Convolution
continued
The Convolution Integral
Since the segments are infinitesimal, there are infinite impulse
responses at various time positions, so the summation has to be done
by integration.
Standard calculus is well equipped to describe this operat
Systems Analysis:
An Introduction to Transfer
Functions
Recall the System Model Approach
System models are represented as an input-output relationship.
Transforming an input stimulus (signal) into a response
Can have multiple inputs (sources)
Solutions
Laplace Transfer Functions
The Inverse Laplace Transform
The equation for the inverse Laplace transform is given as:
x(t) L
1
1
X (s)
2
j
st
X
(
s
)
e
ds
j
Unlike the inverse Fourier transform, this equation is quite
difficult to solve even for simpl
Transfer Functions
Introduction to Bode Plots
Go back to the transfer function concept:
Introduction to Bode plots
The transfer function introduced previously gets its name
because it describes how an input, Input(), is transferred to the
output, Output(
Transfer Functions,
Continued
(text section 5.2)
Review of what we are doing:
Analog Analysis of LTI systems
Systems Analysis of LTI systems
Analog Analysis: Summary
Analog models represent the physiological process using
elements that are, to some degre
Analysis of LTI systems, continued
Introduction to Convolution
Linear (LTI) Systems - recap
The systems model is a process-oriented representation that
emphasizes the influences, or flow, of information between modules.
A systems model describes how proce
The Fourier Transform and the Transfer Function
The Transfer Function and the Fourier Transform
The transfer function can be used to find the output to any
single sinusoidal input.
Fourier series decomposition can be used to break down any
periodic or ap
Data Truncation, Windowing &
Power Spectrum
(Wraps up Chapt. 4)
Data Truncation
A digitized waveform must necessarily be truncated to the length of the memory
storage array, a process described as windowing.
The windowing process can be thought of as mult
Laplace Transform, continued
Using Laplace transform tables
As mentioned earlier, computing Laplace transforms can be
complicated. This is because the definition is an improper
integral.
X (s) L x(t)
x ( t )e
st
dt
0
Infinite interval: One or more of t
Linear Systems:
Introduction
Chapter 5
Linear Signal Analysis ~ An Overview.
So far we have been studying signals
Signals come from, and go through and are modified by, systems.
A system either acts on signals to modify them or a system can be the
origin
BE 2600 Homework #7 Spring 2009 Imaging This week, you will be introduced to the following imaging modalities: 1. Ultrasound 2. Computed Tomography 3. MRI 4. Nuclear Imaging For each of the above imaging modalities, briefly state how the imaging technique
Metallic biomaterials
Primary Application: 1. Traditional devices such as hip and knee prostheses 2. Newer devices such as cardiovascular stents Fundamental requirements: mechanical integrity and biocompatibility
Metallic materials:
commonly used in biome
What governs biomaterial choice?
The specific application
Example problem: One common biomaterial application is the construction of an arterial graft, a device that replaces a section of an artery.
What specific material characteristics should be conside
Biomaterials: brief historical overview
Novel idea: replace from outside the structure-function of the body Necessity 1960s An evolution occurred: combine devices and materials w/ cell biology An off the shelf approach Significant shifts in thinking:
1st
BE/BL 2400 Practice Exam 1. T or F. An enzyme is a catalyst that speeds up a specific reaction so that more of the reaction products will be present when the reaction achieves equilibrium. 2. T or F. Hydrophobic force is important during spontaneous proce
Regulation of Transcription
Gene regulatory proteins can act when they bind DNA even thousands of nucleotide pairs away from the promoter that they influence (made possible by DNA looping) Eucaryotic RNA polymerase cannot initiate transcription on its ow
Chapter 6
How Cells Read The Genome: From DNA to Protein
From DNA to RNA
Much of the DNA in the genome is used to specify the linear order of amino acids for all the proteins in an organism The amino acid sequence dictates how each protein folds to give
Isolated 3T3 cell stained for F-actin (red), for DNA (blue), alpha-tubulin (green), a major component of the microtubule network. Images were recorded with a confocal microscope
GreenFluorescentProtein(GFP) canbeusedtotagindividual proteinsinlivingcellsa
Dark Field Microscopy
Results in very high contrast Useful for visualizing cells that have very low intrinsic contrast
Such as cells in suspension Mitochondria Nucleus
Stains are essentially invisible with this approach
The stained portions of the ce