digital signal processing a merger of mathematics and machines 2002 summer youth program electrical...
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Digital Signal ProcessingDigital Signal ProcessingA Merger of Mathematics and A Merger of Mathematics and
MachinesMachines
2002 Summer Youth ProgramElectrical and Computer Engineering
Michigan Technological University
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Signals and Sounds
The simplest signal is the sinusoid:
t
t
t
t
frequency = 500 Hz
frequency = 1 KHz
frequency = 2 KHz
frequency = 4 KHz
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Signals and Sounds
Sums of sinusoids
0 0.005 0.01 0.015 0.02-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
time (seconds)
ampl
itude
))(cos())(cos()( t12092t9412tx
941 1209 f
‘spectral’ representation
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Signals and Sounds
1 2 3
4 5 6
7 8 9
* 0 #
697 Hz
941 Hz
852 Hz
770 Hz
1209
Hz
1336
Hz
1477
Hz
s t f t f trow column( ) cos( ) cos( ) 2 2
Dual-tone multiple frequency (DTMF)
Frere Jacques
Olympic Fanfare
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Signals and Sounds
time (seconds)
fre
que
ncy
(Hz)
2 4 6 8 10 12
0
500
1000
1500
2000
2500
3000
3500
4000
Olympic Fanfare
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Signals and Sounds
What other signals (or sounds) can we make from sinusoids?
– Answer: ALL OF THEM!
This is Fourier theory and it forms the basis for many branches of electrical engineering.
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
The Common Loon
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Pied-Billed Grebe
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Tundra Swan (Whistling Swan)
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Signals and Sounds
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
time (seconds)
ampl
itude
250 1250
750 1750
2250 f
Signal Spectrum
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Signals and Sounds
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
time (seconds)
ampl
itude
250 f
Signal Spectrum
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
time (seconds)
ampl
itude
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Filtering
One of the key concepts in signal processing is the idea that systems can be built to analyze or modify a signal’s spectrum.
– Applications:• speech recognition• speaker recognition• noise removal
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Filtering
+
noise
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Filtering
0 500 1000 1500 2000 2500 3000 3500 4000 45000
50
100
150
200
250
300
frequency (Hz)
gain
frequency response
H(f)
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Filtering
time (seconds)
fre
que
ncy
(Hz)
0.5 1 1.5 2 2.5 3 3.5 4
0
2000
4000
6000
8000
10000
+
noise
time (seconds)
fre
que
ncy
(Hz)
0.5 1 1.5 2 2.5 3 3.5 4
0
2000
4000
6000
8000
10000
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Filtering
H(f)time (seconds)
fre
que
ncy
(Hz)
0.5 1 1.5 2 2.5 3 3.5 4
0
2000
4000
6000
8000
10000
time (seconds)
fre
que
ncy
(Hz)
0.5 1 1.5 2 2.5 3 3.5 4
0
2000
4000
6000
8000
10000
0 2000 4000 6000 8000 10000 120000
0.5
1
1.5
2
2.5
3
3.5
frequency (Hz)
gain
frequency response
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Digital Signal Processing
A-to-D D-to-ADSPanalog analogdigital digital
Analog signals are continuous in time and amplitude.
Digital signals are discrete in time and amplitude.
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Sampling
16 bits gives 216 = 65,536 amplitude levels
8 bits gives 28 = 256 amplitude levels
4 bits gives 24 = 16 amplitude levels
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Sampling of Sound
16 bits (CD quality) 12 bits 8 bits (phone quality) 16 bits / 8 bits 8 bits / 6 bits 8 bits / 4 bits 8 bits / 2 bits
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Digital Signal Processing
Digital filters are really simple!– four-sample moving average filter
– recursive (feedback) filter
44nx2nx1nxnx
ny)()()()(
)(
)()(.)( nx1ny90ny
Department of Electrical and Computer Engineering
Copyright Michigan Technological University
2002 Summer Youth Program
Pictures Too!