing, chapter 3, asked 2×
- [Pole-zero, magnitude response of y=x+x(n−2)](https://www.bctengineer.com/question.md?key=semester_7%2Fdigital_signal_analysis_and_processing%3Asystem-y-x-plus-x-delay-2) — Digital Signal Analysis and Processing, chapter 3
- [Linear convolution via circular convolution](https://www.bctengineer.com/question.md?key=semester_7%2Fdigital_signal_analysis_and_processing%3Alinear-conv-via-circular) — Digital Signal Analysis and Processing, chapter 7

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- [Transmission zeros and zero shifting by partial pole removal](https://www.bctengineer.com/question.md?key=semester_5%2Ffilter_design%3Atransmission-zeros-zero-shifting) — Filter Design, chapter 4, asked 3×
- [Effect of adding poles and zeros](https://www.bctengineer.com/question.md?key=semester_3%2Fcontrol_systems%3Aeffect-add-pole-zero) — Control Systems, chapter 3, asked 2×