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