Let be a band-limited signal with then is uniquely determined by its samples if where

SAMPLING We live in a continuous-time world most of the signals we encounter are CT signals, e.g. x(). How do we convert them into Dt signals x[n? Sampling, taking snap shots of x(t) every Seconds

Result: Linear phase e simply a rigid shift in time, no distortion Nonlinear phase e distortion as well as shift DT

6.23 Shown in Figure 6.23 is for a lowpass filter. Determine and sketch the impulse response of the filter for each of the following phase characteristics:

Properties of ct Rational system functions a) However, if H(s)is rational, then The system is causal The roc of H(s) is to the right of the rightmost pole

Representation of ct signals Approximate any input x(t) as a sum of shifted, scaled

Convergence Issues Synthesis equation: None. since integrating over a finite interval Analysis Equation: Need conditions analogous to CTFT, e. g

Convolution Property 0(t)=h(t)*(t)←→Y(j)=H(ju)X( where h(t)←→H(ju) A consequence of the eigenfunction property

MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.003: Signals and Systems-Fall 2003 PROBLEM SET 1 SOLUTIONS (E1)(O&W154) (a) For the r=l case, we have

Chapter 1 Signals and Systems (1) A simple RC circuit Source voltage Vs and Capacitor voltage Vc (2) An automobile