What is Fourier transform and how is it different from Laplace transform?

Fourier transform is the special case of laplace transform which is evaluated keeping the real part zero. Fourier transform is generally used for analysis in frequency domain whereas laplace transform is generally used for analysis in s-domain(it’s not frequency domain).

What is a CTFT?

The Continuous-Time Fourier Transform (CTFT) is the version of the fourier transform that is most common, and is the only fourier transform so far discussed in EE wikibooks such as Signals and Systems, or Communication Systems.

What is the difference between Laplace and inverse Laplace?

A Laplace transform which is the sum of two separate terms has an inverse of the sum of the inverse transforms of each term considered separately. A Laplace transform which is a constant multiplied by a function has an inverse of the constant multiplied by the inverse of the function.

How do you calculate CTFT?

The Fourier analysis evaluates signals and systems in the frequency domain. 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.

What is the spectrum of rectangular pulse?

2.3. The Fourier transform of the rectangular pulse is real and its spectrum, a sinc function, is unbounded. This is equivalent to an upsampled pulse-train of upsampling factor L.

What is use of Laplace transform?

The Laplace transform is one of the most important tools used for solving ODEs and specifically, PDEs as it converts partial differentials to regular differentials as we have just seen. In general, the Laplace transform is used for applications in the time-domain for t ≥ 0.

What is the difference between FT and FS?

The Fourier series is used to represent a periodic function by a discrete sum of complex exponentials, while the Fourier transform is then used to represent a general, nonperiodic function by a continuous superposition or integral of complex exponentials.

Is CTFT continuous?

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.