Eecs 16b. It also allows you to look at these labs from a bigger picture and reflect on your design process and choices. 0) EECS 16B Designing Information Devices and Systems II Fall 2022 UC BerkeleyLab Note 5. Veis a EECS 16B Designing Information Devices and Systems II Fall 2023 UC Berkeley Lab Note 5 Part 2A: High-Pass Filter As part of our color organ filter, we will also build a first-order high-pass filter to isolate the frequencies above the desired cutoff frequency. EECS 16B Designing Information Devices and Systems II Spring 2017 Murat Arcak and Michel Maharbiz Discussion 10B Notes Polynomial Interpolation Given n+1 distinct points, we can find a unique degree n polynomial that passes through these points. It’s important because we want to certify that, provided our system inputs are bounded, the outputs will not “blow up”. Contribute to ee16b/public-sp24-lab-notebooks development by creating an account on GitHub. 55 Consider the first-order highpass filter shown in Figure1. 2 Lab Note 5 — Sensing Part 2 (v4. ) . Let Vebe its phasor representation. It is available to all eligible students, regardless of their college. Alternative “second order” perspective on solving the RLC circuit The course sequence provides a comprehensive introduction to core EECS topics in machine learning, circuit design, control, and signal processing while developing key linear-algebraic concepts motivated by application contexts. Min Norm Proofs Recall from the previous problem that we need to find a value of⃗x⋆ ∈Rn that best approximates A⃗x⋆ ≈⃗y (7) where ⃗y ∈Rm. Berkeley-EECS 16B-2021共计27条视频，包括：EECS 16B _ Lecture 1 (Th, 08_26_21)-Te5iL8z6rCs、EECS 16B _ Lecture 2 (Tu, 08_31_21)-4rBMl92oHes、EECS 16B _ Lecture 3 (Th, 09_02_21)-YSwMD9WEQ84等，UP主更多精彩视频，请关注UP账号。 EECS 16B Note 2: Transient Analysis and Inputs 2024-01-20 11:03:24-08:00 1. This ties in with Change of Basis but its a huge concept for a least a month of the class. Using PCA to Detect Fraudulent Transactions (15 pts. Self-grades and HW Resubmissions are due on the following Friday, March 4, 2022, at 11:59PM. jVee−3 would be a valid phasor. 2 Differential Equations with Piecewise Constant Inputs Definition1(PiecewiseConstantInputs) Suppose u(t) is a piecewise constant input. 29183. Let the polynomial p be, p(x)=a 0 +a 1x+a 2x2 + +a nxn Let the n+1 points be, p(x 0)=y 0;p(x 1)=y 1 Nickvec eecs '22 • 2 yr. In the lab ipynb, there is a schematic of how EECS 16B Final PRINT your name and student ID: 2023-12-14 14:49:35-08:00 3. This is called a “rational transfer function. Prof. We recognize though that incidents happen, sometimes unintentionally, that run counter to that goal. (a)Which is the equivalent circuit as seen form the voltage source on the right-hand side of the C++ 16. Niknejad/Ramchandran. Modeling is emphasized in a way that deepens mathematical maturity, and in both labs and homework, students will EECS 16B Note 1: Capacitors, RC Circuits, and Differential Equations 2024-01-18 23:14:59-08:00 The intuition behind this guessing is that equation6has on the left term a derivative and on the right one the function that is being differentiated. Circuits State Space (X pts) EECS 16B Homework 12 2023-04-16 09:04:55-07:00 3. EECS 16AB teaches linear algebra with the intent of preparing you for courses like EECS 127 (Optimization) and EECS 189 (Machine Learning) and provides engineering and machine learning examples and applications for linear algebra. EECS 16B Final PRINT your name and student ID: 2023-11-21 14:00:42-08:00 6. The course sequence provides a comprehensive introduction to core EECS topics in machine learning, circuit design, control, and signal processing while developing key linear EECS 16B Midterm PRINT your name and student ID: 2022-03-10 10:16:34-08:00 4. Jan 17, 2023 · This course is a follow-on to EECS 16A, and focuses on the fundamentals of designing and building modern information devices and systems that interface with the real world. He served in a variety of roles in the US Navy's Submarine Force, traded EECS 16B Designing Information Systems and Devices II UC Berkeley Fall 2023 Homework 7 ThishomeworkisdueonSaturday,October14,2023,at11:59PM. The goal of the EECS 16 series is to introduce students to the various topics in the broad world of EECS while strengthening core mathematical principles to analyze linear systems as engineers. E. Niknejad/Ramchandran Application: Filtering out Noise •Listen to an audio signal and note that while speech and music has a lot of distinct tones, noise is random, with many high pitched and low-pitched parts. An email should come out this week to make it official. ) Suppose we