(MATLAB)I have question about finding the (rmse)Root-mean-square deviation value
ID: 3759829 • Letter: #
Question
(MATLAB)I have question about finding the (rmse)Root-mean-square deviation value in this code. could you please help me how to find it for all value on n=(2,10,20,50,100) at the same graph and show me how does the graph look like ..Thank you
clc
clear all
close all
syms t k L n
evalin (symengine, 'k,type::integer');
a= @(f,t,k,L) int(f*cos(k*pi*t/L)/L,t,-L,L);
b=@(f,t,k,L) int(f*sin(k*pi*t/L)/L,t,-L,L);
fs=@(f,t,n,L) a(f,t,0,L)/2+symsum (a(f,t,k,L)*cos(k*pi*t/L)+b(f,t,k,L)*sin(k*pi*t/L),k,1,n);
f=heaviside(t);
g=inline(vectorize(fs(f,t,2,1)));
h=inline(vectorize(f));
X=-1:.001:1;
subplot(3,2,1),plot(X,g(X),'r'),xlabel('Time(s)'),ylabel('Amplitude'),title('Time Shifting');
hold on
plot(X,h(X))
hold off
title('partial sum with n=2')
g=inline(vectorize(fs(f,t,2,1)));
h=inline(vectorize(f));
X=-1:.001:1;
subplot(3,2,1),plot(X,g(X),'r'),xlabel('Time(s)'),ylabel('Amplitude'),title('Time Shifting');
hold on
plot(X,h(X))
hold off
title('partial sum with n=2')
g=inline(vectorize(fs(f,t,10,1)));
h=inline(vectorize(f));
X=-1:.001:1;
subplot(3,2,2),plot(X,g(X),'r'),xlabel('Time(s)'),ylabel('Amplitude'),title('Time Shifting');
hold on
plot(X,h(X))
hold off
title('partial sum with n=10')
g=inline(vectorize(fs(f,t,20,1)));
h=inline(vectorize(f));
X=-1:.001:1;
subplot(3,2,3),plot(X,g(X),'r'),xlabel('Time(s)'),ylabel('Amplitude'),title('Time Shifting');
hold on
plot(X,h(X))
hold off
title('partial sum with n=20')
g=inline(vectorize(fs(f,t,50,1)));
h=inline(vectorize(f));
X=-1:.001:1;
subplot(3,2,4),plot(X,g(X),'r'),xlabel('Time(s)'),ylabel('Amplitude'),title('Time Shifting');
hold on
plot(X,h(X))
hold off
title('partial sum with n=50')
g=inline(vectorize(fs(f,t,100,1)));
h=inline(vectorize(f));
X=-1:.001:1;
subplot(3,2,5),plot(X,g(X),'r'),xlabel('Time(s)'),ylabel('Amplitude'),title('Time Shifting');
hold on
plot(X,h(X))
hold off
title('partial sum with n=100')
Explanation / Answer
syms t k L n
evalin (symengine, 'k,type::integer');
a= @(f,t,k,L) int(f*cos(k*pi*t/L)/L,t,-L,L);
b=@(f,t,k,L) int(f*sin(k*pi*t/L)/L,t,-L,L);
fs=@(f,t,n,L) a(f,t,0,L)/2+symsum (a(f,t,k,L)*cos(k*pi*t/L)+b(f,t,k,L)*sin(k*pi*t/L),k,1,n);
f=heaviside(t);
g=inline(vectorize(fs(f,t,2,1)));
h=inline(vectorize(f));
X=-1:.001:1;
subplot(3,2,1),plot(X,g(X),'r'),xlabel('Time(s)'),ylabel('Amplitude'),title('Time Shifting');
hold on
plot(X,h(X))
hold off
title('partial sum with n=2')
g=inline(vectorize(fs(f,t,2,1)));
h=inline(vectorize(f));
X=-1:.001:1;
subplot(3,2,1),plot(X,g(X),'r'),xlabel('Time(s)'),ylabel('Amplitude'),title('Time Shifting');
hold on
plot(X,h(X))
hold off
title('partial sum with n=2')
g=inline(vectorize(fs(f,t,10,1)));
h=inline(vectorize(f));
X=-1:.001:1;
subplot(3,2,2),plot(X,g(X),'r'),xlabel('Time(s)'),ylabel('Amplitude'),title('Time Shifting');
hold on
plot(X,h(X))
hold off
title('partial sum with n=10')
g=inline(vectorize(fs(f,t,20,1)));
h=inline(vectorize(f));
X=-1:.001:1;
subplot(3,2,3),plot(X,g(X),'r'),xlabel('Time(s)'),ylabel('Amplitude'),title('Time Shifting');
hold on
plot(X,h(X))
hold off
title('partial sum with n=20')
g=inline(vectorize(fs(f,t,50,1)));
h=inline(vectorize(f));
X=-1:.001:1;
subplot(3,2,4),plot(X,g(X),'r'),xlabel('Time(s)'),ylabel('Amplitude'),title('Time Shifting');
hold on
plot(X,h(X))
hold off
title('partial sum with n=50')
g=inline(vectorize(fs(f,t,100,1)));
h=inline(vectorize(f));
X=-1:.001:1;
subplot(3,2,5),plot(X,g(X),'r'),xlabel('Time(s)'),ylabel('Amplitude'),title('Time Shifting');
hold on
plot(X,h(X))
hold off
title('partial sum with n=100')
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