Transcript An Overview of Delay-and- sum Beamforming Student: Wong Hok Him

DSP Seminar (1st semester, 2006 - 2007)
An Overview of Delay-andsum Beamforming
Student: Wong Hok Him
Supervisor: Professor P.C. Ching
Date: 11th January, 2007
Outline
•
•
•
•
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Objective
Introduction
Delay-and-sum Beamforming
Future Works
Q&A
Objective
Design a small-dimensional microphone
array for beamforming in an acoustic
environment with the presence of noises
Introduction
(1)
Microphone
– Characterized by a spatial directivity pattern,
which specifies the gain and phase shift that
the microphone gives to a signal coming from
a certain direction (angle-of-arrival)
1
0.5
0
0
Fre 1000
que
2000
ncy
(Hz 3000
)
0
45
90
135
Angle (deg)
180
Introduction
(2)
Spatial directivity pattern
– Function of angle-of-arrival and frequency
– Transfer function for source of a particular
frequency  at angle 
Z  , 
H  ,  
S  
Introduction
(3)
Received signals from different microphones
z[k ]
Filtering

f1[k ]
f1[k ]
f 2 [k ]
y1 [ k ]
f1[k ]
f M [k ]
Summing
“Virtual” spatial directivity pattern
y1 [ k ]
y1 [ k ]
y 2 [k ]
y M [k ]
Introduction
(4)
Spatial filter design is based on two factors
– Microphone characteristics
– Microphone array configuration
Introduction
(5)
Beamforming
– Can be thought of as spatial filtering
– Can increase the receiver sensitivity in the
direction of wanted signals
– Can decrease the receiver sensitivity in the
direction of interferences and noises
Introduction
(6)
Two categories of beamforming
– Fixed beamforming
• Delay-and-sum beamforming
• Weighted-sum beamforming
• Filter-and-sum beamforming
– Adaptive beamforming
• LCMV beamforming
• Generalized sidelobe canceller
Covered in this seminar
Introduction
(7)
Basic differences between fixed and
adaptive beamforming
Fixed
beamforming
Adaptive
beamforming
Fixed filters
Adaptive filters
Data-independent
Data-dependent
Introduction
(8)
Assumptions
– Microphone gain = 1 at all angles for all
frequencies
– Far-field source (plane waveforms)
Delay-and-sum Beamforming
(m  1)d cos 
fs
y m k   sk   m  , where  m   
c
Ym  ,    e  j m   S  
1
zk  
M
(m  1)d cos 
y m k   m , where  m 
fs

c
m 1
M
(1)
Delay-and-sum Beamforming
1
Z  ,   
M
1

M
M
e
m 1
M
e
m 1
j m
Ym  ,  
j m
e
 j m  
S  
H  ,   
(2)
Z  ,  
S  
1

M
M
e
m 1
 j  m 1
d cos   cos  
fs
c
Delay-and-sum Beamforming
(3)
Simulation settings
– Number of microphones M = 5
– Distance between neighbouring microphones
d = 0.03 m
– Sampling frequency fs = 16 kHz
– Source frequency f = 5000 Hz
Delay-and-sum Beamforming
(4)
Future Works
• Investigate into adaptive beamforming, e.g.
GSC, which has the ability to minimize
noises
• Perform simulations to compare the
performances of various existing types of
adaptive beamforming in a noisy
environment
Reference
Microphone Array Processing, Marc
Moonen, Dept. E.E., EAST, K.U.Leuven