Motivating examples of digital communications. Spectrum availability and channels. Channel modeling base band and pass band channels. Digital modulation schemes for base band and pass band channels. Line coding, Pulse amplitude modulation, Phase modulation, CPFSK, Frequency shift keying, QAM.

Maximum Likelihood Estimation (MLE): Exact and approximate methods (EM algorithm, alternating maximization, etc.)Cramer-Rao Lower Bound (CRLB) Minimum Variance Unbiased Estimation (MVUE) Sufficient Statistics Best Linear Unbiased Estimation (BLUE) Large and Small Sample Properties of Estimators: Understanding the behavior of estimators in both large and small sample sizes Bayesian Inference and Estimation: Minimum Mean Square Error (MMSE) estimation MAP Estimation (Maximum A Posteriori Estimation)Wiener and Kalman Filtering (Sequential Bayes) Detection Theory: Likelihood Ratio Testing Bayes

Module 1: Human Values (5hrs)

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.