have voltage v(t) = V0 sin(wt). Complex Numbers (4 pts. Suppose that we want to characterize a diode D1 with parasitic resistance Rp, represented by the following model: − V + B D1 EECS 16B Designing Information Systems and Devices II UC Berkeley Spring 2023 Final Exam Location: Draft PRINT your student ID: PRINT AND SIGN your name: , (last) (first) (sign) PRINT your discussion sections and (u)GSIs (the ones you attend): Row Number: Seat Number: Name and SID of the person to your left: Name and SID of the person to your EECS 16B Designing Information Systems and Devices II UC Berkeley Spring 2023 Homework 4 This homework is due on Friday, February 17, 2023 at 11:59PM. Exam location: Proctoring Office. EECS 16B Note 8: Vector Differential Equations 2024-02-26 20:35:36-08:00 1. PRINTyour student ID: PRINT ANDSIGNyour name: , (first and last) (signature) PRINTyour discussion section and GSI(s) (the one(s) you attend): Row Number (front row is 1): Seat Number EECS 16B is a followup course to EECS 16A and can be considered a precursor to CS 70. in Electrical Engineering from the University of Michigan, Ann Arbor, an M. EECS 16B Discussion 8A 2024-03-04 21:09:42-08:00 dIL dt = VC L (6) In summary, the two differential equations are as follows. I am passionate about teaching and research (my interests include vision, lanugage, and computational biology). Honor Code If you have not already done so, please copy the following statements into the box provided for the honor code on your answer sheet, and sign your name. Terms offered: Fall 2024, Summer 2024 8 Week Session, Spring 2024 This course and its follow-on course EECS16B focus on the fundamentals of designing modern information devices and systems that interface with the real world. The course sequence provides a comprehensive introduction to core EECS topics in machine learning, circuit design, control, and signal processing while developing key linear-algebraic concepts motivated by application contexts. Qualitatively sketch the i. Students refine their circuit design and linear algebra skills from EECS 16A, while continuing to learn further about control theory, signal analysis, and Hello, there! I am a third-year EECS major. The following characterization of controllability is the one that is most useful in practice. Power as functions of time. S. Veis a purely imaginary number. ) Suppose we want to shorten the time period of the input square wave i(t) suc EECS 16B Queue EECS 16B Midterm 2 PRINT your name and student ID: 2024-04-04 21:05:27-07:00 3. ” We also like to factor the numerator and denominator, so that they Course Catalog Description section closed. Signal Analysis with DFT (13 points) In this problem we will look at a few examples of signal analysis with DFT and how changes in the characteristics of the signals and/or the DFT window impact the resulting frequency-domain representation. I'm what you would call a "successful" EECS student in that I've done well in every lower div besides 16B, and every upper div I've taken so far. berkeley. Grading basis: letter. This is the typical problem of least squares, but sometimes we can have multiple values of ⃗x that approximate A⃗x ≈⃗y equally well. 1%. Some clown acccounts been poping up lately falsely claiming that it's not removed and then deleting their comments/post within several hours. MCQ (24 pts. ) PCA has many different uses when applied to real-world data. This is where the motor driver circuits come in. ) (a)(3 pts. ) Suppose we have voltage v(t) = V0 sin(ωt). 105L. He received a B. Once again, eigenvalues will play a leading role in helping understand stability of control systems (e. For all PMOS devices in this problem, jVtpj= 0. Class homepage on inst. These courses will introduce you to advanced EECS 16B, Spring 2018, Discussion 4B 1 1. Designing Information Devices and Systems II. Finally, EECS 70, (which can be thought of as the third course in this sequence --- except without any labs), introduces additional discrete structures for modeling problems, and brings in probability. CS/EECS. If you do not, please let us know. MoWe 13:00-13:59. EECS 16B. Come on over to my section if you're ever stuck. The course sequence provides a comprehensive introduction to core EECS topics in machine learning, circuit design, control, and EECS 16B Note 12: Controllability 2024-03-21 22:45:35-07:00 •A model is controllableif and only if any target state is reachable eventually from any initial state. EE 16A. This ALSO used to be a topic covered in 16A but was cut but is ESSENTIAL to 1/2 the content in 16B. edu. Modeling Weird Capacitors For parts (a) - (c) of this problem, pick