Does a Master's Degree Give You an Advantage in Your FE Exam Preparation?

Passing the Fundamentals of Engineering (FE) exam and gaining an Engineering in Training (EIT) certification is the first step in the journey of becoming a licensed professional engineer in the United States. The exam is designed to test an individual's knowledge of fundamental engineering principles and their ability to apply that knowledge in practical ways. Passing the FE exam is required before an engineer can take the Professional Engineering (PE) exam and obtain their engineering license. This begs the question, would having a master's degree give you an advantage when taking the FE exam? There are a few key factors to consider when considering this question.

Does a Master's Degree Give You an Advantage in Your FE Exam Preparation?

1. Academic Knowledge

2. Problem-Solving Abilities

3. Studying and Test-Taking Strategies

4. Self-Motivation

Academic Knowledge

A master's degree will provide you with advanced technical knowledge and a deeper understanding of engineering concepts, which can certainly help when taking the FE exam. The FE will test your knowledge of subjects like mathematics, statistics, chemistry, physics, engineering economics, ethics, and more. All of these general topics will be covered in greater depth and technical detail at the graduate level compared to an undergraduate engineering degree. The advanced coursework and research conducted for a master's program expand your base of engineering knowledge, which you can leverage for the FE exam.

However, it's important to note that the FE exam is focused on only testing fundamentals rather than highly advanced concepts. Much of the exam covers engineering principles and skills that would be introduced and developed in an undergraduate program. So, while additional technical knowledge from a master's can be useful, it's not necessary nor required to pass the FE if you already have a solid grasp of the core fundamentals from an accredited undergraduate engineering program. The FE aims to set a minimum level of competency for all engineers at the early stages of their careers.

Problem-Solving Abilities

More so than just technical knowledge, the FE exam emphasizes critical thinking and problem-solving skills. You have to be able to analyze engineering situations and apply foundational concepts to solve quantitative problems. A master's degree may provide an advantage in that sense, considering several of their courses are aimed at developing strong analytical and problem-solving abilities.

Graduate-level coursework and research require a student to investigate open-ended problems, evaluate alternatives, and think through solutions rigorously. Master's programs also emphasize higher-order skills like critical thinking, data analysis, and logical reasoning. Dealing with complex technical concepts and assignments hones your ability to parse information, extract key insights, and make calculations—abilities all very relevant to the FE exam. While undergraduate studies certainly teach problem-solving as well, the more advanced skills developed in a master's program can further boost your proficiency.

Studying and Test-Taking Strategies

Pursuing a master's degree also helps develop general studying and test-taking abilities that could easily be applied to your FE exam preparation. A master's coursework requires managing a heavy workload, synthesizing large amounts of information, and applying knowledge across multiple domains. Conducting research develops skills like information gathering, statistical analysis, and technical writing. Master's students have to stick to deadlines, manage stress, and get comfortable taking exams in advanced subjects. These skills earned through graduate school prepare examinees for detailed studying, time management, and test-taking, which are invaluable when preparing for and taking the rigorous 6-hour FE exam.

There have been many who have excellent study habits and many who have certainly prepared well for the FE with just an undergraduate background. The experience of pursuing a master's degree provides an additional level of preparation for those who may need it. The demands of graduate-level academics serve as good training for both the content and process of taking the FE exam.

Self-Motivation

Finally, the drive and self-motivation required to pursue a master's degree beyond your undergraduate education also translate into a greater focus on FE exam preparation. Succeeding in a master's program requires disciplined studying, passion for your field, and the ability to self-motivate over an extended period of time. These soft skills around dedication and focus are important when taking on the challenge of the FE exam. If you have the motivation to consistently study and improve over the 1-2 years of a master's program, you will likely also have the right mindset to stay committed to your FE exam preparation.

While someone without a master's can certainly be highly motivated as well, and there have been many who have done so, the determination demonstrated by pursuing (and completing) a graduate degree shows you have the kind of work ethic and persistence needed to pass the FE. If you have conquered the rigors of a master's program, you have also likely developed the self-motivation needed to fully dedicate yourself and put in the hours required to study and be ready for the FE.

