EE 200 Sampling and Reconstruction
The process of sampling the signals is only half of the task. We also need to reconstruct a new continuous time signal, preferably as close as possible to the original continuous-time signal.
Input signal x(t) Sampled si
Signal Processing First
READING ASSIGNMENTS
This Lecture:
Chapter 5, Sections 5-5 and 5-6
Section 5-4 will be covered, but not "in depth"
Lecture 11 Linearity & Time-Invariance Convolution
Other Reading:
Recitation: Ch. 5, Sects 5-6, 5-7 & 5-8
CONVOLUTION
Signal Processing First
READING ASSIGNMENTS
This Lecture:
Chapter 6, Sections 6-1, 6-2, 6-3, 6-4, & 6-5
Lecture 12 Frequency Response of FIR Filters
Other Reading:
Recitation: Chapter 6
FREQUENCY RESPONSE EXAMPLES
Next Lecture: Chap. 6, Sects. 6-6, 6-7 &
Signal Processing First
READING ASSIGNMENTS
This Lecture:
Chapter 6, Sections 6-6, 6-7 & 6-8
Lecture 13 Digital Filtering of Analog Signals
Other Reading:
Recitation: Chapter 6
FREQUENCY RESPONSE EXAMPLES
Next Lecture: Chapter 7
10/6/2003
2003, JH McClel
Signal Processing First
READING ASSIGNMENTS
This Lecture:
Chapter 7, Sects 7-1 through 7-5
Lecture 14 Z Transforms: Introduction
Other Reading:
Recitation: Ch. 7
CASCADING SYSTEMS
Next Lecture: Chapter 7, 7-6 to the end
8/22/2003
2003, JH McClellan & RW
Signal Processing First
READING ASSIGNMENTS
This Lecture:
Chapter 7, Section 7-6 to end
Lecture 15 Zeros of H(z) and the Frequency Domain
Other Reading:
Recitation & Lab: Chapter 7
ZEROS (and POLES)
Next Lecture:Chapter 8
8/22/2003
2003, JH McClellan & R
Signal Processing First
READING ASSIGNMENTS
This Lecture:
Chapter 8, all
Lecture 18 3-Domains for IIR
Other Reading:
Recitation: Ch. 8, all
POLES & ZEROS
Next Lecture: Chapter 9
4/18/2004
2003, JH McClellan & RW Schafer
1
4/18/2004
2003, JH McClellan &
Signal Processing First
READING ASSIGNMENTS
This Lecture:
Chapter 9, Sects 9-1 to 9-5
Lecture 19 Continuous-Time Signals and Systems
Other Reading:
Recitation: Ch. 9, all Next Lecture: Chapter 9, Sects 9-6 to 9-8
4/3/2006
2003-2006, JH McClellan & RW Sch
Systems
Systems transform signals
o Convert to form usable by other systems
Modems change signal to form suitable for transmission
o Filters: extract one part, reduce another part
o Encrypt & decrypt
o State machines: respond to signals and take some ac
State Machines
A state machine generates an output that is a function of the inputs and
the state of the machine.
The next state function and the output function are referred to jointly as
the update function. The update function determines what state t
EE 200 FIR Filters
A running-aveage filter averages a finite number of input samples to produce an output sample
x[n] 4 2 6 4 2 n
y[ n ] = 1 ( x[ n ] + x[ n + 1] + x[ n + 2]) 3
y[n] 14/3 4 4
!
2/3
2
2
2/3
n
1
EE 200 FIR Filters
A causal version of the sam
EE 200 Cascading LTI Systems
Output of the first system becomes the input to the second. Output of the second is the output of the cascade configuration.
x[n] System 1 h1[n] x[n]h1[n] System 2 h2[n] (x[n] h1[n])h2[n]
Commutative and associative properties
EE 200 Signals
Signals carry (or store) information. Something is varied to represent information. That something can be electrical, mechanical, light, etc. We need to represent signals by mathematical functions in order to work with them. Functions that
EE 200 Chapter 5 - Linear Systems
A state machine is define by a five-tuple M = (States, Inputs, Outputs, update, initialState)
N-tuple M-tuple K-tuple
For a input sequence of M-tuples The state update equation generates new N-tuples n Integers, n 0, s(n+
Frequency Response
Example: Find the frequency response of the circuit below with a resistor
and capacitor.
The relationship between the voltages x(t) and y(t) is given by the
differential equation
x(t) = RC dy/dt(t) + y(t)
Assuming the input is a comp
Memory vs. Memoryless
A memoryless system does not use any previous input values (or states) in
order to determine the output.
o Output only depends on the current input
A system with memory uses previous inputs (and/or states) to determine
the current
Sampling
In order for digital hardware to operate on a continuous signal, the signal
must first be changed into a discrete signal. The action of changing the
continuous signal into a discrete signals is known as sampling.
The time span between samples,
Signal Processing First
READING ASSIGNMENTS
This Lecture:
Chapter 10, all
Lecture 21 Frequency Response of Continuous-Time Systems
Other Reading:
Recitation: Ch. 10 all, start Ch 11 Next Lecture: Chapter 11
4/3/2006
2003-2006, JH McClellan & RW Schafer
3
Signal Processing First
READING ASSIGNMENTS
This Lecture:
Chapter 11, Sects. 11-1 to 11-4
Lecture 22 Introduction to the Fourier Transform
Other Reading:
Recitation: Ch. 10
And Chapter 11, Sects. 11-1 to 11-4
Next Lecture: Chapter 11, Sects. 11-5, 11-6
3/
EE 200 Fourier Transforms
In previous chapters we saw how a signal that is periodic in the time-domain could be represented as a weighted sum of complex exponentials (the Fourier series expansion.)
$
p#1
ik" 0 t k
x(t) =
%X e
k=#$
x(n) = $ X k e ik" 0 n
k
Signal Processing First
READING ASSIGNMENTS
This Lecture:
Chapter 2, Sects. 2-3 to 2-5
LECTURE #2 Phase & Time-Shift Complex Exponentials
Appendix A: Complex Numbers Appendix B: MATLAB Next Lecture: finish Chap. 2,
Section 2-6 to end
8/22/2003
2003, JH M