Howtosignalprocessing
- What is the Fourier transform of a Gaussian function?
- What is the Fourier transform of a Gaussian wave packet?
- Is the Fourier transform of a Gaussian pulse is also a Gaussian pulse?
- What is the Fourier transform of SGN function?
What is the Fourier transform of a Gaussian function?
Therefore, the Fourier transform of the Gaussian function is, F[e−at2]=√πa⋅e−(ω2/4a) Or, it can also be written as, e−at2FT↔√πa⋅e−(ω2/4a) The graphical representation of Gaussian function and its frequency spectrum is shown in Figure-1.
What is the Fourier transform of a Gaussian wave packet?
The Gaussian is called a wavepacket because of its Fourier transform: it is a packet of waves with frequencies/wavenumbers clustered around a single value kc (the subscript “c” is for “car- rier”, as we explain below). One of the most important applications of wavepackets is in communication.
Is the Fourier transform of a Gaussian pulse is also a Gaussian pulse?
The Fourier Transform of a Gaussian pulse preserves its shape. The above derivation makes use of the following result from complex analysis theory and the property of Gaussian function – total area under Gaussian function integrates to 1. Thus, the Fourier Transform of a Gaussian pulse is a Gaussian Pulse.
What is the Fourier transform of SGN function?
also sgn(t) = u(t) - u(-t) This signal is not absolutely integrable so we calculate Fourier Transform of sgn(t) as a limiting case of the sum of exponential e-atu(t) - eatu(t) as a → 0. x(t) = sgn(t) = e-atu(t) - eatu(t) Taking Fourier transform of the above equation: X ( ω ) = [ 1 a + j ω − 1 a − j ω ]
