han q le© ece 3336 introduction to circuits & electronics lecture set #10 signal analysis &...

Han Q Le©

ECE 3336 Introduction to Circuits & Electronics

Lecture Set #10Signal Analysis & Processing –Frequency Response & Filters

Dr. Han LeECE Dept.

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Outline• Review• Signal analysis

– Power spectral density• Frequency response of a system (circuit)

– Transfer function– Bode plot

• Filters– Analog– Digital

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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.

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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.

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Applications of mathematical techniques

Fourier transform

Harmonic function

Complex number

&analysisPhasors

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

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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).

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Example

Antenna

Ground

Inductor

Variable Capacitor

Diode (1N34A)

High-Impedance Earphone

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Schematic

Antenna

Ground

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 circuit10 20 30 40 50

-1.5

-1

-0.5

0.5

1

1.5

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Link to Mathematica file: AM FM

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– Power spectral density• Frequency response of a system (circuit)



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Signal Fourier (or harmonic) Analysis

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

xt a 0 n 1 a n C osn t n 1

b n Sinn t In complex (or Euler) representation, Fourier

series coefficients Xm are phasor components,

xt m X m m t

X m X m m

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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 | Xm | vs. frequency,

or usually | Xm |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 fm vs. frequency

X m X m m

X m X m

X m X m m

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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.

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The Electromagnetic Spectrum

Visible

UV & solar blind

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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 H z

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Example of Spectra

0 1000 2000 3000 4000 5000

120

100

80

60

0.79 s 11 025 H z

0 1000 2000 3000 4000 5000 3

2

1

0

1

2

3

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– Power spectral density• Frequency response of a circuit



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Example

R

C

output vout[t]i(t)input vin[t]

t

R

Cinput vin[t] output vout[t]i(t)

t 1

1 t

1

t

Frequency Response

or, Frequency Transfer FunctionH 1

1

H 1

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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:

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Example: Test 1

H C 2 L 2 R 3 21 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

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Bode Plot for Vout in Test 1

1000 104 105 106 3

2

1

0

1

2

3

F requency HzPh

ase

Shif

trad1000 104 105 106

10 4

0.001

0.01

0.1

1

F requency Hz

Am

plit

udeR

espo

nse

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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.

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Example

0.00.51.0 1.52.02.5 3.00.60.40.20.00.20.40.6

0.00.51.0 1.52.02.5 3.0

0.40.20.00.20.4

0.0 0.5 1.0 1.5 2.0 2.5 3.02

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

Cinput vin[t] output vout[t]i(t)

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– Power spectral density• Frequency response of a circuit



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General Filter Concept Review

0 1000 2000 3000 4000 5000

140

120

100

80

60

Frequency H zPow

erS

pect

ralD

ensi

tyThis is a filter This is also filter This is another filter

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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.

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Common Types of Filters

0 1000 2000 3000 4000 5000

140

120

100

80

60

Frequency H zPow

erS

pect

ralD

ensi

tyLow pass filter

Band pass filter

High pass filter

Band stop (notch) filter

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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.

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Example: Test 1 Notch Filter

10 000 100 00050 00020 000 30 00015 000 70 000

0.005

0.010

0.050

0.100

F requency HzA

mpl

itud

eRes

pons

e

10 000 100 00050 00020 000 30 00015 000 70 000 2.5

2.0

1.5

1.0

0.5

0.0

0.5

1.0

F requency Hz

Phas

eSh

iftrad

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Example: Test 1: Bandpass Filter

1000 104 105 106 3

2

1

0

1

2

3

F requency Hz

Phas

eSh

iftrad

1000 104 105 106

10 4

0.001

0.01

0.1

1

F requency Hz

Am

plit

udeR

espo

nse

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Digital Filter• Any filter function can be achieved with digital filter

Micro-processor(DSP)

Signal input

User input

Filtered signal output

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Digital Filter

This is a filterThis is another filter This is another type

of filterThis is a filterThis 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.

han q le© ece 3336 introduction to circuits & electronics lecture set #10 signal analysis &...

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