Computer Sciences and Information Technology
Title : | Advanced Hilbert Transformer Design for High-Fidelity Real-Time Signal Analysis |
Area of research : | Computer Sciences and Information Technology |
Focus area : | Signal Processing |
Principal Investigator : | Dr. Nikhil Agrawal, Indian Institute Of Information Technology, Nagpur, Maharashtra |
Timeline Start Year : | 2024 |
Timeline End Year : | 2027 |
Contact info : | nikhil.agrawal@iiitdmj.ac.in |
Details
Executive Summary : | The Hilbert Transformer (HT) plays a crucial role in many signal processing applications, specially where we have to deal with non-stationary signals. HT is used in computation of the instantaneous frequencies of non-stationary signals, phase deviation and various other applications. HT can be seen as a digital system that does not alter the magnitude of the input signal but only provides a phase shift. Design of practically realizable HT is a challenging task owing to ideal HT having non-causal impulse response. For implementation of practically realizable HT is to use digital filter structure, which are finite impulse response filter (FIR) and infinite impulse response filter (IIR). FIR filter-based design requires too many coefficients to achieve a reasonable response for accurate realization of HT. Whereas, IIR based all pass filter (IIR-APF) is the most efficient way to realize HT. IIR-APF based design suffers the limitation of quantization error due to truncation of the filter coefficients and non-linear phase response. Designing of an IIR filter with linear phase response is challenging task due to the presence of poles in its transfer function. Therefore, our focus is to design the nearly linear phase response, which shall strict the phase of IIR-APF such that its phase response should not deviate more than 5% from the desired phase response. Design of an IIR-APF with such close approximation, requires a detailed mathematical analysis. To achieve the desired accuracy in desired phase response of HT, we are focusing to use fractional derivative constrains (FDC) based design approach in the mean squared error (MSE) minimization. MSE is a classical design method, however there is huge phase error at the edge frequency and the phase of the designed HT swinging to much between the desired band. To ensure the high approximation, the FDC will help in the reduction of the magnitude of swinge. The solution of the proposed problem requires the matrix calculation and its inverse, which are computationally expensive. Also, it depends on the number of FDC and if higher number of constraints are needed then more computational time and resources are required. The design of fractional derivative based method is tested and observed that the design problem is a multi-model. Modern evolutionary techniques (ET) have a potential of finding the optimal solution for such design problems. Therefore, they have been exhaustively tested for such problem, however, their heuristic nature results in deviation in optimal result which is observable when statistical analysis is performed. Thus, for thorough analysis using ET, various repeated analysis are needed to ensure the results obtained by the proposed method are optimal. The HT designed using proposed method will be faster and easy to deploy in real time applications like wearable biomedical devices, real time analysis non statical signals and many more. |
Co-PI: | Dr. Sushmita Dandeliya, Indian Institute Of Information Technology, Nagpur, Maharashtra-441108 |
Total Budget (INR): | 29,59,814 |
Organizations involved