human information processing ii
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Digital Media LabUmeå University
Computational Perception
Human Information Processing II
Haibo Li
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Digital Media LabUmeå University
ComputingSignal Analysis
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Digital Media LabUmeå University
A Typic Signal
Time
Pres
sure
One cycle
Frequency = number of cycles per second
unit of frequency: Hertz (Hz)
e.g. 400 Hz = 400 cycles per second
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Digital Media LabUmeå University
How to Characterize a Signal?
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Digital Media LabUmeå University
Fourier Told Us.........
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Digital Media LabUmeå University
Fourier Transform
Pres
sure
TimeFreq
Pres
sure
Pres
sure
TimeFreq
Pres
sure
SSinewaveinewavepitch ~ frequency
unidimensional (low to high)
range of hearing: 20 Hz – 20000 Hz
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Digital Media LabUmeå University
Consider the situation in which we have two tones of different frequencies presented simultaneously.
+ =
Signal Synthesis
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Digital Media LabUmeå University
A preliminary analysis of a sound mixture into individual frequency components
.
.
.
Signal Analysis
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Digital Media LabUmeå University
Fourier Transform
Pres
sure
Time
Freq
Pres
sure
f 2f
f 3f 5f 7f 9f
1/31/5 1/7 1/9
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Digital Media LabUmeå University
400
Leve
l (dB
)
2400. . . 400Le
vel (
dB)
2400. . .
Signal Characterization
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Digital Media LabUmeå University
Natural Signals
Spatial frequency
Rel
ativ
e am
plitu
de
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Digital Media LabUmeå University
Human Information Processing
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Digital Media LabUmeå University
Signal Transmission
Channelx(t) y(t)
X(f) H(f) Y(f)
Y(f)=X(f)H(f)
H(f)
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Digital Media LabUmeå University
Channel=”Bandpass Filter”
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Digital Media LabUmeå University
Effect of degrading the speech signal by spectral filtering
The original speech signal contains significant energy up to 7 kHz
a) signal bandpass filtered (0.25 - 0.75 kHz)
b) signal bandpass filtered (1.0 – 3.0 kHz)
c) original signal
Effect of Bandpass
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Digital Media LabUmeå University
Brain Wave
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Digital Media LabUmeå University
Bandpass System
Most long-haul transmission systems have a bandpassFrequency response
The transfer function can be written as
)(11)(
ffo
fofjQ
fH−+
=
where the resonant frequency fo and quality factor Q are
LCof
π21= L
CRQ =
Qfo
lu ffB =−=
The 3dB bandwidth between the lower and upper cutoff
frequencies is
=
R
L C
B
fl fo fu
f
1.00.707
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Digital Media LabUmeå University
Bandpass SystemSince practical tuned circuits usually have 10 < Q <100,the fractional bandwidth B/fc should be kept within the range
1.001.0 <<cf
B
As a rough rue of thumb, the carrier frequencies and corresponding nominal bandwidth can be
cfB 02.0≈
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Digital Media LabUmeå University
Bandpass System
1013 Hz5x1014 HzOptical2 GHz1 00 GHzMillimeterwave
100 MHz5 GHzMicrowave2 MHz100 MHzVHF
100 kHz5 MHzShortwave radio2 kHz100 kHzLongwave radio
BandwidthCarrier frequency
Frequency band
Selected carrier frequencies and nominal bandwidth
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Digital Media LabUmeå University
How to Transmit Natural Signals
M
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Digital Media LabUmeå University
Modulation
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Digital Media LabUmeå University
Modems and Modem Standards
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Digital Media LabUmeå University
Nyquist Sampling Rate
t
S(t)
f
S(f)
w
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Digital Media LabUmeå University
Nyquist Sampling Rate
t
S(t)
f
S(f)
w
Error-free reconstruction when
fs >=2W
Signal Analysis
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Digital Media LabUmeå University
Quantization
R= - 1/2 log2 D bits/sample
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Digital Media LabUmeå University
Digital Encoding of Analog Data
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Digital Media LabUmeå University