Transcript
Digital Media LabUmeå University
Computational Perception
Human Information Processing II
Haibo Li
Digital Media LabUmeå University
ComputingSignal Analysis
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
Digital Media LabUmeå University
How to Characterize a Signal?
Digital Media LabUmeå University
Fourier Told Us.........
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
Digital Media LabUmeå University
Consider the situation in which we have two tones of different frequencies presented simultaneously.
+ =
Signal Synthesis
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A preliminary analysis of a sound mixture into individual frequency components
.
.
.
Signal Analysis
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
Digital Media LabUmeå University
400
Leve
l (dB
)
2400. . . 400Le
vel (
dB)
2400. . .
Signal Characterization
Digital Media LabUmeå University
Natural Signals
Spatial frequency
Rel
ativ
e am
plitu
de
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Human Information Processing
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Signal Transmission
Channelx(t) y(t)
X(f) H(f) Y(f)
Y(f)=X(f)H(f)
H(f)
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Channel=”Bandpass Filter”
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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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Brain Wave
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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
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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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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How to Transmit Natural Signals
M
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Modulation
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Modems and Modem Standards
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Nyquist Sampling Rate
t
S(t)
f
S(f)
w
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Nyquist Sampling Rate
t
S(t)
f
S(f)
w
Error-free reconstruction when
fs >=2W
Signal Analysis
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Quantization
R= - 1/2 log2 D bits/sample
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Digital Encoding of Analog Data
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