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EE 314 Signal and Linear System Analysis. Discrete Time Signals. Summary of Last Lecture. Aliasing Distortion which occurs due to under-sampling Sampling frequency was less than 2 x Signal bandwidth => Fs < 2B. Distortion!!. LPF. …. …. f (Hz). -800. -700. -600. -500. -400. -300.
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EE 314 Signal and Linear System Analysis Discrete Time Signals EE 314 Signal and Linear System Analysis
Summary of Last Lecture • Aliasing • Distortion which occurs due to under-sampling • Sampling frequency was less than 2 x Signal bandwidth => Fs < 2B Distortion!! LPF … … f (Hz) -800 -700 -600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600 700 800 EE 314 Signal and Linear System Analysis
Discrete Time SignalsContinuous vs Discrete vs Digital • Continuous vs Discrete vs Digital • Continuous: Uniquely defined for all real values of t (time) • Discrete:Signal is definedonly at • i.e. discrete time • Digital:Signal is discretein both time andamplitude EE 314 Signal and Linear System Analysis
Discrete Time SignalsContinuous vs Discrete vs Digital • Discrete vs Digital 710 = 01112 We will focus on Discrete rather than Digital signals 6.6844 6.6844 EE 314 Signal and Linear System Analysis
Discrete Time Signals • Discrete-time signals x[n] are defined only at integer “times” n. • Continuous-time signals x(t) are defined for all real values of t. • Discrete-time signals can be represented in 3 different ways: • Enclosing all non-zero values in braces: x[n]={3,2,0,4}. The underline indicates x[n] at “time” n=0; here, x[0]=2. • Listing all of the non-zero values: • Using a stem plot: Instead of time “t” we now use sample index “n”!! EE 314 Signal and Linear System Analysis
Discrete Time Signals • Time Shift • Time scale: • Essentially the same as the continuous case!! N is an Integer EE 314 Signal and Linear System Analysis
Discrete Time Signals • Discrete-time Impulse • Discrete-time Sampling property EE 314 Signal and Linear System Analysis
Discrete Time Signals • Discrete-time Step • Relationship between step and Impulse • What is EE 314 Signal and Linear System Analysis
Discrete Time Signals • Discrete-Time Sinusoids • A discrete-time signal is periodic if • Where both and are integers Continuous Time: Discrete Time: Period: Period: ONLY if there exists a k to make an integer!! EE 314 Signal and Linear System Analysis
Discrete Time Signals • An Example • Determine the period of • Period: • If • The continuous signal has a period of 2 seconds • The discrete signal has a period of 20 samples The discrete signal may NOT be periodic even if the continuous signal is!! EE 314 Signal and Linear System Analysis
Discrete Time Signals • Exponentials Discrete Time: Continuous Time: Geometric Signals Exponential Signals EE 314 Signal and Linear System Analysis
Discrete Time Signals • What is the period of ? • Considering the first term • For to be an integer smallest is 1 • Considering the second term • The smallest period which satisfies both terms (least common multiple) is 24 => Period of x[n] is 24 samples EE 314 Signal and Linear System Analysis
Discrete Time Signals EE 314 Signal and Linear System Analysis
Next Lecture • Discrete Time LTI Systems • Reading Assignment: Chap. 7.3 EE 314 Signal and Linear System Analysis