In summary, a master's degree can provide some advantages when preparing for the FE exam, such as:

• Deeper academic knowledge, especially in advanced math/science topics
• Enhanced critical thinking and problem-solving abilities
• Improved study and test-taking strategies
• Higher levels of self-motivation and dedication

However, a master's degree is not required to pass the FE exam; plenty of individuals without a master's degree succeed in passing the exam each year. With proper preparation using undergraduate education and FE exam-specific study materials, you can develop the fundamental engineering knowledge and skills needed to do well. The FE aims to test basic competency and is fully feasible without a master's degree. However, the advanced engineering proficiency and academic maturity gained in graduate studies can provide an incremental benefit.

Conclusion

Ultimately, the FE exam tests your comprehension of core engineering principles and your ability to solve problems efficiently. The pursuit or completion of a master's degree would only strengthen both comprehension and problem-solving through advanced technical knowledge and overall academic development. But, for many, it is not mandatory. With diligent preparation, both master's graduates and undergraduates can perform well on the FE exam and take the first step to professional engineering licensure. The degree to which a master's degree helps mostly depends on the quality of the program and your effort to leverage the experience for your FE exam preparation.

Whether you have a master’s degree or not, we can help you pass your FE exam on your first try! Join the tens of thousands of engineers who’ve passed their FE exam with School of PE. Register now!

About the Author: Khoa Tran

Khoa Tran is an electrical engineer working at the Los Angeles Department of Water and Power and is currently pursuing his master's in electrical Power from the University of Southern California. He is fluent in both Vietnamese and English and is interested in outdoor activities and exploring new things.

Ultimate Guide to Balancing Study Time for the FE Exam

Studying for the Fundamentals of Engineering (FE) exam can feel overwhelming. With so much material to cover, it's crucial to have an effective study plan to manage your time wisely. As a former engineering student who successfully passed the FE exam, I've discovered some time management solutions that have helped me tremendously to maximize my preparation. In this blog post, I'll share the best tips I've learned for developing an FE exam study schedule, sticking to it, and retaining what you learn.

In this Blog,

1. Create a Study Calendar

2. Take Practice Exams

3. Follow the NCEES Practice Exam Format

4. Use Memory Techniques

5. Study in Groups

6. Try Timers for Focused Sessions

7. Review Key Concepts Before Bed

8. Eat Brain Foods

9. Review, Don't Cram

Create a Study Calendar

The first step is to make a realistic calendar that maps out the weeks and months leading up to your exam date. Outline how many hours you can devote to studying each day and week. The general rule of thumb is to study 200-300 hours total over several months. Calculate what pace you need to maintain to reach your target hours.

I recommend studying 10-15 hours per week if you have 3-4 months until test day. Break that down into 3-4 study sessions per week. Studying every day for short bursts of time is more effective than cramming on weekends. Your brain does better at absorbing and retaining information through consistent repetition than through an impulse of learning.

Once you've created your FE exam study calendar, do your best to stick to it! Treat study sessions like important appointments that can't be rescheduled. However, build in some wiggle room for inevitable busy weeks or emergency interruptions. Life happens; adjust your schedule accordingly, but don’t forget to get right back on track the following week.

Take Practice Exams

Taking timed practice exams is one of the most valuable ways to prepare for the FE exam. Full-length practice tests closely simulate the actual testing environment, giving you a realistic assessment of your knowledge. Here are some tips for using practice tests effectively:

• Take your first practice test 2-3 months before the exam to identify weak areas to focus on. Take another one 1-2 months out, and your final test just before exam day.
• Strictly follow the 5-hour 20-minute time limit to build your test-taking endurance.
• Grade each test thoroughly and note the concepts/types of problems you missed. Emphasize reviewing trouble topics in your following study sessions.
• Pay attention to how you felt physically and mentally while taking the practice exam. Adjust your schedule to prevent any onset of burnout.
• Purchase at least 2 different practice exams. Repeating the same test won't help as much. Varying your practice gives a well-rounded experience.

Follow the NCEES Practice Exam Format

The National Council of Examiners for Engineering and Surveying (NCEES) designs the FE exam and regularly updates the exam specs. It is best to follow their test specifications closely when you prepare for your exam. Look for a practice exam in the format of the real exam, like the ones School of PE offers.

The exam covers 110 questions and is 5 hours and 20 minutes long. All the questions will be either multiple choice or alternative item types such as:

• Multiple correct options (allows multiple choices to be correct)
• Point and click (requires examinees to click on part of a graphic to answer)
• Drag and drop (requires examinees to click on and drag items to match, sort, rank, or label
• Fill in the blank (provides a space for examinees to enter a numerical response to the question)

Study with the NCEES breakdown in mind.

