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Spring 2008. Continuous-Time System Properties. Linear Systems and Signals Lecture 2. Linearity. A system is linear if it is both Homogeneous : If we scale the input, then the output is scaled by the same amount:
From Continuous Time System to Discrete Time System . ES400 Jack Ou, Ph.D. Chapter 1. Outline. Modeling Signal System Continuous Time System ADC Discrete Time System. Signals. Signals are divided into two natural categories
Continuous Time Signals. Basic Signals – Singularity Functions Transformations of Continuous Time Signals Signal Characteristics Common Signals. Continuous-Time Signals. Assumptions: Functions , x(t), are of the one independent variable that typically represents time , t .
Continuous time formalism. Exhaustible Problem. Max (e -rt p(t) h(t)) s.t. dx/dt = -h Hamiltonian: Objective function + multiplier * rhs of diffeq. H = e -rt p(t) h(t) – l h. Rules. Exhaustible Resource. Since x >0 it can’t be that h=inf for any measurable length of time.
Spring 2008. Continuous-Time Convolution. Linear Systems and Signals Lecture 5. Convolution Demos. Johns Hopkins University Demonstrations http://www.jhu.edu/~signals Convolution applet to animate convolution of simple signals and hand-sketched signals
EE 313 Linear Systems and Signals Fall 2005. Continuous-Time Convolution. Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin. Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf. Useful Functions.
Continuous Time Convolution . In this animation, the continuous time convolution of signals is discussed. Convolution is the operation to obtain response of a linear system to input x(t). The output y(t) is given as a weighted superposition of impulse responses, time shifted by .
Continuous-time Signals. ELEC 309 Prof. Siripong Potisuk. Signal Transformations. Operations Performed on the Independent and Dependent Variables Reflection or Time Reversal or Folding Time Shifting Time Scaling Amplitude Scaling Amplitude Shifting
Continuous-Time Convolution. Impulse Response. Impulse response of a system is response of the system to an input that is a unit impulse (i.e., a Dirac delta functional in continuous time) When initial conditions are zero, this differential equation is LTI and system has impulse response.
Continuous Time Signals. A signal represents the evolution of a physical quantity in time. Example: the electric signal out of a microphone. At every time t the signal has a value Volts (say). Digital Processing of Continuous Time Signals. ADC. DSP. DAC.