Fourier series of $cos(\omega_0 t)$ in continuous time

1. How do you find the continuous time of a Fourier transform?
2. Can continuous time Fourier series?
3. What is the Fourier transform of Coswt?
4. What is the Fourier transform of COSX?

How do you find the continuous time of a Fourier transform?

Continuous time Fourier transform of x(t) is defined as X(ω)=∫−∞+∞x(t)e−jωtdt and discrete time Fourier transform of x(n) is defined as X(ω)=Σ∀nx(n)e−ωn.

Can continuous time Fourier series?

The continuous-time Fourier series expresses a periodic signal as a lin- ear combination of harmonically related complex exponentials. Alternatively, it can be expressed in the form of a linear combination of sines and cosines or sinusoids of different phase angles.

What is the Fourier transform of Coswt?

Therefore, the Fourier transform of cosine wave function is, F[cosω0t]=π[δ(ω−ω0)+δ(ω+ω0)]

What is the Fourier transform of COSX?

The Fourier Transform of the Sine and Cosine Functions

Equation [2] states that the fourier transform of the cosine function of frequency A is an impulse at f=A and f=-A. That is, all the energy of a sinusoidal function of frequency A is entirely localized at the frequencies given by |f|=A.