{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

LinearSystems-Theory-2011

# LinearSystems-Theory-2011 - Linear Systems Theory Andres...

This preview shows pages 1–7. 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 is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Linear Systems Theory Andres Kriete School of Biomedical Engineering, Science and Health Systems Drexel University 2011 Presentation contains slides translated and/or modified from presentations of B. Preim, MEVIS, J. Pawley / W.Block, Wisconsin and Mikael Jensson, Sweden Linear Systems – why study them? • Develop general analysis tools for all modalities • Applicable beyond medical imaging • Tools provide valuable insights for understanding and design • Rational for further improvement of systems • Build upon your knowledge of one-dimensional theory Communications: time ↔ frequency (1 dimension) Imaging: space ↔ spatial frequency We will work in two dimensions. Cells and Human body is three-dimensional. Extension of 2D theory to three dimensions is straightforward. Properties of linear systems Linearity Conditions Let f 1 (x,y) and f 2 (x,y) describe two objects we want to image. f 1 (x,y) can be any object and represent any characteristic of the object. (e.g. color, intensity, temperature, texture, X-ray absorption, etc.) Assume each is imaged by some imaging device (system). Let f 1 (x,y) → g 1 (x,y) f 2 (x,y) → g 2 (x,y) Let’s scale each object and combine them to form a new object. a f 1 (x,y) + b f 2 (x,y) hat is the output? If the system is linear, output is a g 1 (x,y) + b g 2 (x,y) Linearity Example: Is this a linear system? x x → → Linearity Example: Is this a linear system? 9 → 3 16 → 4 9 + 16 = 25 → 5 3 + 4 ≠ 5 Not linear. x x → → xample in medical imaging: Analog to digital converter Doubling the X-ray photons → doubles those transmitted Doubling the nuclear medicine → doubles source & reception energy...
View Full Document

{[ snackBarMessage ]}

### Page1 / 25

LinearSystems-Theory-2011 - Linear Systems Theory Andres...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online