why cant we use fourier series for non periodic signals?

Any signal in this world can be represented in terms of sine and cosine ...right? why cant we use fourier series for non periodic singals also? why is there fourier transform? what was the need for dtft and then why is dft needed?

Answer 1

[Mathieu NOE]

Any repetitive signal in this world can be represented in terms of sine and cosine

that 's the key point

[amuka anurag]

non peroidic signals are also repititive but their period is indefinite .. it means we dont exactly know at what point of time do they repeat themselves.. so can we use sinusoids for non periodic signals also?

[Walter Roberson]

There are signals that are provably not periodic, assuming infinite continuous space and time. Not just indefinitely. periodic.

Answer 2

[Walter Roberson]

You can use fourier series for non-periodic sequences. For example you can use fourier series for y=x.

However, non-periodic signals need infinite series of coefficients.

It is common for fourier series to require infinite series of coefficients, even for periodic signals. For example the square wave requires infinite series. Every signal that includes a straight line segment needs an infinite series. Every spike impulse requires an infinite series of coefficients.

Please remember the difference between fourier series (commonly infinite series of coefficients, but sometimes finite) and fast fourier transform, which has to do with discrete finite sequences.