Use Memory Techniques

With so many equations, constants, conversions, and formulas to remember, using memory techniques is crucial for recall on test day. Here are two effective strategies I use:

Chunking - Group concepts or steps that go together into "chunks". Then, memorize the chunks as a whole. This prevents your brain from getting overloaded.

Mnemonics - Create acronyms, rhymes, songs, or mental images to represent concepts. Associating information with visuals or music makes it stick better.

Study in Groups

Studying with other FE exam takers has many benefits beyond moral support. Group members can quiz each other, explain tricky concepts, and share study resources. Having to verbalize your knowledge out loud helps strengthen your understanding. Just be sure to stay on task and take breaks to avoid mental fatigue.

If your college doesn't have an FE review group, check social media for local study partners. There are also online FE exam preparation groups where you can connect virtually. Studying together keeps you accountable and motivated!

Try Timers for Focused Sessions

With so much material to cover, maintaining focus is a challenge. Timers and productivity apps are useful for keeping study sessions targeted. Here are some you can try:

• Pomodoro Technique - Study intensely for 25 mins, take a 5 min break. After 4 rounds, take a 30-minute break.
• Forest - This app lets you set a time limit and grow a virtual tree while you stay off your phone. If you switch apps before the timer ends, the tree dies.
• Be Focused - Customize sessions with timed intervals of working, short breaks, and long breaks.
• Focus Keeper - Alternate between focused study and rest periods. Track your daily progress.

I like to switch up my timer style every few sessions to keep my brain engaged. The forced breaks help processing and retention.

Review Key Concepts Before Bed

In the last hour before bedtime, review your highlighted notes or flashcards on foundational concepts. Repetition right before sleep helps strengthen and consolidate memory. This practice really works - I can often recall entire equations the next morning!

Make your "before bed review" quick, about 10 minutes. Don't do any intense problem-solving that will keep your mind too active. The key is falling asleep promptly so memory integration can occur overnight.

Eat Brain Foods

You'll retain so much more studying while properly nourished. Complex carbs provide steady energy, protein aids concentration, and antioxidants boost brain function. Some of my go-to study snacks include:

• Oatmeal with berries
• Greek yogurt with mixed nuts
• Apple with peanut butter
• Carrots with hummus
• Trail mix
• Green tea

Drink plenty of water to stay hydrated as well. Proper nutrition gives both your body and mind the resources to perform at your peak.

Review, Don't Cram

If the exam is just a week or two away, resist the urge to panic cram! Review key concepts methodically instead. Re-work any practice problems that you have struggled with. Skim through flashcards. But don't try digesting new material. Stick to strengthening your existing knowledge.

Cramming overload causes mental fatigue faster. To simulate the endurance needed on exam day, treat the last week as a practice run. Maintain your regular study hours and methods. Get plenty of rest the night before the test. You'll feel confident and prepared walking in.

While studying for a big exam like the FE can feel overwhelming at times, staying organized and managing your time effectively makes reaching your goal totally doable. Implementing just a few of these tips can optimize your study plan. Maintain self-care, stick to your schedule, and keep chipping away consistently. I hope these strategies for balancing FE exam prep with daily life can help maximize your study time. With determination and commitment, you've got this!

If you’re interested in a comprehensive course designed to help you pass your FE exam on your first try, check out School of PE! School of PE's #1-rated engineering exam review courses have provided tens of thousands of professionals with the tools to pass their exams.

About the Author: Khoa Tran

Khoa Tran is an electrical engineer working at the Los Angeles Department of Water and Power and is currently pursuing his master's in electrical Power from the University of Southern California. He is fluent in both Vietnamese and English and is interested in outdoor activities and exploring new things.

FE Exam or Engineering Experience: Which Comes First?

Many engineering students wonder if they need to pass the Fundamentals of Engineering (FE) exam before beginning their engineering careers and gaining industry experience. The short answer is no - you do not have to pass the FE exam before beginning your engineering career. However, there are several good reasons to take and pass the exam as early as possible. Here is an in-depth look at the FE exam and whether you need to pass it before gaining experience.

In this Blog,

1. Do You Have to Pass the FE Before Gaining Experience?

2. How Long to Study for the FE Exam?

3. Should You Work Before Taking the FE Exam?

4. How to Prepare for the FE Exam

5. What's Next After Passing the FE Exam?

6. Key Takeaways

Do You Have to Pass the FE Before Gaining Experience?

Nothing is stopping you from working as an engineer before taking or passing the exam. The FE is not a prerequisite to begin working after graduation.

