Lecture 2 Signal Characteristics and Models

Lecture 2 Signal Characteristics and Models - UCLA Fall...

Info iconThis preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
UCLA Fall 2011 Systems and Signals Lecture 2: Signal Characteristics and Models September 28, 2011 EE102: Systems and Signals; Fall 2011, Jin Hyung Lee 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
Signal Characteristics and Models Operations on the time dependence of a signal Time scaling Time reversal Time shift Combinations Signal characteristics Periodic signals Complex signals Signal Energy and Power EE102: Systems and Signals; Fall 2011, Jin Hyung Lee 2
Background image of page 2
Time Scaling, Continuous Time A signal x ( t ) is scaled in time by multiplying the time variable by a positive constant b , to produce x ( bt ) . A positive factor of b either expands (0 < b < 1) or compresses ( b > 1) the signal in time. -2 -1 0 1 2 1 2 t x ( t ) b = 1 -2 -1 0 1 2 1 2 t x ( 2 t ) b = 2 -2 -1 0 1 2 1 2 t -3 3 b = 1 / 2 x ( t / 2 ) EE102: Systems and Signals; Fall 2011, Jin Hyung Lee 3
Background image of page 3

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

View Full DocumentRight Arrow Icon
Time Scaling, Discrete Time The discrete-time sequence x [ n ] is compressed in time by multiplying the index n by an integer k , to produce the time-scaled sequence x [ nk ] . This extracts every k th sample of x [ n ] . Intermediate samples are lost. The sequence is shorter. 2 4 -2 -4 0 1 3 -1 -3 x [ n ] n y [ n ] = x [ 2 n ] 2 -2 0 1 -1 n Called downsampling , or decimation . EE102: Systems and Signals; Fall 2011, Jin Hyung Lee 4
Background image of page 4
The discrete-time sequence x [ n ] is expanded in time by dividing the index n by an integer m , to produce the time-scaled sequence x [ n/m ] . This specifies every m th sample. The intermediate samples must be synthesized (set to zero, or interpolated). The sequence is longer. 2 -2 0 1 -1 n x [ n ] 2 4 -2 -4 0 1 3 -1 -3 n y [ n ] = x [ n / 2 ] Called upsampling , or interpolation . EE102: Systems and Signals; Fall 2011, Jin Hyung Lee 5
Background image of page 5

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

View Full DocumentRight Arrow Icon
Time Reversal Continuous time: replace t with - t , time reversed signal is x ( - t ) t x ( t ) t x ( - t ) Discrete time: replace n with - n , time reversed signal is x [ - n ] . t 2 4 -2 -4 0 x [ n ] t x [ - n ] 2 4 -2 -4 0 Same as time scaling, but with b = - 1 . EE102: Systems and Signals; Fall 2011, Jin Hyung Lee 6
Background image of page 6
Time Shift For a continuous-time signal x ( t ) , and a time t 1 > 0 , Replacing t with t - t 1 gives a delayed signal x ( t - t 1 ) Replacing t with t + t 1 gives an advanced signal x ( t + t 1 ) -2 -1 0 1 2 1 2 t x ( t + 1 ) -2 -1 0 1 2 1 2 t x ( t ) -2 -1 0 1 2 1 2 t x ( t - 1 ) May seem counterintuitive. Think about where t - t 1 is zero. EE102: Systems and Signals; Fall 2011, Jin Hyung Lee 7
Background image of page 7

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

View Full DocumentRight Arrow Icon
For a discrete time signal x [ n ] , and an integer n 1 > 0 x [ n - n 1 ] is a delayed signal. x
Background image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 39

Lecture 2 Signal Characteristics and Models - UCLA Fall...

This preview shows document pages 1 - 9. Sign up to view the full document.

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