Uniqueness of Fourier Series Representation and the Fourier Transform of Periodic Signals

1. What's the difference between Fourier series and Fourier transform?
2. How does the Fourier series and in the representation of periodic signals?
3. Why Fourier series is necessary in representing periodic signals?
4. Is Fourier series unique?

What's the difference between Fourier series and Fourier transform?

The difference between the Fourier transform and the Fourier series is that the Fourier transform is applicable for non-periodic signals, while the Fourier series is applicable to periodic signals.

How does the Fourier series and in the representation of periodic signals?

Fourier Series Representation of Continuous Time Periodic Signals. A signal is said to be periodic if it satisfies the condition x (t) = x (t + T) or x (n) = x (n + N). These two signals are periodic with period T=2π/ω0. Where ak= Fourier coefficient = coefficient of approximation.

Why Fourier series is necessary in representing periodic signals?

Fourier series is just a means to represent a periodic signal as an infinite sum of sine wave components. A periodic signal is just a signal that repeats its pattern at some period. The primary reason that we use Fourier series is that we can better analyze a signal in another domain rather in the original domain.

Is Fourier series unique?

for any n . So the Fourier series of f is unique.