Need help writing a code with a summation divided by a summation

Hi. I've been stuck trying to write a code that would take values from two arrays I created, applying them to an equation, and then plotting the frequency respose of it.

Below is the equation I'm trying to execute and plot:

Current code:

%Arrays a and b that were created:
a = [0.001, -0.014, 0.098, -0.424, 1.29, -2.96, 5.25, -7.35, 8.21, -7.3513, 5.25, -2.96, 1.297, -0.424, 0.098, -0.014, 0.001];
b = [1, -10.780, 55.31, -179.24, 410.38, -703.78, 934.93, -981.27, 822.29, -551.96, 295.81, -125.25, 41.08, -10.09, 1.75, -0.192, 0.01];

N = 2048; %samples
w = linspace(-pi,pi,N)
k = 0:16;
H = 0;

for ii = 1:length(a)
    
Ha = H + sum(ii.*exp(j.*w).^(16-k)); %Numerator
end
   for jj = 1:length(b)
      Hb = H + sum(jj.*exp(j.*w).^(16-k)); %Denominator
   end
H_ejw = Ha./Hb; 

plot(w,abs(H_ejw));
title('Magnitude Response')

I keep getting the error "Arrays have incompatible sizes for this operation." I'm wondering if it's due to w?

Thank you

Answer 1

[Awais Saeed]

I do not know what graph are you expecting but your loops are for sure not storing any values. You have to store the computed values and then take sum of those. I still do not know if you want to sum rows or coloums. I am suming rows though. You can change it if you want to sum columns.

%Arrays a and b that were created:
a = [0.001, -0.014, 0.098, -0.424, 1.29, -2.96, 5.25, -7.35, 8.21, -7.3513, 5.25, -2.96, 1.297, -0.424, 0.098, -0.014, 0.001];
b = [1, -10.780, 55.31, -179.24, 410.38, -703.78, 934.93, -981.27, 822.29, -551.96, 295.81, -125.25, 41.08, -10.09, 1.75, -0.192, 0.01];
N = 2048; %samples
w = linspace(-pi,pi,N);
k = 0:16;
H = 0;
Ha = [];
for ii = 1:length(a)
    Ha(ii,:) = H + a(ii).*(exp(j.*w)).^(16-k(ii)); % Numerator
    Hb(ii,:) = H + b(ii).*(exp(j.*w)).^(16-k(ii)); % Denominator
end
% sizes before summation
size(Ha)

ans = 1×2

17 2048

size(Hb)

ans = 1×2

17 2048

% sizes after summation
Ha = sum(Ha,1);
Hb = sum(Hb,1);
size(Hb)

ans = 1×2

1 2048

size(Ha)

ans = 1×2

1 2048

H_ejw = Ha./Hb; 
plot(w,abs(H_ejw));
title('Magnitude Response')

[AJ]

Awais, thanks for your help. I used your code and made some tweaks to get the plot I needed, and was able to find my mistakes.

My values for a and b were originally generated using a function that was given to me, but I didn't know how to correctly apply it to a for loop. I thought writing these values out long hand would've been fine, but after running it through, the plot wasn't correct. I ended up deleting my arrays, used the generated values for a and b, and then it gave me the correct plot.

[Awais Saeed]

I'm glad to be of help!

Answer 2

[Torsten]

a = [0.001, -0.014, 0.098, -0.424, 1.29, -2.96, 5.25, -7.35, 8.21, -7.3513, 5.25, -2.96, 1.297, -0.424, 0.098, -0.014, 0.001];
b = [1, -10.780, 55.31, -179.24, 410.38, -703.78, 934.93, -981.27, 822.29, -551.96, 295.81, -125.25, 41.08, -10.09, 1.75, -0.192, 0.01];
N = 2048;
w = linspace(-pi,pi,N);
Ha = zeros(N,1);
Hb = zeros(N,1);
for i = 1:N
    vec = (exp(j*w(i))).^(16-(0:16));
    Ha(i) = a*vec.';
    Hb(i) = b*vec.';
end
H = Ha./Hb
plot(w,abs(H));
title('Magnitude Response')