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Why is frequency a complex number?
3 Answers. Because the phase of different components affects the total signal. The two functions in the plot are both summed from sine waves with periods of pi and 2pi, but the phase of the p=2pi sine waves are different. As you can see, the outputs are not the same.
What is complex frequency?
Definition: A type of frequency that depends on two parameters ; one is the ” σ” which controls the magnitude of the signal and the other is “w”, which controls the rotation of the signal ; is known as “complex frequency”.
Can frequency be a complex number?
magnitude of the signal and the other is “w”, which controls the rotation of the signal ; is known as “complex frequency”.
What is the Laplace transform used for?
The Laplace transform is one of the most important tools used for solving ODEs and specifically, PDEs as it converts partial differentials to regular differentials as we have just seen. In general, the Laplace transform is used for applications in the time-domain for t ≥ 0.
Is there such thing as negative frequency?
If frequency is defined as an absolute number then there can be no negative frequencies, but if it is a real number negative frequencies can exist. You do need two signals to distinguish between positive and negative frequencies, the same as you need two numbers to define a complex number.
How to think of the complex frequency s?
the general complex frequency, s, can be thought of in terms of its real and imaginary parts: or in terms of its period and periodic decay rate: s = T-1ejα. The former is always the most appropriate way to use the complex frequency in a Laplace or Fourier transform, however the latter offers a bit more insight.
How to use the complex frequency in a Fourier transform?
the general complex frequency, s, can be thought of in terms of its real and imaginary parts: or in terms of its period and periodic decay rate: s = T -1e jα. The former is always the most appropriate way to use the complex frequency in a Laplace or Fourier transform, however the latter offers a bit more insight.
Why do you get complex numbers in FFT?
Those complex numbers in the FFT result are simply just 2 real numbers, which are both required to give you the 2D coordinates of a result vector that has both a length and a direction angle (or magnitude and a phase).
What does the complex eigen-frequency imply in physics?
The stiffness and mass matrix should be symmetric and positive (semi-)definite. If you have used the Ansatz \\exp {\\lambda t} a pure imaginary frequency is an oscillating mode. A positive real part means an unstable mode; a negative real part is related to a stable mode.