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# P.E. Exam Prep Question, HELP !

Asked by Alex on 12 Nov 2011

Hey everyone, I'm trying to get prepped from my EE Professional Engineering exam and there is a question that I cannot solve in the prep-guide. I'm hoping that someone might be able to help because it can be solved in MatLab (as noted in the book). Here is the problem description:

*You are an engineer working at a major automotive manufacturer that offers a back-up/obstacle-detection system using sensors installed in the rear bumper. The sensors emit an ultrasonic signal ranging from 40-50 KHz. When an object is present, some of the ultrasonic signal is reflected back and the system will alert to driver to the obstacle. In minimal signal required for this detection is -70dBuV. The amplitude of the returned signal is indicative of the object's size.

Alongside the system, there is an electronic module radiating noise at 75 KHz. The level of this noise can be as high as -60dBuV. In order for this back-up system to function properly, the noise must be 15 dB below the desired signal. Note that the impedance and load impedance is 50 Ohms.

Problem:

Part A. Design an analog filter that will eliminate the impact of the noise on the system in a cost effective manner. Note any impacts that the filter may have on the back-up system.

Part B. Implement an Infinite Impulse Response (IIR) digital filter based on the analog filter in Part A. [Utilize MatLab]

Part C. Implement a Finite Impulse Response (FIR) digital filter that will eliminate the impact of the noise on the system. [Utilize MatLab] *

I really appreciate any help that you all would have to offer! This is the one problem that I haven't been able to solve in the manual!

Thank you!

Walter Roberson on 13 Nov 2011

http://www.mikroe.com/eng/chapters/view/73/chapter-3-iir-filters/

http://www.mathworks.com/help/toolbox/signal/ref/lp2bs.html

Alex on 13 Nov 2011

Hey Walter, I've reviewed your links but do not understand how to apply it to my example. I know it may be a bit to ask, but you could kindly guide me step-by-step through this?

Walter Roberson on 13 Nov 2011

The first link works through the steps you indicated.

The second link is to a specific MATLAB routine that converts low-pass filters to band-stop filters -- and thus does most of the work for you.

I am not qualified to guide you through this step by step -- I haven't designed an analog filter in nearly 40 years, soldering resisters and caps onto breadboards on the kitchen table; and unfortunately at that age I had difficulty understanding impedance (and I had a tendency to overheat the legs on 556 timers, which were new to the market in those days and came out of my allowance...)

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Answer by Naz on 13 Nov 2011

Dont know about question A, but B and C I would do in fdatool in Matlab:

```fdatool
```

Naz on 13 Nov 2011

I guess fdatool is rather for digital filters. Can not give you any advise on analog, sorry. The only thing I would say, filters of higher order will reqiure more delay lines that is more components, more power, more complicated design, however, better frequency response, (phase?).

Naz on 13 Nov 2011

Assuming that you did part A, you should use the parameters of that filter in the part B and C.

Naz on 13 Nov 2011

Oh, yeah. I did not read the actual question. Since they dont say anything about noise below your signal, you can use lowpass filter that will cut off everything above 50kHz. The simplest lowpass filter is just a combination of a resistor and capacitor which is called passive integrator. look this up online.

Answer by Daniel on 13 Nov 2011

While I said I wouldn't answer ...

The question is incomplete requiring assumptions about the phase response and the passband ripple acceptable in the filter. Because of this lack of information you need to choose either a Butterworth or a Chebyshev Type II filter as you analog filters (as they have no passband ripple). Presumably any echo detector is going to be sensitive to phase delays, but there really is nothing you can do in the absence of the required information. This is the type of unspecified job that you should turn down as a professional enigneer.

For the FIR filter, the phase repsonse isn't a problem, but passband ripple is a major problem. In addition a lack of specification on the device implmenting the filter makes evaluating the cost of different filter lengths impossible. Similarly, the frequency at which the signal is sampled isn't specified. In order to prevent aliasing you would need to sample at 150 kHz, but there is no reason to prevent aliasing of a signal you are going to filter out. Creative manipulation of the sampling rate may allow for considerably shorter filters.

## 1 Comment

Alex on 13 Nov 2011

Hey Dan, perhaps this problem isn't worded the best, but this is in the section of the workbook that says there are valid solutions for this problem. There is an entirely different section for problems regarding jobs that professional engineers should or shouldn't take, but this problem is not in that section.

Given that tidbit, from what I've learned, there should be multiple solutions to this problem. Given that the radiating frequency is 75 KHz, we can say that the sampling frequency fs=150 kHz.

I'm having trouble identifying what the pass frequency is in this case (omega_p), the stop frequency (omega_s), the Passband ripple in dB (r_p), and stopband attenuation (r_s).