Review: Linear algebra, matrix calculus, probability and statistics.

Real Time DSP Module: Fixed point representation of signals and introducing fixed point tool box in Matlab. Learning the impact of number representations in signal processing applications-IIR, FIR filter design in C- implementation of signal processing algorithms by applying quantization techniques and analyzing using Mat lab and DSP processor. Audio signal processing-echo cancellation, stream processing, block processing and vector processing of signals using DSP processor application to adaptive filtering, FFT, DCT, Wavelet using DSP processor.

Analysis of LTI system: Phase and Magnitude response of the system, Minimum phase, maximum phase, All- pass. Multirate Signal Processing: Interpolation, Decimation, sampling rate conversion, Filter bank design, Poly phase structures. Time-frequency representation; frequency scale and resolution; uncertainty principle, short- time Fourier transform. Multi-resolution concept and analysis, Wavelet transform (CWT, DWT). Optimum Linear Filters: Innovations Representation of a Stationary Random Process, Forward and Backward linear prediction, Solution of the Normal Equations.

Vectors: Representation and dot products, Norms, Matrices: The four fundamental spaces of a matrix, matrix as a linear operator, geometry associated with matrix operations, inverses and generalized inverses, matrix factorization/decompositions, rank of a matrix, matrix norms. Vector spaces: column and row spaces, null space, solving Ax=0 and Ax=b, independence, basis, dimension, linear transformations.

Orthogonality: Orthogonal vectors and subspaces, projection and least squares, Gram Schmidt orthogonalization.

Vectors: Representation and Dot products, Norms, Matrices: The Four Fundamental Spaces of a Matrix, The Matrix as a Linear Operator, The Geometry associated with matrix operations, Inverses and Generalized Inverses, Matrix factorization/Decompositions, rank of a matrix, Matrix Norms.

Module 1: Role of Interface Electronics, Analog Electronic Blocks, OPAMP – internal structure, Open- loop gain, Input R, Output R, DC noise sources and their drifts, CMRR, PSRR, Bandwidth and stability, Slew rate, Noise – general introduction, OPAMP Circuits and Analysis - Difference and Instrumentation Amplifiers (3-opamp and 2-opamp), Effect of cable capacitance and wire-resistance on CMRR, IA with guards, Biomedical application, Current-mode IA (Howland), Current-input IA, filters, Filters with underdamped response, state-variable filters, All- pass filters, Current Sources (floating and

Introduction and Background of state-of-art sensing and measurement techniques. Contactless potentiometer (resistance-capacitance scheme) – Methodology, Interface Circuits, Overview of Flight Instrumentation. Analog Electronic Blocks, CMRR Analysis (Non-ideal opamps) of an Instrumentation Amplifier, Linearization circuits for single- element wheatstone bridges (application to strain gauge), Direct Digital Converter for Strain gauges, Signal conditioning for Remote-connected sensor elements.

Introduction to high speed links. Review of PCB trace behavior at high frequencies. Concepts of cross-talk, dispersion, inter-symbol interference (ISI). Transceiver schemes. Design of transmitter, output impedance matching, multiplexing techniques, clocking, signaling techniques. Pre-distortion and equalization. Link budgets. Design of receivers – continuous time linear equalizers, slicers, DFE techniques, clocking, critical paths, IIR/FIR implementations. PLLs, clock and data recovery circuits and schemes.

Power-speed-noise trade-off. Ultra-lower power VLSI design. Leakage power vs dynamic power. Minimum energy point concept. Low voltage analog, mixed-signal design. VLSI design for IoT applications. Low voltage memories.

Designing for high speed/performance. Dynamic voltage and frequency scaling. Selected topics on clock skew, clock routing, power routing. Selected topics on layout techniques in mixed-signal circuits – guard rings, etc. Role of calibration in modern ICs.

Analysis of LTI system: Phase and Magnitude response of the system, Minimum phase, maximum phase, Allpass. Multirate Signal Processing: Interpolation, Decimation, sampling rate conversion, Filter bank design, Polyphase structures. Time-frequency representation; frequency scale and resolution; uncertainty principle, short-time Fourier transform. Multi- resolution concept and analysis, Wavelet transform (CWT, DWT). Optimum Linear Filters: Innovations Representation of a Stationary Random Process, Forward and Backward linear prediction, Solution of the Normal Equations.

Electronic integrated circuits, Scaling of electronic devices, Electrical interconnects, issues with electrical interconnection, Optical interconnects-advantages-similarities with electrical interconnects Integration-Photonic Integrated Circuits (PIC)-brief history of PIC-Features- Materials for PIC platform-Si, Silica, SOI, III-V, LiNbO3 Basic theory of Planar and channel waveguide-effective index method-guided modes Types of waveguides-Optical losses in waveguides-(side wall scattering, bending, losses due to metal layer)-waveguide fabrication (LiNbO3 and III-V based)