Convolution - Matlab worked example.

We have worked the convolution of the signals x(t) and h(t):

                                                         Figure 1: It shows the signal x(t).

                                       Figure 2: It shows the impulse response of the system, h(t).

We have solved the convolution problem above, step-by-step. We have used MATLAB to solve this integral, we have included the numerical and analytical solution:

                Figure 4: It shows the common area between both functions.

                Figure 6: convolution process between two functions.

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Pressure amplitude distribution: Horn equation.

The pressure amplitude distribution p(x) of harmonic oscillation, p(x,t) = p(x) cos(wt), in the horn is governed by the equation:

where A(x) is the cross-section are, k is the wavenumber, w=2 pi f is de angular frequency, c = 340 m/s is the sound speed in air, f is the frequency.

Boundary conditions of horn opened at the both sides are: p(0) = p(L)=0.

It shows the first three modes of the second order differential equation given above. It shows clearly the pressure null at ends.

It shows the first 10 modes.

Click on BUY NOW, we have solved the horn equation, step-by-step. We have used MATLAB to solve this equation, we included the code.

RLC series circuit

For the circuit shown find an equation which shows how the current varies with time. Assume zero initial conditions when the switch is closed. Use Laplace transform and Kirchhoff's voltage law:

Click on BUY NOW to see the step-by-step solution, we have plotted the solution with MATLAB.

Signal and System Analysis

It shows the continuous signal as blue line, whereas the red line is the low-pass filter signal with a cutoff frequency of 75 Hz.

It shows the continuous signal as blue line, whereas the red line is when the low-pass filter has been applied. It has a cutoff frequency of 30 Hz.

We have the step-by-step solution of Frequency Modulate and Amplitude Modulate problems... click on BUY  NOW to get the final solution.

Cosmic Microwave Background and Point sources at mm wavelength.

We show a 10x10 sq deg map of the CMB, beam size = 10 arcmin.

A map 2x2 deg^2  CMB + point sources at 220 GHz, beam size = 1.5 arcmin.

This is my own WORK. Prohibited its reproduction.

Optimisation Methods and Simulation

Consider the minimization problem

There is not any constraint on x1 and x2.

We have solve the above problem using Simulated Annealing algorithm, with my own code and MATLAB in-built function, click on BUY NOW to see the step-by-step solution and many more.

Pressure distribution around an airfoil

Theoretical calculations for NACA 23012

Thin Airfoil Theory

Introduction

An airfoil is defined by first drawing a “mean” camber line. The straight line that joins the leading and trailing ends of the mean camber line is called the chord line. The length of the chord line is called chord, and given the symbol ‘c’.To the mean camber line, a thickness distribution is added in a direction normal to the camber line to produce the final airfoil shape. Equal amounts of thickness are added above the camber line, and below the camber line.

                                                                                (a)

                                                                                (b)

The solid blue line represents thin airfoil theory for Cp vs x/c, a) The solid red line is at AOA = 5 deg, b) The solid red line is at AOA = 10 deg.


We have an extensive analysis of pressure distribution around an airfoil, click on BUY NOW... MATLAB code is included.

Control Systems

What is the importance of Pole-zero diagrams in control systems?


What is the importance of Laplace Transformation in control systems?

Solve the differential equation system using MATLAB and analytically using Laplace Transform.

at t=0, x=4, y = 2 and x' = 0 and y' = 0.

We have the step by step solution and many more... 
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Block Reduction Method

Reduce the following block diagram using Block Reduction Method and obtain the overall transfer function

We have obtained step by step the equivalent transfer function....
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Hard-disk read/write head controller and speed control of a DC motor

We have controlled a simple model for the read/write head with differential equation,

We have the analytical and Matlab code for design control, for example:

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