Explaining Fourier Series
PART 2 : FOURIER SERIES
Objective : 1. To show that any periodic function (or signal) can be represented as a series of sinusoidal (or complex exponentials) function. 2. To show and to study hot to approximate periodic functions using a finite number of sinusoidal function and run the simulation using MATLAB.
Scope : In experiment 1, students need to learn using MATLAB by connect it with Fourier series, where students must know how the output changes as higher order terms are added. Students must know to plot the graph. Besides, students must know to add instruction in appropriate line to plot frequencies versus coefficient for each wave form.
Equipment :
MATLAB software.
Experiment 1 : Fourier Series
Generally, student must know the basic concept of Fourier series.
General form :
[pic]
Where :
[pic]
[pic]
For example, x(t) with the highest harmonic value = 2.
[pic]
Task 1 : Simulate Using MATLAB
Procedure :
Table 1 shows coefficient for complex exponential fourier series of half rectified sine wave with A=1, T=1.
|Wave form |Fourier Coefficients |
|Half-rectified sine wave: |[pic] |
Table 2-1 : Complex Exponential Fourier Series of Half-rectified Sine Wave.
Execute program in Listing 1 using 4 inputs : [2 8 20 100].
Listing 1 : • Program to give partial complex exponential fourier sums of a half rectified sine wave of unit amplitude in table 2-1.
clear clc k_max = input (‘Enter vector of highest harmonic values desired (even only) >>’); num_kmax = length (k_max); for z = 1 : num_kmax k = [-k_max (z) : k_max (z)]; L_k = length (k); a_k = zeros (1, L_k); % Form vector of fourier series coefficients, a_k ((L_k+1)/2+1) = -0.25*j; % all odd-terms are zero except A(1)
Objective : 1. To show that any periodic function (or signal) can be represented as a series of sinusoidal (or complex exponentials) function. 2. To show and to study hot to approximate periodic functions using a finite number of sinusoidal function and run the simulation using MATLAB.
Scope : In experiment 1, students need to learn using MATLAB by connect it with Fourier series, where students must know how the output changes as higher order terms are added. Students must know to plot the graph. Besides, students must know to add instruction in appropriate line to plot frequencies versus coefficient for each wave form.
Equipment :
MATLAB software.
Experiment 1 : Fourier Series
Generally, student must know the basic concept of Fourier series.
General form :
[pic]
Where :
[pic]
[pic]
For example, x(t) with the highest harmonic value = 2.
[pic]
Task 1 : Simulate Using MATLAB
Procedure :
Table 1 shows coefficient for complex exponential fourier series of half rectified sine wave with A=1, T=1.
|Wave form |Fourier Coefficients |
|Half-rectified sine wave: |[pic] |
Table 2-1 : Complex Exponential Fourier Series of Half-rectified Sine Wave.
Execute program in Listing 1 using 4 inputs : [2 8 20 100].
Listing 1 : • Program to give partial complex exponential fourier sums of a half rectified sine wave of unit amplitude in table 2-1.
clear clc k_max = input (‘Enter vector of highest harmonic values desired (even only) >>’); num_kmax = length (k_max); for z = 1 : num_kmax k = [-k_max (z) : k_max (z)]; L_k = length (k); a_k = zeros (1, L_k); % Form vector of fourier series coefficients, a_k ((L_k+1)/2+1) = -0.25*j; % all odd-terms are zero except A(1)