Symmetry property of fourier transform

1. What is symmetry property of Fourier transform?
2. What is symmetry in Fourier series?
3. Is A Fourier transform Symmetric?
4. What are the properties of Fourier transform?

What is symmetry property of Fourier transform?

Symmetry Properties

Represent x(t) as the sum of an even function and an odd function (recall that any function can be represented as the sum of an even part and an odd part). x(t)=xo(t)+xe(t) Express the Fourier Transform of x(t), substitute the above expression and use Euler's identity for the complex exponential.

What is symmetry in Fourier series?

The symmetry which is hidden by the DC component is known as hidden symmetry. This symmetry can be obtained by removing the offset (adding or subtracting the DC). If x(t) has some hidden symmetry, then its Fourier series contains DC and sine or DC and cosine terms depending upon the symmetry.

Is A Fourier transform Symmetric?

When we take the the Fourier Transform of a real function, for example a one-dimensional sound signal or a two-dimensional image we obtain a complex Fourier Transform. This Fourier Transform has special symmetry properties that are essential when calculating and/or manip- ulating Fourier Transforms.

What are the properties of Fourier transform?

The important properties of Fourier transform are duality, linear transform, modulation property, and Parseval's theorem.