波束成形技术（Beamforming 101） 2008-11-27 19:20
Beamforming enables you to find problems in your system before they occur. As Martin explains， you can perform your own investigation with a computer， a dual-channel A/D card墨田， a pair of microphones， and some software.
Tensions are high and a hostile submarine lurks in the waters just off the coast. A patient exhibits troubling symptoms-do layers of tissue mask a tumor？ A driver checks his mirrors and begins to change lanes but never es the truck hiding in his blind spot.
It‘s better to go looking for trouble than to have it find you. But how do you do that？ Whether it's subhunting sonar， medical ultrasound，or collision-avoidance radar， how do you uncloak danger？
One important arrow in your quiver is beamforming. Think of it as a way to focus and measure the energy falling on an array of nsors as you "look" in different directions. You
can do your own handson investigation with only a computer牙龈肿怎么办，美容洗脸手法教程a dual-channel A/D card， a pair of microphones人意险， and the software developed in this article.
Beamforming techniques come in two flavors： adaptive and fixed. Adaptive methods are haute cuisine. Fixed methods are burgers with fries. Each has its place， but blue-collar fare will be rved up here.
TIME DOMAIN BEAMFORMING
To understand how beamforming works， picture a line of identically spaced microphones. Next， imagine a wavefront consisting of noi plus the signal you want to detect， striking this uniform line array. Finally，make two common simplifications，valid for many applications. One，assume that the wavefront originated in the far field so that it can be approximated as a flat surface propagating toward the array and any curvature it possd near the source can be disregarded. Second， ignore the three-dimensional quality of wave propagation and restrict your attention to the two-dimensional plane. With
this in mind， Figure 1 shows what it would look like if you wanted to focus the energy arriving perpendicular （broadside我国的基本国情）感统课to the array.
Each phone is excited by the same wavefront at the same time. To get the total energy falling on the array at any instant， sum together the data from each phone. Refer to Figure 2 if you want to focus the energy from some other direction.
To sum the energy across a given wavefront， you need to inrt delays becau the wa
vefront has to travel a different distance to strike each phone. The extra distance the wavefront travels from one phone to the next is d sin θ， where d is the uniform spacing between the phones and θ，the look direction， is by convention measured clockwi from broadside to the array. If the wavefront travels through the medium（e.g.， air or water） at speed c， then the difference between the time it strikes one phone and the next is （d sin θ）/c. Generalizing， from Figure 2 the wavefront strikes phone p at （pd sin θ）/c units of time before it strikes the reference phone. So， for phone p and time t， if you call the phone‘s respon yp（产品等级t）， then the time-shifted summed output of the line array is given by：
where P is the number of phones in the line array， numbered from 0 to P - 1.
Great， you're done. Just sweep around the array and find the direction that gives the m
aximum respon， right？ Actually， in practice，this time domain， delay， and sum beamformer has drawbacks becau the data acquired is sampled精神明亮的人， not continuous.
For an ADC clocking in data at some constant interval Δt， t can assume only values that are integer multiples of Δ。 Of cour， that also means y is known only at integer multiples of the sample interval as well. Equation 1 says you want the value read from each phone （the y values） at time：
With Δt， d， and c fixed， and n and k restricted to be integers，this limits the available choices for the look direction， θ。What should you do？
PHASE SHIFT BEAMFORMING
If you‘re looking for periodic signals， like the vibration produced by rotating machinery，you can u the Fourier transform and work with Equation 1 in the frequency domain instead of the time domain. （If you're not familiar with the Fourier transform，you can treat it as a black box who output provides the magnitude and pha of the frequencies inherent in a time domain input.）
To begin， let the frequency-dependent function Yp（ω） be the Fourier transform of the time-dependent function yp（t）。 Then， according to the shifting property， the Fourier transform of：
is as follows：
Equation 1 transforms as：
The variables in Equation 5 are continuous. However， becau your data is sampled， in practice you will apply the discrete Fourier transform with N bins， and for a reprentative bin n the discrete form of Equation 5 is：
