lec18 - 6.003: Signals and Systems CT Fourier Transform...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 6.003: Signals and Systems CT Fourier Transform November 12, 2009 Mid-term Examination #3 Wednesday, November 18, 7:30-9:30pm, Walker Memorial (this exam is after drop date). No recitations on the day of the exam. Coverage: cumulative with more emphasis on recent material lectures 118 homeworks 110 Homework 10 will not collected or graded. Solutions will be posted. Closed book: 3 page of notes ( 8 1 2 11 inches; front and back). Designed as 1-hour exam; two hours to complete. Review sessions during open office hours. Conflict? Contact freeman@mit.edu by Friday, November 13, 2009. CT Fourier Transform Representing signals by their frequency content. X ( j )= x ( t ) e jt dt (analysis equation) x ( t )= 1 2 X ( j ) e jt d (synthesis equation) generalizes Fourier series to represent aperiodic signals. equals Laplace transform X ( s ) | s = if ROC includes j axis. inherits properties of Laplace transform. complex-valued function of real domain . simple inverse relation more general than table-lookup method for inverse Laplace. duality. filtering. applications in physics Visualizing the Fourier Transform Fourier transform is a function of a single variable: frequency . Time representation: 1 1 x 1 ( t ) 1 t Frequency representation: 2 X 1 ( j ) = 2 sin Check Yourself Signal x 2 ( t ) and its Fourier transform X 2 ( j ) are shown below. 2 2 x 2 ( t ) 1 t b X 2 ( j ) Which is true? 1. b = 2 and = / 2 2. b = 2 and = 2 3. b = 4 and = / 2 4. b = 4 and = 2 5. none of the above Check Yourself Find the Fourier transform. X 2 ( j ) = 2 2 e jt dt = e jt j 2 2 = 2 sin 2 = 4 sin 2 2 4 / 2 Check Yourself Signal x 2 ( t ) and its Fourier transform X 2 ( j ) are shown below. 2 2 x 2 ( t ) 1 t b X 2 ( j ) Which is true? 3 1. b = 2 and = / 2 2. b = 2 and = 2 3. b = 4 and = / 2 4. b = 4 and = 2 5. none of the above Fourier Transforms Stretching time compresses frequency. 1 1 x 1 ( t ) 1 t 2 X 1 ( j ) = 2 sin 2 2 x 2 ( t ) 1 t 4 / 2 X 2 ( j ) = 4 sin 2 2 Fourier Transforms Stretching time compresses frequency....
View Full Document

Page1 / 53

lec18 - 6.003: Signals and Systems CT Fourier Transform...

This preview shows document pages 1 - 10. Sign up to view the full document.

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