However, there are a few reasons why you may want to take the FE exam as soon as you can:

1. The concepts are fresh in your mind.

Engineering students typically take the FE exam right after graduation, as the test material is still fresh in their minds. The FE tests your comprehension of basic engineering principles, which you should have learned during your undergrad.

Engineering knowledge is freshest after graduation, making the FE exam a bit easier. Your undergraduate coursework should have prepared you with broad engineering and scientific fundamentals to handle the breadth of the FE.

Studying and passing the exam only gets more difficult and time-consuming the longer you are out of school. Preliminary review suggests new graduates have higher FE exam pass rates than those further into their careers.

The further you get from your college courses, the harder it will be to recall conceptual topics that you may not use regularly in your job. Reviewing and relearning concepts you’re rusty on will require extra time and effort.

2. You must take it before taking the PE exam and earning your PE license.

To get your PE license, the first step is to pass the FE exam and gain relevant work experience, usually four years. If your goal is to become a licensed Professional Engineer, you’ll want to pass the FE exam as soon as possible.

Gaining the 4+ years of experience required to take the PE exam and your PE license takes time. Knocking out the FE exam requirement early lets you get the licensure clock ticking as soon as possible.

The FE and PE exams are spaced apart by design. Passing the FE as soon as you can after graduation clears a major hurdle on the path to licensure. The PE license application process can't formally start until you pass the FE. Waiting to take the test delays earning your PE credential.

3. Some employers require it.

While not all engineering jobs require the FE or PE, there are always some exceptions to the rule. Certain employers make passing the FE an official condition of hiring and continued employment for engineering positions.

For example, civil engineers working on public construction projects may need licensure to comply with contracts. Their employer likely requires passing the FE.

If your target companies do not require the FE upfront, you still gain an edge over other applicants by passing the exam early. It shows commitment to professional development.

4. It will boost your resume.

While not strictly required for non-licensure careers, passing the FE exam still looks impressive on a resume. It demonstrates you have acquired a body of engineering knowledge and possess analytical problem-solving skills.

The FE shows initiative to go above and beyond and master your foundational engineering education. Some companies may offer promotions and raises to engineers who pass the FE or pursue licensure.

How Long to Study for the FE Exam?

Studying for the FE exam takes dedication. The test covers a wide range of engineering topics, so thorough prep is essential.

On average, examinees spend 80-100 hours studying to pass the FE exam. Preparation time depends on your engineering discipline and academic background.

Some accelerated FE exam prep courses claim you can cram in just 5 weeks. However, most examinees study for 2-3 months to truly cement knowledge and practice working speed. Don’t underestimate the exam - take time to prepare properly.

The FE exam recently transitioned to a computer-based format, allowing year-round testing. This gives flexibility to take the FE when you feel ready rather than waiting for specific dates. Just be sure to meet registration deadlines.

Earning an engineering degree shows you have the knowledge. Passing the FE proves you can apply that knowledge efficiently. Dedicate the time to refresh concepts and practice working on exam problems at a brisk pace.

Should You Work Before Taking the FE Exam?

There are no rules saying you can't gain engineering experience before passing the FE exam. Working for a few years before taking the test is fairly common.

However, don't wait too long after graduation. Some pros of gaining experience before attempting the FE include:

• Earning money to finance FE prep materials and expenses
• Gaining some field experience to inform exam studying
• Having more "think like an engineer" problem-solving practice

Yet, spending too long outside of school can work against you. Engineering concepts won't get reinforced and will become rustier. Plus, you may find it harder to find the time and motivation for rigorous FE studying after starting your career.

Ideally, take the FE exam within two years of finishing your engineering degree. This strikes a balance between allowing some field experience while concepts are still fresh.

How to Prepare for the FE Exam

Whatever your experience level, disciplined preparation helps boost FE exam success:

• Use the NCEES exam specifications to focus studying on the topics covered. Review college textbooks and notes.
• Work through many practice problems under timed conditions. Practice builds speed and accuracy.
• Learn the FE exam format and how to strategically tackle questions. Don't waste time on difficult problems.
• Master your calculator to efficiently handle mathematical computations. Bring spare batteries.
• Brush up on fundamentals you haven’t used recently, like chemistry, physics, or advanced math.
• Take a review course with a top-ranked exam prep provider like School of PE.
• Keep taking practice exams to evaluate preparedness until consistently scoring over 70%.
• Rest up the day before. Have what you need ready so you're not rushing around.

