A new Fourier transform with applications to signal processing

Project Title

A new Fourier transform with applications to signal processing

Project Area of Specialization Information & Communication TechnologyProject Summary

This project will aim to introduce and analyze a new integral transform for absolutely integrable functions .The new integral transform is a direct generalization of the well- known Fourier transform. Existence, uniqueness and convergence results under Suitable assumptions will be derived. Various important operational properties , for example, scaling, shifting, convolution,Parseval's formula,and linearity will then be established.New  transform of several elementary and generalized functions will be computed for further understandings. Application of the new transform will be then explored to analyze some well- known signals represented by piecewise continuous functions. A computer program using MATHEMATICA software will be developed to test the theoratically established results.

Project Objectives

The aims and objectives of this proposed project are:

1.To develope a new transform for signal and image processing

2.To get better understanding of the signal and image processing through the new transform

3.To develop a MATHEMATICA program for signals /image processing representable by piecewise continuous functions

4.To seek applications of the new transform to more complex signals, if possible

5.To highlight strength and weakness of the new transform in practical applications

6. To link existing results with the new obtained results

Project Implementation Method

In the first phase, we will design the theoratical framework based on the existing literature for simple input signals. In the second phase theory will be tested through the developed MATHEMATICA program. Then we will extend the established results to some practical problems both in theory and practice.

Benefits of the Project

The benefits of this proposed work include but not limited to:

1. Generalization of the existing results

2. More effective analysis of the signals by having more degrees of freedom

3. Paving the path for future researchers working in the field of image and signal processing

Technical Details of Final Deliverable

A new integral transform will be available to do more effective analysis of signalsin the time frequency domain. A prototype computer program for some basic examples in signal processing.

Final Deliverable of the Project Software SystemCore Industry EducationOther IndustriesCore Technology OthersOther TechnologiesSustainable Development Goals Quality Education, Decent Work and Economic Growth, Industry, Innovation and InfrastructureRequired Resources

Item Name	Type	No. of Units	Per Unit Cost (in Rs)	Total (in Rs)
			Total in (Rs)	80000
Computer / Laptop	Equipment	1	70000	70000
Expenditures	Miscellaneous	1	10000	10000