Electrical Engineering 20N - Fall 2000 - Midterm 1

Electrical Engineering 20N - Fall 2000 - Midterm 1 - 1...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 EECS20n, Solution to Midterm 1, 10/20/00 1. 10 points The function x : Reals Reals given by t Reals x ( t )=s in(2 π × 440 t ) is a mathematical example of a signal in the signal space [ Reals Reals ] . Give mathematical examples of signals in the following signal spaces. (a) (2 pts) [ Ints Reals ] n Ints ,x ( n )= n (b) (2 pts) [ Nats 0 EnglishWords ] n Nats 0 ( n the (c) (2 pts) [ Reals Reals 2 ] t Reals ( t )=( t, 2 t ) (d) (2 pts) [ { 0 , 1 , ··· , 600 }×{ 0 , 1 , , 400 }→{ 0 , 1 , , 255 } ] ( m,n ) ∈{ 0 , 1 , , 600 0 , 1 , , 400 } ( m + n ) mod 255 (e) (2 pts) Give an example of a practical space of signals whose mathematical representa- tion is [ { 0 , 1 , , 600 0 , 1 , , 400 0 , 1 , , 255 } ] . This is the appropriate signal space for images of size 600 × 400 pixels with an 8-bit color map index.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 2. 10 points The function H :[ Reals + Reals ] [ Nats 0 Reals ] given by: x [ Reals + Reals ] , n Nats 0 ,H ( x )( n )= x (10 n ) , is a mathematical example of a system with input signal space [ Reals + Reals ] and output signal space [ Nats 0 Reals ] . Give mathematical examples of systems whose (a) 5 pts input and output signal spaces both are [ Nats 0 Bin ] . The simplest example is the identity system: x, n, H ( x )( n x ( n ) . (b) 5 pts input signal space is [ Nats 0 Reals ] and output signal space is [ Nats 0 →{ 0 , 1 } ] . A simple example is a system which converts negative values to 0 and positive values to 1: x, n, H ( x )( n ( 0 , if x ( n ) 0 1 , if x ( n ) > 0 (c) 5 pts input signal space is [ Ints Reals ] and output signal space is [ Reals Reals ] .
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/17/2009 for the course EE 20N taught by Professor Ayazifar during the Spring '08 term at University of California, Berkeley.

Page1 / 8

Electrical Engineering 20N - Fall 2000 - Midterm 1 - 1...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online