Is Fourier transform continuous or discrete?

Discrete Time Fourier Transform is for signals which are aperiodic and discrete in time domain. It’s periodic and continuous in frequency domain.

What is the Fourier transform of the continuous time signal?

Continuous time Fourier transform of x(t) is defined as X ( ω ) = ∫ − ∞ + ∞ x ( t ) e − j ω t d t and discrete time Fourier transform of x(n) is defined as X(ω)=Σ∀nx(n)e−ωn. Also, both the continuous time and discrete time Fourier transforms are defined in the frequency domain, which is a continuous domain.

What is a finite duration signal?

Finite vs. Infinite Duration Signals A discrete signal x[n] is finite duration if there exists two integers -∞ < N1 ≤ N2 < ∞, such that x[n] ≠ 0 only for N1 ≤ n ≤ N2. Otherwise, it is of infinite duration.

What is the difference between Fourier transform of continuous signal and the Fourier transform of the discrete-time signal?

The difference is pretty quickly explained: the CTFT is for continuous-time signals, i.e., for functions x(t) with a continuous variable t∈R, whereas the DTFT is for discrete-time signals, i.e., for sequences x[n] with n∈Z.

What is continuous time Fourier series?

The continuous-time Fourier series expresses a periodic signal as a lin- ear combination of harmonically related complex exponentials. The Fourier series for periodic signals also provides the key to represent- ing aperiodic signals through a linear combination of complex exponentials.

Is continuous time Fourier transform periodic?

Fourier Transform Summary The continuous time Fourier series synthesis formula expresses a continuous time, periodic function as the sum of continuous time, discrete frequency complex exponentials. The continuous time Fourier series analysis formula gives the coefficients of the Fourier series expansion.

What is the z-transform of the finite duration signal?

What is the ROC of z-transform of finite duration anti-causal sequence? Explanation: Let us an example of anti causal sequence whose z-transform will be in the form X(z)=1+z+z2 which has a finite value at all values of ‘z’ except at z=∞. So, ROC of an anti-causal sequence is entire z-plane except at z=∞.

Which signal is infinite signal?

Energy signal is a signal whose energy is finite and power is zero whereas Power signal is a signal whose power is finite and energy is infinite.

Can Fourier transform be used for continuous time?

Fourier Transforms for Continuous/Discrete Time/Frequency The Fourier transform can be defined for signals which are discrete or continuous in time, and finite or infinite in duration. This results in four cases. As you might expect, the frequency domain has the same cases: discrete or continuous in frequency, and

What is the difference between the Fourier transform of discrete and periodic?

The Fourier Transform of the discrete signals also repeats with the fundamental frequency, the only difference being that the DTFT is continuous where the DTFS spectrum is discrete. CTFT of an aperiodic signal aperiodic and continuous CTFT of a periodic signal discrete and periodic.

Is the Fourier transform real or imaginary?

Fourier transform is purely imaginary. For a general real function, the Fourier transform will have both real and imaginary parts. We can write f˜(k)=f˜c(k)+if˜ s(k) (18) where f˜ s(k) is the Fourier sine transform and f˜c(k) the Fourier cosine transform. One hardly ever uses Fourier sine and cosine transforms.

What is the relation between sinusoids and Fourier series?

One way to think of how they relate: Fourier series can represent any “reasonable” periodic function as a sum of sinusoids. Each sinusoid in the series is defined so that the number of cycles in the period of the function it represents is an integer.