Multirate Signal Processing using Python Ilmenau University of Technology Full Course

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#python #signalprocessing #freecourse • Multirate Signal Processing with Python Examples - Ilmenau University of Technology- Full Course • 00:00:00 Introduction • What is Multirate Signal Processing? • Discrete Time Signal Example • Python Live Plot of a Microphone Signal • Javascript Live Plot of a Microphone Signal • Nyquist Theorem • Simple Sample Rate Conversion Example • Basic Building Blocks of MSP • Example: Basic Building Blocks • Critical Sampling • Analysis Filter Bank • Analysis Filter Bank Explanation • Synthesis Filter Bank • 00:24:01 Multiresolution • Uniform Filter Banks • Live Spectrogram Example • Non-Uniform Filter Banks • Notation • DTFT - Discrete-Time Fourier Transform • DFT - Discrete Fourier Transform • DCT - Discrete Cosine Transform • z-Transform • z-Transform Examples • STFT - Short-Time Fourier Transform • 001:06:50 Frequency Response • Frequency Response • Frequency Response using Noise • Black Box System / Noise • Gaussian Noise • Output of Black Box 01 • Transfer Function Black Box 01 • Impulse Response Black Box 01 • Butterworth Filter • Frequency Response using Sweeping Sinusoid • Transfer Function using Sweeping Sinusoid • Convolution as Matrix Multiplication • z-Transform Frequency Response • Python FreqZ Function • Frequency Response Other Plots • dB Revision • Cascaded Filters • 01:50:40 Filters • Ideal Low Pass Filter • Delay (Shift) Operator • Ideal Low Pass Filter Impulse Response • 02:01:23 Filters and Windows • Finite Impulse Response (FIR) Low Pass Filter • Parseval Theorem • Rectangular Window Frequency Response • 02:32:32 Window Functions • Window Design using Optimization • Error Function for Optimization • Raised Cosine Window • Kaiser Window • Window Function used in Vorbis I • Approximation of an Ideal Low Pass Filter • 02:47:52 Filter Design with the Window Method • The Window Method • Kaiser Window Example • Kaiser Window Example: Python • Kaiser Window Longer Example: Python • High Pass and Band Pass Ideal Filter Design • High Pass and Band Pass with Modulation • HP and BP with Modulation: Python Example • HP and BP with Modulation: Python Example II • 03:08:08 Sampling • Python Example - Downsampling • 03:14:30 Effects in the z-Domain • The z-Transform • Modulation and Time Reversal • 03:23:36 Non-Ideal Filters • Filter Banks • Aliasing Cancellation • Analysis Filter Bank • Live Spectrogram in Python • Fast Implementation • 03:41:25 Transforms as Filter Banks • Equivalent Analysis Filters of a Discrete Fourier Transform (DFT) • Equivalent Synthesis Filter Bank • Python Example • Example Transform as Filter Bank • 00:03:57 Discrete Cosine Transform and Polyphase Representation • DCT Type 4 • Polyphase Introduction • Polyphase Python Example • Polyphase Faster Implementation • Polyphase Application Example • Auxiliary Python Functions • 04:20:46 Polyphase Representation • Filter Bank of N Filters • Synthesis Filter Bank • Perfect Reconstruction • 04:32:17 Modified Discrete Cosine Transform (MDCT) • MDCT • Python Example: MDCT Filters • Analysis and Synthesis Polyphase Matrices • Symmetries of a Cosine Modulation Function • Sparse Matrices and the MDCT • Factorization: Python Example • The Delay Matrix • Python Examples • The Python Folding Matrix Function • The Factorization • Perfect Reconstruction • Nested 2x2 Sub-Matrices • Orthogonality and Para-Unitarity • Fa Matrix • Summary • MDCT Python Implementation, Analysis • MDCT Synthesis Filter Bank • 05:29:20 Low Delay Filter Banks (LDFB) • Folding Matrix Fa • Zero-Delay Matrix • Zero-Delay Matrix and its Inverse Sympy Implementation • Python Sympy Example: Folding Matrix and Zero-Delay Matrix • Drawbacks of Zero-Delay Matrices • Python Fast Implementation Example • 05:52:20 Optimization of Filter Banks • Goal • Problem to Solve • Optimization Approach • Newton's Method • Gradient • Hesse Matrix • Gradient Descent • Python Example for the Optimization of an MDCT Filter Bank • 06:21:20 Artificial Neural Networks • Neural Networks as Cascaded Filter Banks • Deep Neural Networks • Activation Function • Diagram of a 3-layer Artificial Neural Network • Gradient Descent • Back Propagation • Python Example: MNIST Digit Recognition • Convolutional Neural Networks • Python Keras CNN Example • Python PyTorch Example • Convolutional Implementation Using a Dense Net • Real-Time Online Implementation of Convolutional Neural Networks • GitHub with Slides and Code: https://github.com/GuitarsAI/MRSP_Not...

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