What is the physical interpretation of the absolute value of a fourier transformed signal, $\left| F(t)\right|$?

1. What is the absolute value of Fourier transform?
2. What is the physical interpretation of Fourier transform?
3. Why do we use absolute value of FFT?
4. What is the significance of the Fourier transform in signal analysis?

What is the absolute value of Fourier transform?

For each frequency, the magnitude (absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that frequency, and the argument of the complex value represents that complex sinusoid's phase offset. If a frequency is not present, the transform has a value of 0 for that frequency.

What is the physical interpretation of Fourier transform?

The role of the Fourier transform in physics is as a bi-directional one-to-one mapping between conjugate variables. The most famous example of a conjugate variable pair is position/momentum, but there are many others. Some examples of conjugate variable pairs: position and momentum over Planck's constant [x,p/ℏ]

Why do we use absolute value of FFT?

Absolute value is useful if you want to know exact value(say 5V) of a certain sinusoid. In case you want to just compare spectrum components you might display the output in dB. 2) I suppose you talk about real FFT. If you compute FFT for a complex set of input values there is no symmetry.

What is the significance of the Fourier transform in signal analysis?

The Fourier transform is a mathematical formula that transforms a signal sampled in time or space to the same signal sampled in temporal or spatial frequency. In signal processing, the Fourier transform can reveal important characteristics of a signal, namely, its frequency components.