Sinusoids and Its Orthogonality

  • Abhinav Ranjan
  • Shraddha PrasadEmail author
Conference paper


In many digital signal processing (DSP) applications and communication systems, the main component is the fast Fourier transform (FFT) processing. A characteristic of sinusoids is that they are orthogonal at distinct frequencies whether they are complex or real at any amplitude and phase. All that matters are that the frequencies be different. This property of sinusoid will be implemented to propose a new approach to design and implement fast Fourier transform (FFT) using Radix-42 algorithm, and also how the multidimensional index mapping reduces the complexity of FFT computation will be proposed and discussed in an easy understanding manner. Using mathematical analysis on Radix-4 DFT (discrete Fourier transform) kernel, the formal Radix-4 butterfly structure can be remodeled. This will make the design perspective so simple to implement the mathematical algorithm into the hardware realization model.


DFT (discrete Fourier transform) Radix-4 FFT (fast Fourier transform) 


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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Faculty of Science and EngineeringJharkhand Rai UniversityRanchiIndia
  2. 2.Applied Science DepartmentJharkhand Rai UniversityRanchiIndia

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