Syllabus

Module 1: Introduction to Signal Transforms [6 hr.]
Orthonormal vector and functional space and variations - Metric Preservation - Parseval’s Theorem in orthonormal space

Module 2: Hilbert and Fourier Transforms [7 hr.]
Hilbert Transform - Hilbert-Huang Transform - Fourier Transform - Fourier series - Generalized Fourier transform properties - Convolution theorem

Module 3: Discrete Transforms and Short-Time Analysis [7 hr.]
Discrete Cosine Transform (DCT) - Discrete Sine Transform (DST) - Short Time Fourier Transform (STFT)

Module 4: Wavelet Transform and Quantization [7 hr.]
Wavelet Transform: Method & Properties - Multi-resolution analysis - M Band QMF filter banks - Quantization and coding of transform coefficients

Module-5: Frame Theory and Advanced Transforms [8 hr]
Frame Theory: Signal approximation & compressed sampling - Parseval’s Theorem in redundant space - Curvelet transform & beyond: Method & Properties

To make the students adept to visualizing the domain of signal transforms

To make the students adept to represent signals in compact transform domain

To make the students adept to develop algorithms to map from signal to other transform domain

To make the students adept to implement the algorithm in software/Hardware

The students will be able to
CO1 Understand the concept of orthonormal vectors and functional spaces, and their properties, analyzing variations and applications in these spaces.
CO2 Apply metric preservation and Parseval’s theorem in orthonormal spaces, understanding its significance in signal processing and energy conservation.
CO3 Analyze and apply Fourier transforms, Fourier series, Hilbert transforms, generalized Fourier transforms, and the convolution theorem in signal processing tasks.
CO4 Implement and utilize discrete transforms like Discrete Cosine Transform (DCT), Discrete Sine Transform (DST), and Short Time Fourier Transform (STFT) in practical signal processing.
CO5 Explore and apply wavelet transforms, multi-resolution analysis, M-band QMF filter banks, quantization of transform coefficients, and Frame Theory in signal approximation and compressed sampling.

Truong Nguyen & Gilbert Strang, Wavelets and Filter Banks, Wellesley-Cambridge Press , Latest Ed.

K. R. Rao and P. Yip, Discrete Cosine Transform: Algorithms, Advantages, Applications, Academic Press , Latest Ed.

Khalid Sayood, Introduction to Data Compression, Elsevier , 2011 or Latest Ed.

Gilbert Strang, Linear Algebra and Its Applications, Nelson Engineering , 2007 or Latest Ed.