# Lecture Set #10

Τεχνίτη Νοημοσύνη και Ρομποτική

24 Νοε 2013 (πριν από 4 χρόνια και 7 μήνες)

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ECE 3336

Introduction to Circuits & Electronics

Lecture Set
#10

Signal Analysis & Processing

Frequency Response & Filters

Dr.
Han Le

ECE
Dept.

Outline

Review

Signal analysis

Power spectral density

Frequency response of a system (circuit)

Transfer function

Bode plot

Filters

Analog

Digital

Concept Review: Signal Processing

All electronics around us involve signal
processing.

Signal represents information. That information
can be something we generate (e.g. texts,
sounds, music, images) or from sensors.
(discussion: examples of sensors)

Electronics deal with signals: signal processing is
to transform the signal and extract the desired
information.

Concept Review: Signal Processing
(
cont
.)

Signal processing is a general concept, not a single
specific thing. It includes:

signal synthesis or signal acquisition

signal conditioning (transforming): shaping, filtering,
amplifying

signal transmitting

signal receiving and analysis: transforming the signal,
converting into information

Signal processing is mathematical operation;
electronics are simply tools.

Computation is high
-
level signal processing: dealing
directly with information rather than signal.

Applications of mathematical
techniques

Fourier
transform

Harmonic
function

Complex
number
&analysis

Phasors

Signal and AC circuit
problems

RLC or any time
-
varying linear
circuits. Applicable to linear
portion of circuits that include
nonlinear elements

Signal processing

signal analysis (spectral
decomposition)

filtering, conditioning (inc
amplification)

synthesizing

Note: The main lecture material is in the
Mathematica

file

this is only for concept summary

Homework (to be seen in HW 8)

Choose an electronic system around you (e. g. a TV, DVD
player, phone,…); show a functional block diagram
and
describe
the signal processing sequence
(end to end).

Example

Antenna

Ground

Inductor

Variable Capacitor

Diode
(1N34A)

High
-
Impedance Earphone

Schematic

Ante
nna

Grou
nd

Inductor

Variable
Capacitor

Diode
(1N34A)

High
-
Impedance
Earphone

Soundwave

Electrical signal
(voltage or current)

Antenna

10
20
30
40
50
-1.5
-1
-0.5
0.5
1
1.5
Carrier wave

(sound) signal

Resonance circuit

10
20
30
40
50
-1.5
-1
-0.5
0.5
1
1.5

Mathematica

file: AM FM

Outline

Review

Signal analysis

Power spectral density

Frequency response of a system (circuit)

Transfer function

Bode plot

Filters

Analog

Digital

Signal Fourier (or harmonic)
Analysis

Treat each time
-
finite signal as if it is composed of
many harmonics, using Fourier series

x
t
a
0
n 1
a
n
Cos
n
t
n 1
b
n
Sin
n
t

In

complex (or Euler) representation, Fourier
series coefficients
X
m

are
phasor

components,

x
t
m
X
m
m
t

X
m
X
m
m

Signal Fourier (or harmonic)
Analysis (cont)

If the signal is real (all cases involving real physical
quantity), then:

Hence, we need to keep only

positive frequencies

A signal can be represented

by a plot of |

X
m

| vs.
frequency, or
usually |

X
m

|
2

if x(t) is voltage or current,
known as the signal magnitude
spectrum
, or its
power
spectral density
.

Equally important is the phase spectrum: plot of
f
m

vs.
frequency

X
m
X
m
m

X
m
X
m

X
m
X
m
m

Do not be confused between the word
“spectrum” in the general English sense vs.
specific definition of “spectrum” in power spectral
density, or phase spectrum.

