Video 51: Solution of State Equations (Homogeneous & Nonhomogeneous) with MATLAB Simulation

 

Hello Viewers, in this video, the theory of solution of state equations is explained. Both the cases of homogeneous and non-homogeneous equations are considered. To clear the concept, some numerical examples are also solved. Also a MATLAB code is developed which is very efficient and capable to solve any state equations for any types of inputs. With this MATLAB program, students can solve questions of their text books and can verify their theoretical outcomes.

This video includes following contents:

• State Space model of systems.
• Solution of homogeneous state equation.
• State Transition Matrix (STM) and its properties.
• Example of solution of homogeneous state equation.
• Solution of non-homogeneous state equation.
• Examples of solution of non-homogeneous state equation.
• MATLAB code for solution of state equations.

Link for previous videos,

1. Introduction to State Space Analysis: Click Here

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Video 50: Introduction to State Space Analysis (Physical Systems Modelling) (With MATLAB Code)

 

Hello Viewers, in this video, the theory of state space modelling is explained. the modern approach based on state space is compared with classical approach of system modelling which is based on transfer functions highlighting advantages of state space method.

Also various physical systems such as Electrical and Mechanical systems are considered for state space modelling. 

The relationship between TF and SS for an LTI system is also established. Also a MATLAB code is explained to model a system in SS and to do various analysis of it.

This video includes following contents:

• Why State Space? (Classical and Modern approach of system modelling).
• Introduction to State space system modelling.
• Basic Definitions: State variables, State, State vector and State space.
• State space modelling of physical systems (Mechanical/ Electrical).
• State space to transfer function conversion and vice-versa. 
• MATLAB code for State space modelling.

Link for previous videos,

1. LTI System Analyzer using MATLAB GUI: Click Here

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Video 49: LTI System Analyzer using MATLAB GUI (With Code)

 

Hello Viewers, in this video, a graphical user interface (GUI) is created to analyze any LTI system. This GUI can plot various time response curves such as Impulse response, Step response, Ramp response. It can also give various stability plots such as Root locus, Nyquist plot, Bode plot, Log magnitude vs phase plot and Pole-zero plot.

This tutorial also covers basics of LTI systems. 

This video includes following contents:

• Introduction to LTI systems.
• Various (Time domain/ Freq. domain) analysis of LTI systems.
• Creating MATLAB GUI for LTI system analyzer using GUIDE.
• MATLAB code of Call Back functions for various GUI components.
• Program Simulation.

Link for previous videos,

1. Device Control using DTMF signals and MATLAB App designer: Click Here

2. Producing Colors with RGB LEDs using Arduino and MATLAB: Click Here

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Video 48: Denoising of Signals and Images using Wavelet Packet Transform

 

Hello Viewers, in this video, denoising of signals and images using Wavelet Packet Transform (WPT) is explained.

This tutorial explains the basic theoretical background of WPT based denoising scheme, noise variance estimation and universal threshold calculation. The denoising is implemented in MATLAB to do experiments with different noisy 1D and 2D signals. The concept of full tree and best tree based decomposition is also included.

This video includes following contents:

• Introduction to Wavelet Packet Transform (WPT).
• Objective and Noise Model.
• WPT based Denoising scheme.
• Noise variance estimation and finding universal threshold.
• Thresholding methods.
• MATLAB functions for WPT and WPT based denoising.
• MATLAB code for denoising 1D signals (Audio).
• MATLAB code for denoising 2D signals (Images).

Link for previous videos,

1. Introduction to wavelet theory and Its applications: Click Here

2. Wavelet Packet Transform of Signals and Images: Click here

3. Wavelet based denoising of audio signals using MATLAB & Simulink: Click Here

4. Wavelet based denoising of images using MATLAB: Click Here

Download Resources: 

1. Test Images: Download 

2. Test Audio Clips: Download

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Video 47: Wavelet Packet Transform (WPT) of signals and Images

Hello Viewers, in this video, the Wavelet Packet Transform (WPT) of signals and images is explained.

The wavelet packet transform is generalization of wavelet transform. In WPT, the detailed coefficients are also split into approximation and detailed coefficients, while in WT, only approximation coefficients are split in further levels.

Also WPT shows superior performance in spectral analysis of signals. It finds suitability in various applications such as denoising, compression, feature extraction and image classification.

This tutorial explains the basic theoretical background of WPT including construction of WPs, WP tree and optimal selection of WP tree.

This video includes following contents:

• Introduction to Wavelet Packets (WP).
• Construction of Wavelet Packets.
• Atoms of Wavelet Packets.
• Organization of Wavelet Packets (WP Tree).
• Selecting Optimal Wavelet Packets Tree .
• Comparing Wavelets and Wavelet Packets decomposition.
• Wavelet Packets decomposition of Images.

Links for previous videos,

1. Introduction to wavelet theory and Its applications: Click Here

2. CWT of 1D signals using MATLAB and Python: Click Here

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Video 46: Object Classification using HOG features and ECOC Multi-Class SVM (With Matlab Code)

Hello Viewers, in this video, a multi-class object classification problem using HOG features is explained. To demonstrate the implementation, simple geometrical shapes (Circle, Square, Star and Triangle) are taken for classification. As a classifier, ECOC (Error Correcting Output Codes) based multi-class SVM is used. The shapes image database is obtained from Kaggle. 

The HOG feature is very popular and widely used for object detection in images. To understand the HOG feature computation, viewers are requested to watch my previous video of HOG feature computation.

This video includes following contents:

• Introduction.
• Proposed scheme for object Classification.
• Image Database Preparation.
• ECOC based Multi-Class SVM.
• Appropriate Cell Size selection for HOG feature.
• MATLAB Code for Shapes Classification (Multi-Class).
• MATLAB Code for Discrete Testing.

1. Link for previous video on HOG feature computation: Click Here

2. Link for Kaggle Dataset: https://www.kaggle.com/smeschke/four-shapes

3. Link to download original paper of N. Dalal and Bill Triggs:

https://lear.inrialpes.fr/people/triggs/pubs/Dalal-cvpr05.pdf

Download Resources: 

1. Image Dataset (Modified): Download (Source: Kaggle)

2. Distorted Test Images: Download

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