I'll use this thread to ask other math realted questions such as:
I have a property, in the context of Fourier Transform properties that says:
\(\delta \left ( a\cdot t \right ) = \frac{1}{a}\cdot \delta \left ( t \right )\)
and I need to apply it to the following expresison:
\(\delta \left ( \frac{\omega }{2} -1\right )\)
I say the result should be:
\(\begin{matrix} 1\rightarrow \delta \left ( \frac{\omega }{2} -1\right )\\ \\ 2\rightarrow \delta \left ( \frac{1}{2} \cdot \left ( \omega -2 \right )\right )\\ \\ 3\rightarrow 2\cdot \delta \left ( \omega -2 \right ) \end{matrix}
\)
where at:
\(2\)
I consider my 'a' to be:
\(\frac{1}{2}\)
and my 't' to be
\(\omega - 2\)
after looking to the left side of the property stated at the beginning.
My teacher wrote in the whiteboard that the result is:
\(\frac{1}{2}\delta \left ( \omega -2\right )\)
Am I wrong?
I have a property, in the context of Fourier Transform properties that says:
\(\delta \left ( a\cdot t \right ) = \frac{1}{a}\cdot \delta \left ( t \right )\)
and I need to apply it to the following expresison:
\(\delta \left ( \frac{\omega }{2} -1\right )\)
I say the result should be:
\(\begin{matrix} 1\rightarrow \delta \left ( \frac{\omega }{2} -1\right )\\ \\ 2\rightarrow \delta \left ( \frac{1}{2} \cdot \left ( \omega -2 \right )\right )\\ \\ 3\rightarrow 2\cdot \delta \left ( \omega -2 \right ) \end{matrix}
\)
where at:
\(2\)
I consider my 'a' to be:
\(\frac{1}{2}\)
and my 't' to be
\(\omega - 2\)
after looking to the left side of the property stated at the beginning.
My teacher wrote in the whiteboard that the result is:
\(\frac{1}{2}\delta \left ( \omega -2\right )\)
Am I wrong?