What's Next After Passing the FE Exam?

Congratulations, you've passed the FE exam! Now you can:

• Update your resume and LinkedIn profile to highlight your accomplishments.
• Join engineering associations and networks like the National Society for Professional Engineers.
• Formally start accruing the professional engineering experience needed for PE licensure. Track hours.
• Identify a PE mentor at your company who can provide guidance.
• Continue developing technical skills in your field. Seek opportunities to gain experience in areas covered on the PE exam.
• Maintain knowledge by attending engineering seminars and events or taking continuing education courses. Stay up to date on regulations.
• Save FE exam references and resources in case you need to brush up again for the PE exam.

Passing the FE opens opportunities in your engineering career. For those pursuing licensure, it's the critical first step to becoming a Professional Engineer. For others, it strengthens your foundation to grow professionally even without the PE.

Key Takeaways

• You do NOT have to pass the FE exam before starting your engineering career or gaining experience. Nothing prevents working as an engineer before or without FE certification.
• However, it is wise to take the test as soon as possible after finishing your accredited engineering degree. Knowledge is freshest, and the exam is often easier right out of college.
• Passing the FE exam early starts the licensure clock if your goal is to become a licensed Professional Engineer. It also boosts your resume and competitiveness.
• Disciplined studying is key to succeeding on the broad FE exam, which covers many engineering topics. On average, examinees spend 80-100 hours preparing.
• The FE exam is your chance to prove your comprehension and ability to apply foundational engineering concepts. Take advantage while the material is still fresh after graduation.

Ready to pass your FE exam on the first try? Don't leave it to chance. Choose School of PE, the top-rated engineering exam prep provider. Our expert-led courses and comprehensive study materials will equip you with the knowledge and confidence to succeed. Check out our courses here!

About the Author: Khoa Tran

Khoa Tran is an electrical engineer working at the Los Angeles Department of Water and Power and is currently pursuing his master's in electrical Power from the University of Southern California. He is fluent in both Vietnamese and English and is interested in outdoor activities and exploring new things.

Mastering Digital Signal Processing: Your Essential Guide for the FE Electrical Exam

The FE requires examinees for the FE Electrical exam to be able to solve DSP equations. Here, we will provide a brief introduction to the topic and several useful equations that will help prepare you for your upcoming exam.

In this Blog,

1. Sampling
a. Nyquist Theorem
b. Aliasing

2. Digital Filters
a. Difference Equation
b. Z-Transform
c. Finite Impulse Response (FIR)
d. Infinite Impulse Response (IIR)

Sampling

The sampling theorem states that in order to accurately reconstruct a continuous-time signal from its samples, the sampling rate must be at least twice the highest frequency component in the signal. This minimum sampling rate is known as the Nyquist rate. If the sampling rate is below the Nyquist rate, aliasing occurs, leading to distorted or misleading reconstructions.

1. Nyquist Theorem

A signal can be represented in its sample and can be recovered back when using the sampling frequency (f_s) or sampling angular frequency (ω_s=2πf_s) is greater or equal to twice the max frequency component of the signal (McClellan et al., 2021, 111) where:

f_s≥2f_max or ω_s≥2ω_max   (1)

For instance, considering the constraints of human auditory perception, the upper limit of discernible frequencies for human hearing is approximately 20 kHz (D et al., 2001). Consequently, to accurately capture and reproduce audio signals while adhering to the Nyquist Theorem, widely adopted media formats such as compact discs (CDs) and numerous digital audio files employ a sampling frequency of 44.1 kHz.

During the sampling process, it is customary to adhere to the Nyquist rate to ensure a faithful representation of the original signal. However, it is worth noting that alternate approaches, such as oversampling or undersampling, can also be employed to capture signals with distinct characteristics. 

2. Aliasing

Aliasing occurs when the sampling rate is less than the Nyquist rate, causing overlapping of the frequency components of the continuous-time signal. Aliasing leads to the creation of false frequency components, making it difficult to accurately reconstruct the original signal.

However, the signal can be reconstructed by filtering out frequencies above ¹/₂ f_s. To ensure accurate sampling, it is crucial that the signal to be sampled possesses a frequency content that is limited to half the sampling frequency. Failure to adhere to this requirement leads to aliasing, an undesirable phenomenon where different frequency components overlap and distort the reconstructed signal.

