how can i multiply two large arrays of different sizes?

I'm trying to figure out how to get a value for k when I have two variables w and t that are of different sizes.

sigma = 0               %can set sigma to any positive integer number but choosing 0 to simplify things for now

w = (0:2*pi:30000*pi)   % required parameters

z = sigma + 1i.*w       %gives me a complex array of 1x15001 using the values of w above.

dt=1/44000;             %my sample rate is 44000

t = 0:dt:2              %gives me an array of 1x88001 

k = exp(-z.*t);         %this is where my problem comes in because i can't multiply two arrays of different sizes

Answer 1

[Chunru]

sigma = 0               %can set sigma to any positive integer number but choosing 0 to simplify things for now

sigma = 0

w = (0:2*pi:10*pi)   % required parameters (small value for illustration)

w = 1×6

0 6.2832 12.5664 18.8496 25.1327 31.4159

z = sigma + 1i.*w       %gives me a complex array of 1x15001 using the values of w above.

z = 
   0.0000 + 0.0000i   0.0000 + 6.2832i   0.0000 +12.5664i   0.0000 +18.8496i   0.0000 +25.1327i   0.0000 +31.4159i

dt=1/44000;             %my sample rate is 44000
t = 0:dt:4*dt;              %gives me an array of 1x88001  (smaller size)

t = 1×5

1.0e+-4 * 0 0.2273 0.4545 0.6818 0.9091

% k is a matrix k(i_z, i_t).  I guess this is what you want
k = exp(-z.'*t)

k = 
   1.0000 + 0.0000i   1.0000 + 0.0000i   1.0000 + 0.0000i   1.0000 + 0.0000i   1.0000 + 0.0000i
   1.0000 + 0.0000i   1.0000 - 0.0001i   1.0000 - 0.0003i   1.0000 - 0.0004i   1.0000 - 0.0006i
   1.0000 + 0.0000i   1.0000 - 0.0003i   1.0000 - 0.0006i   1.0000 - 0.0009i   1.0000 - 0.0011i
   1.0000 + 0.0000i   1.0000 - 0.0004i   1.0000 - 0.0009i   1.0000 - 0.0013i   1.0000 - 0.0017i
   1.0000 + 0.0000i   1.0000 - 0.0006i   1.0000 - 0.0011i   1.0000 - 0.0017i   1.0000 - 0.0023i
   1.0000 + 0.0000i   1.0000 - 0.0007i   1.0000 - 0.0014i   1.0000 - 0.0021i   1.0000 - 0.0029i