Return to Answer

Real sinusoids can't in reality.

A full answer would take an entire text book but the basic answer is:

In signal processing, signals are often discussed as a sum of complex sinusoids (\$e^{j\omega t}\$) because it's mathematically convenient.

This leads to Euler's formula:

\$e^{j\omega t} = \cos(wt) + j \cdot \sin(\omega t)\$

Which leads to its inverse:

\$\cos(\omega t) = \frac{1}{2} \cdot (e^{j\omega t} + e^{-j\omega t})\$

Which implies that both positive and negative frequency complex sinusoids are present, which is where it pops up in signal processing discussion.

It can't in reality.

A full answer would take an entire text book but the basic answer is:

In signal processing signals are often discussed as a sum of complex sinusoids (\$e^{j\omega t}\$) because its mathematically convenient.

This leads to Euler's formula:

\$e^{j\omega t} = cos(wt) + j \cdot sin(\omega t)\$

Which leads to its inverse:

\$cos(\omega t) = \frac{1}{2} \cdot (e^{j\omega t} + e^{-j\omega t})\$

Which implies that both positive and negative frequency is present which is where it pops up in signal processing discussion.

It can't in reality.

A full answer would take an entire text book but the basic answer is:

In signal processing signals are often discussed as a sum of complex sinusoids (\$e^{j\omega t}\$) because its mathematically convenient.

This leads to Euler's formula:

\$e^{j\omega t} = cos(wt) + j \cdot sin(\omega t)\$

Which leads to its inverse:

\$cos(\omega t) = \frac{1}{2} \cdot (e^{j\omega t} + e^{-j\omega t})\$

Which implies that both positive and negative frequency is present which is where it pops up in signal processing discussion.

Real sinusoids can't in reality.

A full answer would take an entire text book but the basic answer is:

In signal processing, signals are often discussed as a sum of complex sinusoids (\$e^{j\omega t}\$) because it's mathematically convenient.

This leads to Euler's formula:

\$e^{j\omega t} = \cos(wt) + j \cdot \sin(\omega t)\$

Which leads to its inverse:

\$\cos(\omega t) = \frac{1}{2} \cdot (e^{j\omega t} + e^{-j\omega t})\$

Which implies that both positive and negative frequency complex sinusoids are present, which is where it pops up in signal processing discussion.

It can't in reality.

A full answer would take an entire text book but the basic answer is:

In signal processing signals are often discussed as a sum of complex sinusoids (\$e^{j\omega t}\$) because its mathematically convenient.

This leads to Euler's formula:

\$e^{j\omega t} = cos(wt) + j*sin(\omega t)\$

Which leads to its inverse:

\$cos(\omega t) = \frac{1}{2} * (e^{j\omega t} + e^{-j\omega t})\$

Which implies that both positive and negative frequency is present which is where it pops up in signal processing discussion.

It can't in reality.

A full answer would take an entire text book but the basic answer is:

In signal processing signals are often discussed as a sum of complex sinusoids (\$e^{j\omega t}\$) because its mathematically convenient.

This leads to Euler's formula:

\$e^{j\omega t} = cos(wt) + j \cdot sin(\omega t)\$

Which leads to its inverse:

\$cos(\omega t) = \frac{1}{2} \cdot (e^{j\omega t} + e^{-j\omega t})\$

Which implies that both positive and negative frequency is present which is where it pops up in signal processing discussion.