systems-harmonics.slides.printing

systems-harmonics.slides.printing - When a system is...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Generalized Harmonic Functions Generalized Harmonic Functions CS 450: Introduction to Digital Signal and Image Processing Bryan Morse BYU Computer Science
Background image of page 1

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

View Full DocumentRight Arrow Icon
Generalized Harmonic Functions Harmonic Functions What does f ( t ) = e i 2 π ut look like? Imaginary Real i 1 -i -1
Background image of page 2
Generalized Harmonic Functions Harmonic Functions as Sinusoids Real Part Imaginary Part < ( e i 2 π ut ) = ( e i 2 π ut ) cos ( 2 π ut ) sin ( 2 π ut ) So, e i 2 π ut is just a way to write a cosine function (real part) and a sine function (imaginary part) simultaneously—each has frequency u . This is called a generalized harmonic .
Background image of page 3

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

View Full DocumentRight Arrow Icon
Generalized Harmonic Functions Harmonics and Systems What happens when we feed a generalized harmonic into a linear, shift-invariant system? f ( t ) = e i 2 π ut f ( t ) H ( u ) f ( t ) where H ( u ) is a complex multiplier.
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: When a system is applied to a harmonic signal, the result is the same harmonic signal multiplied by a complex constant that depends on the frequency. Generalized Harmonic Functions Transfer Functions H ( u ) is called the transfer function : how inputs transfer to outputs. Expressing H ( u ) in polar (magnitude-phase) form: H ( u ) = | H ( u ) | e i ( H ( u )) Recall that the magnitudes multiply and the phases add: H ( u ) e i 2 ut = | H ( u ) | e i ( u ) e i 2 ut = | H ( u ) | e i ( 2 ut + ( u )) | H ( u ) | is the Modulation Transfer Function (MTF) ( H ( u )) is the Phase Transfer Function (PTF)...
View Full Document

Page1 / 5

systems-harmonics.slides.printing - When a system is...

This preview shows document pages 1 - 5. Sign up to view the full document.

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