Spectral Signal Analysis

This lecture overviews Spectral Signal Analysis that has many applications in periodicity estimation and acoustic/speech/music/biomedical signa analysis. It covers the following topics in detail: Power Spectrum, autocorrelation function and Fourier Transform. Power Spectrum and random signals. Bartlett Method, Welch Method Blackman – Tukey Method for Power Spectrum estimation.

Adaptive Filters

This lecture overviews Adaptive Filters that has many applications in signal processing, automatic control, robotics and autonomous systems. It covers the following topics in detail: Adaptive Filters, Minimum Mean Square Error (MMSE), Widrow LMS Algorithm, Properties of the LMS Algorithm, CLMS Algorithm, Nonlinear Feedforward Complex Adaptive Filters, Kernel Adaptive Filters, KLMS Algorithm.

Error Analysis in Digital Filters

This lecture overviews Error Analysis in Digital Filters that has many applications in digital signal processing and analysis. It covers the following topics in detail: Digital Filters, Quantization errors, Statistic Error Analysis in FIR filters, Statistic Error Analysis in IIR filters.

Fast 1D Convolution Algorithms

1D convolutions are extensively used in digital signal processing (filtering/denoising) and analysis (also through CNNs).  As their computational complexity is of the order O(N^2), their fast execution is a must.

This lecture will overview linear systems, linear and cyclic convolution and correlation. Then it will present their fast execution through FFTs, resulting in algorithms having computational complexity of the order O(Nlog2N). Optimal Winograd 1D convolution algorithms will be presented having theoretically minimal number of computations. Parallel block-based 1D convolution/calculation methods will be overviewed.

Digital Filter Structures

This lecture overviews Digital Filter Structures that has many applications in digital signal processing. It covers the following topics in detail: IIR Filter Structures (Direct Filter Structure, Cascade Filter Structure, Parallel Filter Structure, Transposed Filter Structure). FIR Filter Structures (Direct Filter Structure, Cascade Filter Structure, Parallel Filter Structure, Frequency Sampling Structure).

FIR Filter Design

This lecture overviews FIR Filter Design that has many applications in digital signal processing and deep neural networks. It covers the following topics in detail: Window Method, Optimization Methods, Frequency Sampling Method, Equiripple FIR Filter Design.