Mathematical Transform Technique Through the Sound Waves

Dhanorkar, Gajanan; Jakkewad, Shrikant; Thakur, Rugved

Indian Journal of Mathematics

Mathematical Transform Technique Through the Sound Waves

Author(s): Gajanan Dhanorkar Gajanan Dhanorkar Department of Mathematics
University of Mumbai
Rayat Shikshan Sanstha’s Karmaveer Bhaurao Patil College Vashi,
Navi Mumbai
India. gdhanorkar@mail.com 0000-0002-8577-1562 , Shrikant Jakkewad Shrikant Jakkewad Department of Mathematics
University of Mumbai
Rayat Shikshan Sanstha’s Karmaveer Bhaurao Patil College Vashi,
Navi Mumbai
India. shrikantjakkewad171991@gmail.com , Rugved Thakur Rugved Thakur Department of Mathematics
University of Mumbai
Rayat Shikshan Sanstha’s Karmaveer Bhaurao Patil College Vashi,
Navi Mumbai
India. rugvedt25@gmail.com

Vol. 68, No. 1 (2026) • pp. 69–85

Published 15-10-2026 Article History Received 01-04-2026 Revised 28-09-2026 Published 15-10-2026

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Abstract

This paper contains a encoding of input data into audio signal based transform technique to get original output. In this process data transformed into a distinct frequency using a linear mapping function. These frequencies are synthesized as discrete-time sinusoidal signals and concatenated to form an encrypted audio waveform. In decoding frequency-domain analysis through the Discrete Fourier Transform (DFT) and its computationally efficient variant, the Fast Fourier Transform (FFT). By detecting the dominant frequency present in each time segment, the original prime number and corresponding alphabetic character are accurately recovered. The proposed system integrates number theory, trigonometry, sampling theory, and harmonic analysis, providing an interdisciplinary framework suitable for cryptography education, digital signal processing demonstrations, and mathematical visualization of encryption concepts.

Keywords

String; Cryptography; Encryption; Decryption.

2020 Mathematics Subject Classification

54C30; 42A38; 65T50

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Allahabad Mathematical Society

Mathematical Transform Technique Through the Sound Waves

Abstract

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2020 Mathematics Subject Classification

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