**Author details**

From **Table 2**, we can see that the optimal values of *N* (in terms of computation efficiency) are in the middle of the tested range, 9 and 10 for both the 2d-GBM and 2d-NIG models. The decline in performance for larger values of *N* is due to the increased memory requirements. When compared to 2d-GBM, 2d-NIG seems to have less of an increase in performance when executed on GPU, which could be because it is more computationally heavy (such as calculating the characteristic function *Φ*NIGð Þ *u*; *T* , which involves two square root and exponential calculations,

*Real Perspective of Fourier Transforms and Current Developments in Superconductivity*

In this work, we built on the literature on fast and accurate pricing of spread options based on two-dimensional FFT method using parallel computation. We examined the effectiveness of this approach by comparing the computational times of CPU and GPU implementations of the FFT Spread Option Pricing Algorithm in MATLAB. We have taken benchmarks prices from Monte Carlo simulations with 1000000 paths and 100 discretization time steps. Our results decisively conclude that the execution of the algorithm on a GPU significantly improves computational performance, decreasing the time taken to run by a factor of up to almost 60x. Considering how common spread options are in the financial market, a faster way to price these securities means increased efficiency in transactions involving spread options, and the FFT algorithm implemented for this project also vastly improves

as opposed to simply one in the GBM model).

*Numerical results for spread option pricing.*

**4. Conclusion**

**98**

**Figure 1.**

Shiam Kannan<sup>1</sup> and Mesias Alfeus2,3\*


\*Address all correspondence to: malfeus@uow.edu.au; mesias@sun.ac.za

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Chapter 9**

**Abstract**

**1. Introduction**

pressure (BP).

**101**

Use of Transforms in Biomedical

Biomedical signals like electrocardiogram (ECG), photoplethysmographic (PPG) and blood pressure were very low frequency signals and need to be processed for further diagnosis and clinical monitoring. Transforms like Fourier transform (FT) and Wavelet transform (WT) were extensively used in literature for

processing and analysis. In my research work, Fourier and wavelet transforms were utilized to reduce motion artifacts from PPG signals so as to produce correct blood oxygen saturation (SpO2) values. In an important contribution we utilized FT for generation of reference signal for adaptive filter based motion artifact reduction eliminating additional sensor for acquisition of reference signal. Similarly we

**Keywords:** Fourier transform, biomedical signals, electrocardiogram signal,

The essence of mathematical design cannot be ignored in the analysis of real world engineering applications i.e. the research in engineering and mathematics is a two way parallel track that interrelates and coordinates towards value added research. In specific, the use of transforms in the field of electrical, electronic and communication engineering is unimaginable. In the present scenario of Covid-19 pandemic, world is looking to sustainable development of biomedical devices for critical monitoring and efficient vaccination for human survival [1–4]. In general, the Fourier transform (FT) is a mathematical tool which transforms the time domain signal into a frequency domain representation used in analysis of biomedical, wireless communication, signal and image processing applications. In literature, many researchers had used this tool in frequency domain analysis of all biomedical signals like electrocardiogram (ECG), photoplethysmographic (PPG) and blood

In continuation to FT, different transforms were developed to analyze and design of various applications based on the requirement [5, 6]. In general, the FT is used in analysis of stationary signals; the wavelet transform (WT) is a mathematical tool used in analysis of both stationary and non-stationary signals. Discrete wavelet transform (DWT) used in enormous application in various engineering fields. So, in this chapter we addressed some of the research challenges in ECG and

PPG signal processing using Fourier and Wavelet transforms.

Signal Processing and Analysis

*Ette Harikrishna and Komalla Ashoka Reddy*

utilized the transforms for other biomedical signals.

photoplethysmographic signal, wavelet transform