When the highest frequency in the signal is greater than half of the sampling frequency, then aliasing occurs. Through graphical analysis, it can be observed that the frequency (f) that surpasses half the sampling frequency will result in a signal reconstruction with aliasing at the difference between the sampling frequency (f_s) and f, denoted as f_s - f.

For 0.5f_s < f <1.5f_s, the aliasing will appear at |f_s-f|.

For 1.5f_s < f <2.5f_s, the aliasing will appear at |2f_s-f|.

For 2.5f_s< f <3.5f_s, the aliasing will appear at |3f_s-f| and so on (Hasegawa, 2021, 23).

Example: 

What is the frequency (Hz) of the artifact in the reconstructed signal if the function is Acos(640πt+Φ) and the signal is sampled at 120 Hz?

Solution:

1. Since the question is asking for frequency (Hz), we need to identify the max frequency and sampling frequency:

f_max=640π/2π=320 (Hz)

f_s=120 (Hz)

2. Check the criteria of f_max compare to f_s. You will need to keep testing until the right criteria is reached.

2.5f_s< f <3.5f_s

2.5(120)<320<3.5(120)

300<320<420

3. Find the artifact frequency via |3f_s-f|

f_artifact=|3(120)-320|=40 (Hz)

Digital Filters

Based on the FE Electrical and Computer topic list, the subtopics covered in the Digital Filters are Difference Equation and Z-Transform. However, Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) shall not be neglected even though they were not listed. 

1. Difference Equation

A difference equation is a mathematical equation that represents the relationship between the input and output signals of a discrete-time system. It describes how the current and past input values, as well as the current and past output values, are combined to compute the current output value (McClellan et al., 2021, 147).

A general form of a difference equation is:

y[n]=a₀ x[n]+a₁ x[n-1]+...+b₀ y[n-1]+b₁ y[n-2]+...   (x)

Where, 

y[n] is the current output at discrete time n.

x[n] is the current input at discrete time n.

x[n-1],... is the past input values.

y[n-1],... is the past output values.

a₀, … and b₀,... are the coefficients of the difference equation.  

Example: 

y[n]=4x[n]+2y[n-1]+2y[n-2]; y[n]=0 for n<0

What is the impulse response of a system described by the difference equation? 

Solution: 

1. For impulse response, x[n]=δ[n] and δ[0]=1 and δ[n≥1]=0

. n=0

y[0]=4δ[0]+2y[0-1]+2y[0-2]=4(1)+y[-1]+y[-2]=4+0+0=4

. n=1

y[1]=4δ[1]+2y[1-1]+2y[1-2]=4(0)+2y[0]+2y[-1]=0+2(4)+2(0)=8

. n=2

y[2]=4δ[2]+2y[2-1]+2y[2-2]=4(0)+2y[1]+2y[0]=4+2(8)+2(4)=28

You can keep computing for n approaches ∞ but the solution right is h[n]={4.8,28,...}

2. Z-Transform

The z-transform provides a way to represent discrete-time signals or sequences as functions of a complex variable, denoted as "z." It is defined as the sum of the sequence multiplied by powers of z, where z can be any complex number (McClellan et al., 2021, 348). The z-transform of a discrete-time sequence x[n] is given by:

∞
X(z)=∑	x[n]z-n(x)
n = 0

In the exam, a table of z transform paris is provided in the Reference Handbook p.372. 

Example: 

Find the z-transform X(z) of the following signal: 

x[n]=δ[n]+1/5 δ[n-2]-3/4 δ[n-4]

Solution: 

1. Use the summation definition (equation x) to solve for the z transform:

∞
X(z)=∑	x[n]z-n
n = 0

2. x[n] is zero for all values of n except when n=0,2,and 4.

x[n]={1,0,1/5,0,-3/4}

. n=0, z transform is

x[0]z^-0=1⋅1=1

. n=2, z transform is

x[2]z^-2=1/5⋅z^-2

. n=4, z transform is

x[4]z^-2=-3/4⋅z^-4

So, X(z)=1+1/5 z^-2-3/4 z^-4

3. Finite Impulse Response (FIR)

The FIR system, or, as we often refer to them, FIR filter, is a type of digital filter whose output is determined by a weighted sum of past and present input samples (McClellan et al., 2021, 147).

The output of the FIR filter can be calculated as:

∞
Y(n)=∑	bnx[n-k]
k = 0

4. Infinite Impulse Response (IIR)

In contrast to FIR filter, the output of IIR filter is the sum of the values of past inputs plus past outputs (McClellan et al., 2021, 394).

