Contents
What does imaginary part mean?
the imaginary part represents the frequency (and also phase some times) of the wave. Wave has two parts amplitude and frequency, so we need two numbers to represent it. We always manipulate the amplitude of the wave, not the frequency. The real part represents the amplitude of the wave.
Can Fourier coefficients be imaginary?
A real-valued Fourier expansion amounts to an expansion in terms of only cosines, which is the simplest example of an even signal. Therefore, the Fourier coefficients are purely imaginary.
Why are complex numbers used in Fourier transform?
Since Fourier Transforms are used to analyze real-world signals, why is it useful to have complex (or imaginary) numbers involved at all? It turns out the complex form of the equations makes things a lot simpler and more elegant. As such, everyone uses complex numbers, from physicists, to engineers, and mathematicians.
What is 5i equal to?
The imaginary number i is equal to the square root of -1. In other words, i2 equals -1. The square root of a negative number is not a real number and it is not a variable. For example, the square root of -25 is written as 5i because 5i times 5i equals 25 times -1 or -25.
What are pure imaginary numbers?
: a complex number that is solely the product of a real number other than zero and the imaginary unit.
When does the imaginary part of a Fourier transform vanish?
This is a Fourier sine transform. Thus the imaginary part vanishes only if the function has nosine components which happens if and only if the function is even. For an odd function, theFourier transform is purely imaginary. For a general real function, the Fourier transform willhave both real and imaginary parts. We can write
Is the Fourier transform of an integrable function continuous?
The Fourier transform of an integrable function is continuous and the restriction of this function to any set is defined. But for a square-integrable function the Fourier transform could be a general class of square integrable functions.
What is the multiplication factor of a Fourier transform?
Fourier transform of a system is its transfer function and gives the multiplication factor when e j ω t is the input. ω is frequency. If you consider the input as current, the transfer function or Fourier transform as impedance then the output is potential.
Where is the delayed unit pulse in the Fourier transform?
In the second row is shown g(t), a delayed unit pulse, beside the real and imaginary parts of the Fourier transform. The Fourier transform decomposes a function into eigenfunctions for the group of translations.