Howtosignalprocessing
- Why do we need complex Fourier series?
- What is the absolute value of Fourier transform?
- What does the complex part of a Fourier transform mean?
- How do you find the absolute value of a complex signal?
Why do we need complex Fourier series?
The complex Fourier series obeys Parseval's Theorem, one of the most important results in signal analysis. This general mathematical result says you can calculate a signal's power in either the time domain or the frequency domain.
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 does the complex part of a Fourier transform mean?
The complex versions have a complex time domain signal and a complex frequency domain signal. The real versions have a real time domain signal and two real frequency domain signals. Both positive and negative frequencies are used in the complex cases, while only positive frequencies are used for the real transforms.
How do you find the absolute value of a complex signal?
For a complex number z = x + yi, we define the absolute value |z| as being the distance from z to 0 in the complex plane C. This will extend the definition of absolute value for real numbers, since the absolute value |x| of a real number x can be interpreted as the distance from x to 0 on the real number line.
