Question

This is a MATLAB Question. Below is my base code for a Fourier Series of a half triangle wave.

clear all; close all; T = 1; % Total time fs = 256; % Assumed sample frequency N = fs*T; % Calculate number of points t = (1:N) *T/N; % Generate time vector f = (1:N)*fs/N; % and frequecy vector for plotting x = [t(1:N/2) zeros (1,N/2)]; % Generate the signal, first a ramp plot(t, x); figure; xf = fft(x); % Take Fourier Transform, scale Mag = abs(Xf(2:end))/(N/2); % and reomve first point (DC value) Phase = -angle(xf (2:end))*(360/(2*pi)); plot(f(1:20), Mag(1:20),'.k', 'MarkerSize', 12); hold on; % Plot magnitude only lower frequenc xlabel('Frequency (Hz), 'FontSize', 14); ylabel('X(f) l', 'FontSize', 14); % Calculate fft using basic equations for m = 1:20 a(m) = (2/N)*sum(x.*(cos(2*pi*m*t))); $ Eq 3.11 b(m) = (2/N)*Sum(x.*(sin(2*pi*m*t))); % Eq. 3.12 C(m) = sqrt(a(m).^2 + b(m).^2); $ Eq. 3.9 theta(m) = (360/(2*pi)) * atan2 (b(m), a(m)); % Eq. 3.10 end disp([a(1:4)' 6(1:4)' C(1:4)' Mag(1:4)' theta(1:4)' Phase(1:4)']) plot(f(1:20), C(1:20), 'sk', 'MarkerSize', 10); % Plot sumperimposed

So I am being asked to isolate the first 8 components so that only those first 8 components of the half triangle function are calculated by MATLAB fft function, and then afterwards I am asked to do the same thing but with the first 20 components rather than the first 8. How do I isolate the first x number of components so that only those are calculated by the MATLAB fft routine?? And can you show me the codes for #1-2 and #1-3 so that I can see this pattern, and can you explain HOW you do it so that I understand?? Im a beginner to coding so this is very hard for me.

Answer 1

Explanation:

Code:

clc;
clear all;
close all;
T = 1; % Total time
fs = 256; % Assumed Sample Frequency
N = fs*T; % Calculate Number of points
t = (1:N)*T/N; % Generate Time vector
f = (1:N)*fs/N; % Frequency vector for plotting
x = [t(1:N/2) zeros(1,N/2)]; % Generate the signal
figure,
plot(t,x);
Xf = fft(x); % Take Fourier Transform, scale
Mag = abs(Xf(2:end))/(N/2); % and remove first point (DC value)
Phase = -angle(Xf(2:end))*(360/(2*pi));
figure,
plot(f(1:8),Mag(1:8),'.k','MarkerSize',6); hold on;
xlabel('Frequency (Hz)','FontSize',14);
ylabel('|X(f)|','FontSize',14);
title('First 8 point Magnitude');
figure,
plot(f(1:8),Phase(1:8),'.k','MarkerSize',6); hold on;
xlabel('Frequency (Hz)','FontSize',14);
ylabel('Phase of X(f)','FontSize',14);
title('First 8 Point Phase');
figure,
plot(f(1:20),Mag(1:20),'.k','MarkerSize',12); hold on; % Plot magnitude only lower frequencies
xlabel('Frequency (Hz)','FontSize',14);
ylabel('|X(f)|','FontSize',14);
title('First 20 Point Magnitude');
figure,
plot(f(1:20),Phase(1:20),'.k','MarkerSize',12); hold on;
xlabel('Frequency (Hz)','FontSize',14);
ylabel('Phase of X(f)','FontSize',14);
title('First 20 Point Phase');

SCREENSHOT OF THE CODE:

1 4 5 6 7 8 9 10 11 12 15 16 17 clc; clear all; close all; T = 1; % Total time fs = 256; % Assumed Sample Frequency N = fs T; % Calculate Number of points t = (1:N) *T/N; % Generate Time vector f = (1:N) fs/N; % Frequency vector for plotting x = [t(1:N/2) zeros(1,N/2)]; % Generate the signal figure, plot(t, x); % XF = fft(x); % Take Fourier Transform, scale Mag = abs(XF(2:end))/(N/2); % and remove first point (DC value) Phase = -angle (XF(2:end))*(360/(2*pi)); figure, plot(F(1:8), Mag(1:8),'.k', 'MarkerSize', 6); hold on; xlabel('Frequency (Hz)', 'FontSize', 14); ylabel('|X(F)|', 'FontSize', 14); title('First 8 point Magnitude'); figure, plot(F(1:8), Phase(1:8),'.', 'MarkerSize',6); hold on; xlabel('Frequency (Hz)', 'FontSize', 14); ylabel('Phase of X(f)', 'FontSize', 14); title('First 8 Point Phase'); figure, plot(F(1:20), Mag(1:20),'.k', 'MarkerSize',12); hold on; % Plot magnitude only lower frequencies xlabel('Frequency (Hz)', 'FontSize', 14); ylabel('X(f)l', 'FontSize', 14); title('First 20 Point Phase'); figure, plot(f(1:20), Phase(1:20),'.k', 'MarkerSize', 12); hold on; xlabel('Frequency (Hz)', 'FontSize', 14); ylabel('Phase of X(f)', 'FontSize', 14); title('First 20 Point Phase'); 19 23 24 26 30 31 32 33 34 35

OUTPUT:

0.5 0.4 0.3

For the first 8 Point Magnitude:

First 8 point Magnitude 0.25 TTTTTT 0.15 X(f) 0.1 - 0.05 Frequency (Hz)

For the First 8 point Phase:

First 8 Point Phase Phase of X(f) Frequency (Hz)

For the First 20 Magnitude:

First 20 Point Magnitude 0.15 |(3)x 0.1 0.05 Frequency (Hz)

For the First 20 point Phase:

First 20 Point Phase Phase of X(f) . 79 Frequency (Hz)

Thank you.