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This shows how we analyzed the returned signal to get out the information on velocity.

Approach: simulating signal

Another part of the RADAR system is that it can determine the velocity of objects. For our project, we had to build up a signal to send out. Then we simulated what that signal would be if it bounced off of an object in space moving at a certain velocity.

We decided that the simplest waveform to send out was a pulse train with each pulse being a certain width of L samples (like a boxcar signal in continuous time). Here is the function: pulsetrain.m . The pulses occured every M samples. There are N total pulses in the sent signal. An example is given below for L=7, M=19, and N=8.

Signal of train pulses

Signal sent for L=7, M=19, and N=8.

Velocity analysis block diagram

Velocity Analysis Block Diagram

Then to simulate the channel, we added noise to the signal (complex Gaussian noise). To simulate the signal reflecting off of a moving object, we added a phase shift to the signal (multiplied the signal by a complex exponential with a certain phase.)

Why a phase shift? When a wave bounces off of a moving object, the frequency of the returning signal changes. This effect is well known as the Doppler shift. An other example of this would be the siren of an ambulance. While the ambulance is moving towards you, the sound of the siren is higher in frequency because the movement of the ambulance compresses the soundwaves a little bit. If the ambulance is moving away, the siren sounds lower in pitch. This is similar to what the RADAR does. The wave bounces off the object, and if the object is moving towards the RADAR device, then the waves are compressed and the frequency is shifted up. On the other hand, if the object is moving away from the RADAR device, then the frequency is shifted down.

Approach: analyzing the signal for veloctiy

After simulating the signal, we had to design a system that would analyze this received signal and approximate the velocity of the object moving. In order to detect the frequency shift between the original sent signal and the received signal, we first had to take into account the DC offset. This is easily managed by subtracting the mean of the signal from the signal itself. Now it is possible to take the FFT of both the sent and received signal and to see the spectrum of the two. The shift of the spectrum from the one to the other signal shows the Doppler shift.

Original fft

FFT of sent signal

Shifted fft

FFT of received signal (notice the phase shift?)

Once we had the two spectrum to compare, we had to find a way to detect the shift between the two. What we decided was that we would look at the peaks of each and tell what frequencies represented them. In order to improve on this, we initially found the peak from the fft, then we did another fft of higher resolution on a tighter range around the initially detected peak in order to get a more accurate location of it. After this, we compared the two peak frequencies by subtracting the peak of the received signal from that of the sent signal. This was the doppler shift that we were looking for.

Now the math was simple. There is an equation (given below) that can calculate the velocity given your doppler shift, the carrier frequency of the radar, and the speed of light. Note that because we were sampling the signal at a given sampling rate, this equation needs to be modified a little by dividing the right hand side by the sampling frequency as well.

f d 2 v f c c

Solving this equation for the velocity (v), we came up with the approximation for the velocity of the moving object. The Matlab function that combines many of these steps can be seen here: imptrainconv.m

Other Matlab functions that helped: ptsamp.m , chirptrain.m , convchirp.m .

Now to Results: Results for Velocity

Questions & Answers

can someone help me with some logarithmic and exponential equations.
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sure. what is your question?
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I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
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what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
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a perfect square v²+2v+_
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or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
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Kristine 2*2*2=8
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Differences Between Laspeyres and Paasche Indices
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No. 7x -4y is simplified from 4x + (3y + 3x) -7y
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Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
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after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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Source:  OpenStax, Ece 301 projects fall 2003. OpenStax CNX. Jan 22, 2004 Download for free at http://cnx.org/content/col10223/1.5
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