The output of the IIR filter can be calculated as: 

y[n] = ∑_l=0^∞ b_l x[n-l] + ∑_k=0^∞ a_k y[n-k]

Example: 

With the given filter below

y[n]=x[n]+1/6 x[n-1]

What type of filter is it?

Solution: 

1. By looking at the function, the output contains the sum of the current and past inputs. Therefore, it is an FIR filter. 

2. Do a z-transform to determine if it is a low-pass, high-pass, band-pass, or band-reject filter. 

y[n]=x[n]-1/6 x[n-1]

Use the z-transform pair from Reference Handbook p.372, we have 

Y(z)=X(z)-1/6 X(z)z^(-1)

H(z)=(Y(z))/(X(z))=1-1/6 z^(-1)=(z-1/6)/z

Conclusion

This blog aims to serve as a valuable point of reference, offering concise explanations and practical examples for each topic addressed in the exam. It is important to note, however, that while the blog provides a helpful overview, it may not encompass all aspects related to digital signal processing. For a more thorough and comprehensive study plan, I recommend visiting School of PE’s FE Electrical exam review course FE Electrical exam review course, which offers an extensive and detailed curriculum to ensure a comprehensive understanding of the subject matter.

References

D, P., GJ, A., & D, F. (2001). Neuroscience 2nd edition. Sunderland (MA): Sinauer Associates. https://www.ncbi.nlm.nih.gov/books/NBK10924/

Hasegawa, M. (2021). Lecture 6: Sampling and Aliasing. Retrieved June 6, 2023, from https://courses.engr.illinois.edu/ece401/fa2021/lectures/lec06.pdf

McClellan, J. H., Schafer, R. W., & Yoder, M. A. (2021). DSP First Second Edition. Pearson.

About the Author: Khoa Tran

Khoa Tran is an electrical engineer working at the Los Angeles Department of Water and Power and is currently pursuing his master's in electrical Power from the University of Southern California. He is fluent in both Vietnamese and English and is interested in outdoor activities and exploring new things.

Ready to Step into the Metaverse? AR & VR Explained

Imagine being able to virtually tour your dream home before it's built or see how a new piece of furniture would look in your living room before you buy it. How about watching your favorite band perform up close in a simulated concert or traveling to exotic locations without ever leaving the comfort of your own home? With augmented reality (AR) and virtual reality (VR), these imagined scenarios are now far closer to reality than fiction. These exciting technologies are changing the way we interact with the world.

In this Blog,

1. What Exactly Is AR and VR?

2. From Entertainment to Education

3. Endless Possibilities Await

4. The Rapid Pace of Innovation

5. Real Life Application

What Exactly Is AR and VR?

First things first, what exactly are AR and VR? Augmented reality overlays digital information and objects onto the real world that you see through a device. For example, you could look at a menu through your smartphone camera and see menu prices and reviews overlaid right on the menu. Virtual reality, on the other hand, is a fully immersive, computer-generated simulation of an environment or scenario. With a VR headset on, you're transported into a digital world where you can look around and interact as if you were really there.

Simply speaking, as the name suggests, augmented reality adds to the reality that we see, while virtual reality is an entirely simulated reality to interact with.

From Entertainment to Education

Both AR and VR are being embraced in entertainment and education spaces. Amusement parks have already included AR/VR rollercoaster experiences and VR gaming has become increasingly popular, allowing you to battle monsters or aliens from the comfort of your living room. Museums are using AR to bring exhibits to life with additional digital content about artifacts, and students have been offered fully immersive virtual field trips with the use of VR and interactive detailed models of historical sites and objects have been made possible through AR.

Healthcare has also begun adopting these revolutionary technologies for training surgeons and treating phobias and anxiety disorders.

The technology is still emerging, but huge players like Meta, Microsoft, and Google are investing heavily into AR and VR, and furthering their development. More affordable consumer devices such as the Meta Quest 2 VR headset (as of 2024, priced under $300) deliver high-quality experiences and accuracy that rival its pricier competitors. As the technology continues to improve and costs come down, mass adoption will skyrocket; soon, AR and VR will become the norm.

Endless Possibilities Await

With enhanced online shopping experiences, instant interior design, and fully interactive virtual travel, AR and VR are opening up tremendous new opportunities. As the technology advances, new industries will start to sprout and existing ones will begin to incorporate it into their products and services. We've only scratched the surface of what this emerging field can achieve—the possibilities are expansive.

