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

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

Another(important! ) example: Periodic Impulse train n(t)=∑(t Sampling function important for sampling .2T

Portrait of Jean Baptiste Joseph Fourier Image removed due to copyright considerations Signals& Systems, 2nd ed. Upper Saddle River, N.J. Prentice Hall, 1997, p 179

1Some examples of systems 2 System properties and examples CAusality

1. DTFT Properties and Examples 2. Duality in fs& ft 3. Magnitude/Phase of Transforms and Frequency Responses

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

then, assuming we choose wM