Unnikrishna Pillai received his Ph.D. degree in systems engineering from the University of Pennsylvania in 1985 and MTech in Electrical Engineering from the Indian Institute of Technology, Kanpur, India in 1982. He joined Brooklyn Polytechnic, New York, in 1985 as an assistant professor in electrical engineering, and since 1995 he has been a professor of electrical and computer engineering (currently New York University). He is the author of several widely used textbooks including Probability, Random Variables and Stochastic Processes (A. Papoulis and S. U. Pillai) (2002), has over 250 online video lectures, and has published extensively. He is the 4-th most cited Google scholar under ‘Radar.’ His research interests include synthetic aperture radar (SAR) imaging, waveform design, power control for wireless mobiles, electronic signal identification, rational and stable approximation of norational systems, array signal processing, portfolio optimization, and applications of non-linear differential equations for modeling physical systems with time-varying characteristics. He is a life Fellow of IEEE.Anuj Patel received his MS degree in Electrical and Computer Engineering from New York University Tandon School of Engineering (2025) and his undergraduate degree from Vellore Institute of Technology, India (2023). Towards his MS degree, he has worked as a researcher at NYU WIRELESS on Millimeter-Wave Beamforming and MIMO Channel Estimation.Beyond academics, Patel was also involved with the NYU Tandon Graduate Student Council and the NYU Student Government Assembly. He is the recipient of Emerging Leaders Award, Distinguished Engagement Award and the Tandon Community Excellence Award.

• Introduction.- Fourier Series.- Fourier Transforms.- Amplitude Modulation.- Angle Modulation.- Digital Modulation Techniques.- Conclusion.

Unnikrishna Pillai received his Ph.D. degree in systems engineering from the University of Pennsylvania in 1985 and MTech in Electrical Engineering from the Indian Institute of Technology, Kanpur, India in 1982. He joined Brooklyn Polytechnic, New York, in 1985 as an assistant professor in electrical engineering, and since 1995 he has been a professor of electrical and computer engineering (currently New York University). He is the author of several widely used textbooks including Probability, Random Variables and Stochastic Processes (A. Papoulis and S. U. Pillai) (2002), has over 250 online video lectures, and has published extensively. He is the 4-th most cited Google scholar under ‘Radar.’ His research interests include synthetic aperture radar (SAR) imaging, waveform design, power control for wireless mobiles, electronic signal identification, rational and stable approximation of norational systems, array signal processing, portfolio optimization, and applications of non-linear differential equations for modeling physical systems with time-varying characteristics. He is a life Fellow of IEEE.Anuj Patel received his MS degree in Electrical and Computer Engineering from New York University Tandon School of Engineering (2025) and his undergraduate degree from Vellore Institute of Technology, India (2023). Towards his MS degree, he has worked as a researcher at NYU WIRELESS on Millimeter-Wave Beamforming and MIMO Channel Estimation.Beyond academics, Patel was also involved with the NYU Tandon Graduate Student Council and the NYU Student Government Assembly. He is the recipient of Emerging Leaders Award, Distinguished Engagement Award and the Tandon Community Excellence Award.

• Introduction.- Fourier Series.- Fourier Transforms.- Amplitude Modulation.- Angle Modulation.- Digital Modulation Techniques.- Conclusion.

Unnikrishna Pillai received his Ph.D. degree in systems engineering from the University of Pennsylvania in 1985 and MTech in Electrical Engineering from the Indian Institute of Technology, Kanpur, India in 1982. He joined Brooklyn Polytechnic, New York, in 1985 as an assistant professor in electrical engineering, and since 1995 he has been a professor of electrical and computer engineering (currently New York University). He is the author of several widely used textbooks including Probability, Random Variables and Stochastic Processes (A. Papoulis and S. U. Pillai) (2002), has over 250 online video lectures, and has published extensively. He is the 4-th most cited Google scholar under ‘Radar.’ His research interests include synthetic aperture radar (SAR) imaging, waveform design, power control for wireless mobiles, electronic signal identification, rational and stable approximation of norational systems, array signal processing, portfolio optimization, and applications of non-linear differential equations for modeling physical systems with time-varying characteristics. He is a life Fellow of IEEE.Anuj Patel received his MS degree in Electrical and Computer Engineering from New York University Tandon School of Engineering (2025) and his undergraduate degree from Vellore Institute of Technology, India (2023). Towards his MS degree, he has worked as a researcher at NYU WIRELESS on Millimeter-Wave Beamforming and MIMO Channel Estimation.Beyond academics, Patel was also involved with the NYU Tandon Graduate Student Council and the NYU Student Government Assembly. He is the recipient of Emerging Leaders Award, Distinguished Engagement Award and the Tandon Community Excellence Award.

• Introduction.- Fourier Series.- Fourier Transforms.- Amplitude Modulation.- Angle Modulation.- Digital Modulation Techniques.- Conclusion.