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Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Reconstruction of Signal using Interpolation

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Downsampling

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Properties of DTFT I

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Sampling Theorem

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In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.

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Related Experiment Video

Updated: Jun 25, 2025

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Hadamard Error-Correcting Codes and Their Application in Digital Watermarking.

Michael Windisch¹, Jakob Wassermann¹, Monica Leba²

¹Faculty Electronic Engineering & Entrepreneurship, University of Applied Sciences Technikum Wien, 1200 Vienna, Austria.

Sensors (Basel, Switzerland)

|May 25, 2024

Summary

A new Enhanced Hadamard Error-Correcting Code (EHC) significantly improves video watermarking robustness against high compression. This novel technique outperforms the Reed-Solomon Code in preserving watermarks under severe attacks.

Keywords:

2D Hadamard transform Enhanced Hadamard Code Hadamard matrix Hamming distance basis images digital watermarking error-correcting capability visual light communication VLC

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Area of Science:

Communication Technologies
Information Security
Digital Signal Processing

Background:

Error-correcting codes are vital for digital watermarking, wireless sensor networks (WSNs), and visual light communication (VLC).
Existing watermarking schemes struggle with high compression rates (approx. 1:200) common in video dissemination.
Robust error correction is essential for watermark integrity against sophisticated attacks.

Purpose of the Study:

To introduce and evaluate a novel Enhanced Hadamard Error-Correcting Code (EHC) for video watermarking.
To compare the efficacy of EHC against the established Reed-Solomon Code in watermark resilience.
To demonstrate the practical application and performance of EHC in video watermarking schemes.

Main Methods:

Developed Enhanced Hadamard Error-Correcting Code (EHC) based on 2D Hadamard Basis Images.
Implemented a 1D Hadamard decoding approach on transformed 2D base images for enhanced decoding.
Applied a multi-level interframe wavelet transform and low-pass filtering for watermark embedding in videos.

Main Results:

EHC demonstrated superior performance compared to the Reed-Solomon Code in maintaining watermarks.
The EHC exhibits high resilience against severe MPEG compression attacks.
The technique shows potential to exceed theoretical error-correcting capacity thresholds.

Conclusions:

The Enhanced Hadamard Error-Correcting Code (EHC) is a viable and effective technique for robust video watermarking.
EHC offers significant advantages over traditional methods like Reed-Solomon Code for high-compression scenarios.
Future work may explore 3D EHC for potentially even better error correction capabilities.