Arrays have incompatible sizes for this operation

my objective is to plot the FRF transform using method of partial sums

%Initialize Parameters 
x0=1; %peak amplitude 
t0=2; %period (sec)
k=-20:1:20; %range for index k
w0= 2*pi/t0; %frequency in
t= 0:0.001:5; %time range 
nk=length(k);
j= 1i;


%Loop for coefficients 
ck = [];
for i=1:length(k)
    if k(i)~=0
        ck=[ck ,(t*x0/t0).*(sin((t*k(i)*w0)/2) / (t*k(i)*w0)/2)];
    end 
    if k(i)==0
        ck=[ck , (t*x0) / t0];
    end 
end 

%Partial Sum for Sawtooth Wave 
x_t=[];
for n=1:length(t)
    x_t = [x_t, sum(ck.* exp(j*k*w0*t(n)))];
end

Arrays have incompatible sizes for this operation.

%plot of coefficients
subplot(1,2,1)
stem(k,abs(ck))
title('Rectangular Coefficients (Bohlen)')
xlabel('k index value')
ylabel('Magnitude of ck')
grid on


%plot of partial sum
subplot(1,2,2)
plot(t,x_t)
title('Rectangular Wave for -20<k<20 (Bohlen)')
xlabel('Time (sec)')
ylabel('Amplitude of Full Wave Rectified')
grid on

Arrays have incompatible sizes for this operation.

Error in Rectangular_HW3 (line 29)

x_t = [x_t, sum(ck.* exp(j*k*w0*t(n)))];

>> whos

Name Size Bytes Class Attributes

ck 1x205041 1640328 double

i 1x1 8 double

j 1x1 16 double complex

k 1x41 328 double

n 1x1 8 double

nk 1x1 8 double

t 1x5001 40008 double

t0 1x1 8 double

w0 1x1 8 double

x0 1x1 8 double

x_t 0x0 0 double

Answer 1

[Shivam]

Hi Peter,

The error you're encountering is due to incompatible array sizes in the calculation of the partial sum for the sawtooth wave. Specifically, the issue arises from how ck is being constructed and subsequently used in the partial sum calculation.

You can use the modified code which correctly constructs the ck and calculates the partial sum.

% Initialize Parameters 
% .
% ..

nk = length(k);
j = 1i;

% Loop for coefficients. Initialize ck as a vector of zeros
ck = zeros(size(k)); 
for i = 1:nk
    if k(i) ~= 0
        ck(i) = (x0/t0) * (sin(k(i)*w0*t0/2) / (k(i)*w0*t0/2));
    else
        ck(i) = x0 / t0;
    end 
end 

% Partial Sum for Sawtooth Wave. Initialize x_t as a vector of zeros
x_t = zeros(size(t)); 
for n = 1:length(t)
    x_t(n) = sum(ck .* exp(j*k*w0*t(n)));
end

% Plot of coefficients
subplot(1,2,1)
stem(k, abs(ck))
title('Rectangular Coefficients (Bohlen)')
xlabel('k index value')
ylabel('Magnitude of ck')
grid on

% Plot of partial sum
subplot(1,2,2)
plot(t, x_t)

Warning: Imaginary parts of complex X and/or Y arguments ignored.

title('Rectangular Wave for -20<k<20 (Bohlen)')
xlabel('Time (sec)')
ylabel('Amplitude of Full Wave Rectified')
grid on

●

[Walter Roberson]

Plotting the imaginary part separately

%Initialize Parameters 
x0=1; %peak amplitude 
t0=2; %period (sec)
k=-20:1:20; %range for index k
w0= 2*pi/t0; %frequency in
t= 0:0.001:5; %time range 

nk = length(k);
j = 1i;

% Loop for coefficients. Initialize ck as a vector of zeros
ck = zeros(size(k)); 
for i = 1:nk
    if k(i) ~= 0
        ck(i) = (x0/t0) * (sin(k(i)*w0*t0/2) / (k(i)*w0*t0/2));
    else
        ck(i) = x0 / t0;
    end 
end 

% Partial Sum for Sawtooth Wave. Initialize x_t as a vector of zeros
x_t = zeros(size(t)); 
for n = 1:length(t)
    x_t(n) = sum(ck .* exp(j*k*w0*t(n)));
end

% Plot of coefficients
subplot(2,2,1)
stem(k, abs(ck))
title('Rectangular Coefficients (Bohlen)')
xlabel('k index value')
ylabel('Magnitude of ck')
grid on

% Plot of partial sum
subplot(2,2,3)
plot(t, real(x_t), 'b')
title('Rectangular Wave for -20<k<20 (Bohlen)')
xlabel('Time (sec)')
ylabel('Amplitude of Full Wave Rectified')
grid on
subplot(2,2,4)
plot(t, imag(x_t), 'r')
title('Imaginary Rectangular Wave for -20<k<20 (Bohlen)')
xlabel('Time (sec)')
ylabel('Amplitude of Full Wave Rectified')
grid on

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