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EE104: Lecture 13 Outline

EE104: Lecture 13 Outline. Midterm Announcements Review of Last Lecture Linear Time-Invariant Systems System Impulse Response Filtering as Convolution in Time Frequency Response Distortionless Transmission. Midterm Announcements (See announcements link on website). HW 3 due now

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EE104: Lecture 13 Outline

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  1. EE104: Lecture 13 Outline • Midterm Announcements • Review of Last Lecture • Linear Time-Invariant Systems • System Impulse Response • Filtering as Convolution in Time • Frequency Response • Distortionless Transmission

  2. Midterm Announcements(See announcements link on website) • HW 3 due now • No new homework until after exam • OHs this week: • My OHs: TW 11-12, T 4-5. • TA OHs: T 7-9 in 106 Packard • Practice midterms • 10 bonus pts for taking any practice exam (1.5 hours) • Solutions available today, due before MT • Midterm: Wednesday, 2/12, 12:50-2:05 in class • Covers Chapters 1-2 • Open book and notes • Review session today, 6:15-7:05, TCSEQ103

  3. 0 Ts -Ts Review of Last Lecture • Signal Reconstruction: • Sampling in Frequency • Unit Step Function • Integration Revisited Xs(f) x(t) Correct zero crossing location

  4. x(t-t) y(t-t) ax1(t)+bx2(t) ay1(t)+by2(t) LTI System LTI System LTI Systems • Devices or media that produce an output signal in response to an input signal • Typically channels or filters • Linearity and Time Invariance y(t) x(t) LTI System Linearity Time Invariance

  5. System Impulse Response • System output to delta function input • Assumes zero initial conditions • Hard to measure in practice h(t) d(t) LTI System

  6. Filtering as Convolution LTI System Indicates that the system has memory

  7. Measured using eigenfunctions H(fc) Frequency Response • Fourier transform of impulse response • Typically complex: amplitude and phase response • Exponential eigenfunctions x(t) x(t)*h(t) H(f)=|H(f)|ejH(f) h(t) X(f) H(f)X(f) h(t)

  8. Distortion • Distortionless Transmission • Output equals input except for amplitude scaling and/or delay • Simple equalizers invert channel distortion • Can enhance noise power x(t) Kx(t-t) h(t)=Kd(t-t) X(f) Kej2pftX(f) H(f)=Kej2pft Equalizer Channel N(f) H(f) 1/H(f) X(f)+N(f)/H(f) X(f) +

  9. Main Points • Communication channels and filters are LTI systems • The output of an LTI system is the convolution of its impulse response with the input signal • LTI system output in frequency domain is the product of the input Fourier transform with the system frequency response • Spectrum analyzers use eigenfunction property of sinusoids to measure amplitude and phase response of an LTI system • An LTI system is distortionless if it only gives rise to a delay (linear phase shift) • Most communication channels introduce distortion

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