All-Orders Quadratic-Logarithmic Behavior for Amplitudes

Benjamin Basso1, Lance J Dixon2, Yu-Ting Liu2,3

  • 1Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, F-75005 Paris, France.

Related Concept Videos

Transfer function and Bode Plots-II01:23

Transfer function and Bode Plots-II

In the standard form, the transfer function is shown in constant gain, poles/zeros at origin, simple poles/zeros, and quadratic poles/zeros; each contributing uniquely to the system's overall response. The term represents the magnitude of the simple zero:
395
Bode Plots01:26

Bode Plots

Bode plots are graphical tools that use logarithmic scales for frequency on the x-axis and gain in decibels on the y-axis. This logarithmic method allows a wide range of frequencies to be compactly displayed, enabling the analysis of component effects on circuit behavior across a broad frequency spectrum.
A network function represents the ratio of a system's output to its input, with the magnitude and phase angle derived from the complex network function. The decibel logarithmic gain is...
745
Damped Oscillations01:07

Damped Oscillations

In the real world, oscillations seldom follow true simple harmonic motion. A system that continues its motion indefinitely without losing its amplitude is termed undamped. However, friction of some sort usually dampens the motion, so it fades away or needs more force to continue. For example, a guitar string stops oscillating a few seconds after being plucked. Similarly, one must continually push a swing to keep a child swinging on a playground.
Although friction and other non-conservative...
5.8K
Exponential Fourier series01:24

Exponential Fourier series

In audio signal processing, the exponential Fourier series plays a crucial role in sound synthesis, allowing complex sounds to be broken down into simpler sinusoidal components. This decomposition process is fundamental in analyzing and reconstructing musical notes and other audio signals. The exponential Fourier series expresses periodic signals as the sum of complex exponentials at both positive and negative harmonic frequencies, providing a powerful tool for signal analysis.
Euler's identity...
252
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...
251
Exponential and Sinusoidal Signals01:18

Exponential and Sinusoidal Signals

The exponential function is crucial for characterizing waveforms that rise and decay rapidly. This continuous-time exponential function is defined using exponential terms with constants α and A. When both constants are real, the function is represented as,
316