State – Space Equations

This lecture overviews State –Space Equations that has many applications in digital filters, systems theory and deep learning. It covers the following topics in detail: Multiple Input-Output Systems, Single Input-Output Systems, IIR state-space system implementation, RNNs.

Fast Fourier Transform

This lecture overviews Fast Fourier Transform that has many applications in digital signal processing and analysis and in power spectrum estimation. It covers the following topics in detail: Transition from DFT to FFT, Decimation in Time (DIT) FFT, Decimation in Frequency (DIF) FFT, FFT Computation issues, Goertzel Algorithm, Bluestein Algorithm.

Discrete Fourier Transform

This lecture overviews Discrete Fourier Transform that has many applications in digital signal processing and analysis and in power spectrum estimation. It covers the following topics in detail: Discrete-Time Fourier Transform, Discrete Fourier Transform, Fast Convolution with DFT.

Z Transform

This lecture overviews  Z Transform that has many applications in signal processing and systems theory. It covers the following topics in detail:  Z transform, Inverse Z transform,  Z Transform Properties, Transfer Function of a Digital System, Z  transform and Laplace Transform.

Signal Sampling

This lecture overviews Signal Sampling that has many applications in signal acquisition, processing and analysis. It covers the following topics in detail: Discrete/Continuous Signals, Signal Sampling, Signal Reconstruction, Signal Quantization.

Laplace Transform

This lecture presents Laplace Transform (LT) and its region of convergence.  Its relation to Laplace transform is presented. Notable LT properties are reviewed: time shift, convolution, signal differentiation/integration. Its use in defining Linear Time-Invariant (LTI) continuous-time systems transfer function is also presented and stability issues are overviewed. Various types of such systems are presented with examples (e.g., RC electric filters, temporal diffusion systems).