Why is fft symmetric

1. Why are FFTs symmetrical?
2. Is A Fourier transform Symmetric?
3. Why is DFT symmetric?
4. Why is FFT two sided?

Why are FFTs symmetrical?

Because both the positive and negative frequency sinusoids are 90 degrees out of phase and have the same magnitude, they will both respond to real signals in the same way.

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.

Why is DFT symmetric?

And without going into mathematical details, DFT of real valued function is symmetric, i.e. resultant Fourier function has both real and imaginary parts which are mirror images with respect to 0 frequency component.

Why is FFT two sided?

The two-sided results from the analysis functions include the positive half of the spectrum followed by the negative half of the spectrum, as shown in Figure 1. is the root mean square (rms) amplitude of the sinusoidal component at frequency k.