HW1_ece220_2007

# HW1_ece220_2007 - Homework 1(ECE220 Fall 2007 Due Thursday...

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Homework 1 (ECE220 - Fall 2007) Due: Thursday, September 6 at the beginning of lecture. Reasoning and work must be shown to gain full/partial credit. WRITE YOUR NAME AND NET ID ON ALL PAGES HANDED IN! 1. (20 points) Premise You are familiar with the concept of variable. Signals are a more sophisticated mathematical objects that extend the static concept of variable in order to capture a variable that changes dynamically. It may evolve in time, space, or with respect to some other, ehm, variable. Conventionally one refers to the dimensions of the independent variable, for example, time is 1-D (one-dimensional), space can be 2-D in an image or 3-D in actuality, when specifying what kind of signal we are dealing with. A 3-D signal is a video, which is a set of images evolving with time. This is not referring to the signal itself, which if studied as a vector, lies in a space usually with a great deal of more dimensions than its index. (20 points) There are two classes of signals. The ones that we commonly experience ﬁt best the abstraction of analog signals . A 1-D analog signal is denoted for ex- ample as s ( t ) : s ( t ) R or C and t R . An analog image signal would be: s ( x,y ) : s ( x,y ) R or C and x,y R . The deﬁnition can be clearly extended to multidimensional signals s ( x 1 ,...,x n ) where, ( x 1 ,...,x n ) R n . Also, the signal itself sometimes takes only discrete values, which is an obvious special case. Digital signals

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## This note was uploaded on 05/31/2008 for the course ECE 2200 taught by Professor Johnson during the Fall '05 term at Cornell.

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HW1_ece220_2007 - Homework 1(ECE220 Fall 2007 Due Thursday...

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