Lesson_4 - Lesson 4 Lesson 4 Spectral Analysis Challenge 03...

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

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

View Full Document

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

View Full Document

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

View Full Document

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lesson 4 Lesson 4: Spectral Analysis Challenge 03: Lesson 04 (Sect. 3.1-3.4) Spectrum Sum and product spectrum Periodicity Introduction to Fourier Series Challenge 04 Lesson 4 Challenge 03 You where asked to analyze the RC circuit shown under the assumption that V(j ϖ ) = 8 ∠ ° at ϖ = 1000 r/s. It was established that V R (j ϖ )= 4.44 ∠ 56.3 ° . Using Kichoff’s Law, the capacitor voltage can be computed using phasor algebra as shown below. 20 +- i(t)-j30 v C (t) V =8 ∠ ° = V R + V C V R =4.44 ∠ 56.3 ° v C (t)=6.66 cos(1000t – 33.7 ° ) V C = V- V R =6.66 ∠-33.7 ° V C Phasor Lesson 4 Chapter 3 Spectral representation Lesson 4 Spectrum Suppose a signal has be representation given by: Euler says that the signal representation is complex. The signal consists of complex components residing at positive, negative, and zero (DC) frequencies. How can this information be graphically represented? ( 29 C a e a t x k N N k t kf j k ∈ = ∑- = ; 2 π Lesson 4 Spectrum Complex spectrum representation choices: Magnitude and phase response (phasor) Real and imaginary spectrum (complex) Each displays the frequency spectrum of the signal under study. Variations on this theme are: Log (dB) magnitude vs. linear frequency (semi-log) Log (dB) magnitude vs. log frequency (log-log or Bode plot) Lesson 4 Spectrum Example: x(t)=cos( ϖ t) = (1/2)e j ϖ t + (1/2)e-j ϖ t for some ϖ . Magnitude 0 Phase Real 0 Imaginary Lesson 4 Spectrum Example: x(t)=sin( ϖ t) = (-j1/2)e j ϖ t + (j1/2)e-j ϖ t for some ϖ . Magnitude 0 Phase 0 Real 0 Imaginary 0 90 °-90 °-1/2 ° 1/2 ° Lesson 4 Product Spectrum For multiplication (product modulation) opérations...
View Full Document

{[ snackBarMessage ]}

Page1 / 31

Lesson_4 - Lesson 4 Lesson 4 Spectral Analysis Challenge 03...

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

View Full Document
Ask a homework question - tutors are online