Although these ideas existed in our imagination at first, people are now able to have their own holodecks like in Star Trek, witness their homes be redecorated with an infinite amount of options, and enable those who are financially constrained to explore the world without restriction. Innovations in AR and VR are turning imagination into reality. The possibilities these technologies provide are limited only by our creativity. Get ready, enjoy the explosive development, and welcome to the future!

The Rapid Pace of Innovation

The capabilities of AR and VR technologies are continuously evolving as new techniques and hardware innovations emerge. Just look at how far we’ve come in a few short years. Early VR headsets were bulky, expensive, and had major limitations, but thanks to rapid advancements, consumer-grade devices today provide stunningly realistic visuals and movement tracking that rivals systems costing thousands more just 5-10 years ago.

With some of the top technology companies engaged in fierce competition to improve AR and VR, the pace of innovation shows no signs of slowing down. Major investments in research and development are further driving breakthroughs across several key areas:

• Display Technology – To enhance realism, headsets are implementing higher display resolutions, faster refresh rates, and wider fields of view. New types of advanced displays like micro-LEDs will push visual fidelity even further (Sprigg, 2023).
• Tracking Systems – More precise and responsive sensors, computer vision technology and deep learning algorithms will continue to refine a headset’s ability to track the position and movement of a user’s head, hands, and body (Mechatech Embrace Technology, n.d.).
• Expanded Applications – Engineers are finding new ways to integrate AR and VR across more fields like healthcare, design, training, and manufacturing. The possibilities for transformational use cases are endless.

Real Life Application

The implementation of augmented reality (AR) technologies like Integrated Visual Augmentation Systems (IVAS) in the military shows promise for enhancing combat capabilities through improved situational awareness, targeting, and decision-making. However, there are some significant challenges regarding human factors, overreliance on technology, data integrity, electromagnetic signatures, environmental durability, and vulnerabilities to disruption that could render AR ineffective or even counterproductive on the battlefield if not properly addressed.

A balanced approach is required that leverages AR's advantages while mitigating limitations through rigorous testing and evaluation across diverse conditions and echelons. Network connectivity, cognitive overload, basic skill retention, and adversarial spoofing must be considered to prevent over-dependence and lack of flexibility. AR adoption must be done methodically, identifying and prioritizing risks and limitations for mitigation before full-scale deployment, so these technologies can serve as force multipliers that augment soldiers’ capabilities without detracting from their core combat competencies and resilience. With prudent implementation, AR can deliver enhanced tactical advantages and effectiveness to the military (Kallberg et al., 2022).

Conclusion

As with any groundbreaking technology, there are challenges to address on the road ahead. Most consumers still view AR and VR as intriguing but cost-prohibitive novelties. As more people get exposure to affordable mobile-based AR experiences, and standalone VR headsets like the Meta Quest 2 lower financial barriers, adoption will accelerate. Increased adoption will then fuel further innovation in a positive feedback loop.

Motion sickness and potential health risks from overuse are also valid concerns. However, solutions are in development - like wider fields of view, eye tracking, and body position monitoring. Responsible use guidelines will also be important. There’s no doubt we’re just scratching the surface of how AR and VR will transform our lives. The future looks bright.

References

Kallberg, D. J., Beitelman, V., Mitsuoka, V., Pittman, J., Boyce, D. M. W., & Arnold, T. W. (2022, May - June). The Tactical Considerations of Augmented and Mixed Reality Implementation. Army University Press. Retrieved August 7, 2023, from https://www.armyupress.army.mil/Portals/7/PDF-UA-docs/Kallberg-UA.pdf

Mechatech Embrace Technology. (n.d.). How do common virtual reality tracking systems work? Mechatech. Retrieved August 7, 2023, from https://www.mechatech.co.uk/journal/how-do-common-virtual-reality-tracking-systems-work

Sprigg, S. (2023, February 6). MIT engineers invent full-color micro-LEDs for AR & VR devices. Auganix.org. Retrieved August 7, 2023, from https://www.auganix.org/vr-news-mit-engineers-invent-vertical-full-color-microscopic-leds-for-use-in-ar-and-vr-devices/

About the Author: Khoa Tran

Khoa Tran is an electrical engineer working at the Los Angeles Department of Water and Power and is currently pursuing his master's in electrical Power from the University of Southern California. He is fluent in both Vietnamese and English and is interested in outdoor activities and exploring new things.