Ofcourse x(2(t-3))=x(2t-6), but my question is in terms of operations on signals. In what order does the shifting and scaling happens in the case of x(2(t-3)) and how is it different from the ones that happens with x(2t-3). And is this different in terms of systems ?
In my head I always have the image of x(2(t-3)) as shift three units and then scale . But I am just confused with the signals and systems jargon .
Thank you in advance
All is about the order of operations and nothing more. Consider operation 1 to be shifting 3 units to right and operation 2 to be compressing the signal by a factor of 2.
Signal $x(2t-3)$ is first shifted 3 units to right and then the result is compressed by a factor of 2.
Signal $x(2(t-3))$ is first compressed by a factor of 2 and then the result is shifted 3 units to right.