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I want to create a matrix with the pattern below for N = 1000, i.e a 1000 X 2 matrix?

James Tursa
on 17 May 2021

Edited: James Tursa
on 17 May 2021

N = 1000;

a = 2 * pi * f * T * (0:N-1)';

x = [cos(a) -sin(a)];

Paul Hoffrichter
on 17 May 2021

Edited: Paul Hoffrichter
on 17 May 2021

Since you did not specify T and f, I assume you wanted symbolic notation. (I picked N = 10 to show a brief output.)

N=10;

n = 0:N-1;

syms T f

vec1 = cos(2*pi*f*n/T).';

vec2 = -sin(2*pi*f*n/T).';

X = [vec1 vec2]

Output (on R2020a):

X =

[ 1, 0]

[ cos((2*pi*f)/T), -sin((2*pi*f)/T)]

[ cos((4*pi*f)/T), -sin((4*pi*f)/T)]

[ cos((6*pi*f)/T), -sin((6*pi*f)/T)]

[ cos((8*pi*f)/T), -sin((8*pi*f)/T)]

[ cos((10*pi*f)/T), -sin((10*pi*f)/T)]

[ cos((12*pi*f)/T), -sin((12*pi*f)/T)]

[ cos((14*pi*f)/T), -sin((14*pi*f)/T)]

[ cos((16*pi*f)/T), -sin((16*pi*f)/T)]

[ cos((18*pi*f)/T), -sin((18*pi*f)/T)]

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