The Electromagnetic Spectrum

Visible

UV & solar
blind

Example of Spectra

0
1000
2000
3000
4000
5000
140
120
100
80
60
0
1000
2000
3000
4000
5000
3
2
1
0
1
2
3
0.89
s
11
025
Hz

Example of Spectra

0
1000
2000
3000
4000
5000
120
100
80
60
0.79
s
11
025
Hz
0
1000
2000
3000
4000
5000
3
2
1
0
1
2
3

Outline

Review

Signal analysis

Power spectral density

Frequency response of a circuit

Transfer function

Bode plot

Filters

Analog

Digital

Example

R

C

output
v
out
[t]

i
(t
)

input
v
in
[t
]

t

R

C

input
v
in
[t
]

output
v
out
[t
]

i
(t
)

t

1
1
t
1
t
Frequency Response

or, Frequency Transfer Function

H
1
1
H
1

Frequency Transfer Function

(Frequency Response Function)

H
P
Q
a
0
a
1
a
2
2
a
m
m
b
0
b
1
b
2
2
b
n
n
For many linear RLC circuits, the frequency
response function usually has the form:

Example: Test 1

H
C
2
L
2
R
3
2
1
C
2
L
2
2
R
1
L
1
C
1
R
1
R
3
1
C
1
R
1
C
2
R
1
L
1
L
2
C
1
R
1

Bode Plot for
Vout

in Test 1

1000
10
4
10
5
10
6
3
2
1
0
1
2
3
Frequency
Hz
Phase
Shift
1000
10
4
10
5
10
6
10
4
0.001
0.01
0.1
1
Frequency
Hz
Amplitude
Response

Applications of Frequency
Transfer Function

Any signal can be decomposed as a sum of
many
phasors

(Fourier components)

For a linear system, each component can be
multiplied by H[
w
] to obtain the output
phasor

The signal output is simply the sum of all the
individual
phasor

(Fourier component)
outputs.

Example

0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.6
0.4
0.2
0.0
0.2
0.4
0.6
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.4
0.2
0.0
0.2
0.4
0.0
0.5
1.0
1.5
2.0
2.5
3.0
2
0
2
4
6
8
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0
2
4
6
8
R

C

input
v
in
[t
]

output
v
out
[t
]

i
(t
)

Outline

Review

Signal analysis

Power spectral density

Frequency response of a circuit

Transfer function

Bode plot

Filters

Analog

Digital

General Filter Concept Review

0
1000
2000
3000
4000
5000
140
120
100
80
60
Frequency
Hz
Power
Spectral
Density
This is a filter

This is also filter

This is another filter

General Filter Concept

A system (electronic circuit) can be
designed such that its transfer function
H[
w
] has preference (let through) certain
ranges of frequencies while attenuating
(blocking) other frequencies

Such a circuit is called a filter. Filter is a
concept about the function of a circuit, not
the circuit itself.

Filter includes both amplitude response
and phase shift. Usually, only amplitude is
plotted.

Common Types of Filters

0
1000
2000
3000
4000
5000
140
120
100
80
60
Frequency
Hz
Power
Spectral
Density
Low pass
filter

Band pass
filter

High pass
filter

Band stop
(notch) filter

Design of Filters

A circuit designed to perform filtering
function on an analog signal is called an
analog filter.

If a signal is digital (converted into a
sequence of number), a filter can be
realized as a mathematical operation, this is
called digital filter.

Digital filter can be done with any
computing device: from a DSP chip to a
computer.

Example of Simple Analog Filters

RC band stop filter.

RC bandpass filters

Example of Simple Analog Filters

RLC resonant filter

Example of Simple Analog Filters

Notch filter application: rejection line 60
-
Hz signal

Example: Test 1 Notch Filter

10
000
100
000
50
000
20
000
30
000
15
000
70
000
0.005
0.010
0.050
0.100
Frequency
Hz
Amplitude
Response
10
000
100
000
50
000
20
000
30
000
15
000
70
000
2.5
2.0
1.5
1.0
0.5
0.0
0.5
1.0
Frequency
Hz
Phase
Shift

Example: Test 1: Bandpass Filter

1000
10
4
10
5
10
6
3
2
1
0
1
2
3
Frequency
Hz
Phase
Shift
1000
10
4
10
5
10
6
10
4
0.001
0.01
0.1
1
Frequency
Hz
Amplitude
Response

Digital Filter

Any filter function can be achieved with digital filter

Micro
-
processor

(DSP)

Signal input

User input

Filtered
signal
output

Digital Filter

This is a filter
This is another filter
This is another type
of filter
This is a filter
This is another filter
This is another type
of filter

Digital filter can also be designed with sharp cut
-
off edge
that is difficult with analog filter.