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Unformatted text preview: 6.003 Homework 1 Due at the beginning of recitation on Wednesday, September 16, 2009 . Problems 1. Waves Assume that the height of a water wave is given by g ( x vt ) where x is distance, v is velocity, and t is time. The function g is defined in the following plot and is zero outside the indicated range. g ( r ) r 3 2 1 1 2 3 a. Assume x = 0 and v = 1. Sketch f 1 ( t ) = g ( t ), which illustrates the height of the wave as a function of time, as it passes the point x = 0. b. Assume x = 0 and v = 2 and sketch f 2 ( t ) = g ( 2 t ). Explain the important differences between f 1 and f 2 . c. Sketch f 3 ( x ) = g ( x 1). Suggest a physical interpretation for f 3 ( x ). d. Sketch f 4 ( t ) = g (1 t ). Suggest a physical interpretation for f 4 ( t ). e. Is the wave traveling in the positive or negative x direction? Explain. 2. Even and Odd Let x [ n ] represent the signal shown in the following plot, where all values outside the indicated range are zero. x [ n ] n 3 2 1 1 2 3 1 1 Assume that x [ n ] can be written as the sum of an even part ( x e [ n ] = x e [ n ]) and an odd...
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This note was uploaded on 08/24/2011 for the course EECS 6.003 taught by Professor Dennism.freeman during the Spring '11 term at MIT.
- Spring '11