Sine function produces unexpected results

Good morning community,

I've got some troubles using the MATLAB sine function ( sin() ) and I hope somebody can help me to solve this wrong line of thought :)

However, let me describe the issue I'm troubling with. I'm trying to give the sine function a time vector and a frequency to calculate the amplitude as follow:

omega = pi; % define frequency

t = 0:.1:1; % define time vec

A = sin(1i*omega.*t)

The result I get from this operation is the following:

The strange thing and what I really don't understand is, why I do get the correct result, if I'm not using a variable for t but typing the vector definition directly in the function call command as you can see bellow:

Even if I leave off the complex number in the first case, I'm not getting the result I expect, however this shouldn't change anything.

So, I hope there is somebody, who has an idea why it behaves like this. I would be very thankful.

Best regards.

Answer 1

[Stephan]

Hi,

note:

>> t = 0:0.1:1

t =

  Columns 1 through 8

         0    0.1000    0.2000    0.3000    0.4000    0.5000    0.6000    0.7000

  Columns 9 through 11

    0.8000    0.9000    1.0000

>> pi .* t

ans =

  Columns 1 through 8

         0    0.3142    0.6283    0.9425    1.2566    1.5708    1.8850    2.1991

  Columns 9 through 11

    2.5133    2.8274    3.1416

But now:

>> pi .* 0:0.1:1

ans =

  Columns 1 through 8

         0    0.1000    0.2000    0.3000    0.4000    0.5000    0.6000    0.7000

  Columns 9 through 11

    0.8000    0.9000    1.0000

Using brackets makes things going to be correct:

>> pi .* (0:0.1:1)

ans =

  Columns 1 through 8

         0    0.3142    0.6283    0.9425    1.2566    1.5708    1.8850    2.1991

  Columns 9 through 11

    2.5133    2.8274    3.1416

Answer 2

[Joachim Wagner]

All right, that's true. Thank you very much, that fits it for the moment but can maybe still someone explain, why I get those complex numbers in the first case? I don't really get it.

[Star Strider]

‘The strange thing and what I really don't understand is, why I do get the correct result, if I'm not using a variable for t but typing the vector definition directly in the function call command ...’

Not really strange. It relates to the way MATLAB defined the two vectors in:

omega = pi; % define frequency
t = 0:.1:1; % define time vec
A = sin(1i*omega.*t)

and:

A = sin(1i*omega*0:.1:1)

In the first one, the imaginary operator 1i multiplies the entire vector ‘t’. In the second one, 1i multiplies only the first element of the vector, here 0 (so the first element remains 0 and is not complex) and none of the others.

The second is equivalent to the first if you put parentheses around the vector:

A = sin(1i*omega*(0:.1:1))

[John D'Errico]

It is an order of operators thing. The colon operator is quite low on the totem pole, so other operations are done first.

That means while you might expect that this operation

1 + 0:5

will add 1 to each element of the vector 0:5, in fact, it adds 1 to 0, then uses that as the first operand of colon. So we see this:

1 + 0:5
ans =
     1     2     3     4     5

The same applies to what you did.

Answer 3

[Joachim Wagner]

Right perfect, it now becomes clear. Thanks a lot to all of you!