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.
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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… Continue reading Laplace Transform
Orthogonal Signal Transforms. Fourier Series
This lecture overviews Orthogonal Signal Transforms. Fourier Series that has many applications in signal processing, analysis and compression. It covers the following topics in detail: Vector calculus, Orthogonal functions, Trigonometric Fourier Series, Exponential Fourier Series, Triangular Fourier Series, Discrete Orthogonal Signals, Discrete Fourier Transform, Discrete Cosine Transform.
Fourier Transform
This lecture overviews the topics of continuous-time periodic signals, signal frequencies and Fourier Transform (FT). Its relation to Laplace transform is presented. Notable FT properties are review: time shift, time scaling, convolution, signal differentiation/integration, energy preservation. Its use in defining Linear Time-Invariant (LTI) continuous-time systems frequency response is presented. Various types of such systems, notably… Continue reading Fourier Transform