the circuit option from below that best models the given physical capacitor. Class Schedule (Spring 2024): EECS 16A – MoWe 18:30-19:59, Pimentel 1 – Babak Ayazifar. I'm studying the recommended content from the piazza, but was wondering if anyone would be willing to share/dm their cheat sheets with EECS 16B: FALL 2015 – MIDTERM 1 2/14 PROBLEM 1. Catalog Description: This course and its follow-on course EE16B focus on the fundamentals of designing modern information devices and systems that interface with the real world. When you are qualitatively sketching, you may define your own axes and scaling. (1) and eq. Modeling is emphasized in a way that deepens mathematical maturity, and in both labs and homework, students will EE16B is terrible. Aug 26, 2021 · 16B Big Picture Themes and Story; EECS Student Climate & Incident Reporting Form. Together, this course sequence provides a comprehensive EECS 16B Midterm PRINTyour name and student ID: 2022-10-13 13:16:09-07:00. The course sequence provides a comprehensive introduction to core EECS topics in machine learning, circuit design, control, and signal processing while developing key linear EECS 16B Designing Information Systems and Devices II UC Berkeley Spring 2022 Final PRINT your student ID: PRINT AND SIGN your name: , (last) (first) (sign) PRINT your discussion sections and (u)GSIs (the ones you attend): Instructions Remember, you are supposed to write your answers for every part of every question on a fresh sheet of paper. The course sequence provides a comprehensive introduction to core EECS topics in machine learning, circuit design, control, and EECS C106AB, EE C128. It also allows you to look at these labs from a bigger picture and reflect on your design EECS 16B Midterm PRINT your name and student ID: 2024-02-28 11:39:35-08:00 3. (e)(2 pts. Tracking Terry Terry is a mischievous child, and his mother is interested in tracking him. EECS 16B is a followup course to EECS 16A and can be considered a precursor to CS 70. 1. The input signal is given by EECS 16B Designing Information Devices and Systems II Fall 2021 Note 18: Justifying PCA Via The Eckart-Young Theorem In this note we will discuss the proof of the so-called Eckart-Young theorem, which is a result we put off in the last note for the sake of brevity, since the proof is rather lengthy. Course Catalog Description section closed. Please note that EECS 16A is a prerequisite for EECS 16B. in EECS from our department, and an MBA from the Haas School of Business. (You should already have access to the EE16B Spring 2018 forum. The terminology is analogous to systems of linear equations. As if people didn't have enough reasons to shit on Sahai's version of the class Now we have a 12 page, 15 hour homework assignment due in the middle of dead week. EECS 16B Designing Information Systems and Devices II UC Berkeley Spring 2024 Note 7: Bode Plots Overview In this note, we introduce the concept of Bode Plots, which are piecewise-linear approximations of transfer function plots. EECS 16A. Together, this course sequence provides a comprehensive foundation for core EECS topics in signal processing EECS 16B Designing Information Devices and Systems II Fall 2023 UC Berkeley Lab Note 3 when you test it with the power supply, the Arduino cannot supply enough current to power the motors (the motors each need 100-200 mA to run, while the Arduino can only supply around 20 mA from its pin). Spring 2024 EECS 16B Lab Notebooks. EECS 16B: FALL 2015 – MIDTERM 1 2/14 . Students who fall into categories 2-5 may wish to use Phase I units to enroll in this course. The EECS minor, offered through the College of Engineering, is an optional program for students declared in another major but interested in coherent EECS study. Mark all that are true. Hence you must check the EE16B Piazza page frequently throughout the term. EECS 16B Midterm PRINT your name and student ID: 2022-07-28 19:14:15-04:00 is taken permits no current so VGS = Vin. ) A capacitance and its voltage with respect to time is shown below. self-driving cars). 2 Matrix Form for Differential Equations We will refer to a collection of differential equations, similar to eq. We can replace them with a single resistor of value Req = R2 ∥R3 = R2R3 R2+R3 EECS 16B Note 1: Capacitors, RC Circuits, and Differential Equations 2023-08-29 21:13:30-07:00 2. EE16A. 1 Low-Pass Filter: Magnitude Bode Plot In addition to plotting the magnitude of the frequency response (that is, the exact transfer function mag- EECS 16B: 001: LEC: Designing Information Devices and Systems II: Aakarsh Vermani Jean-Paul Tennant Jeshua Thomas Gustafson Jessica Jing Fan Leon M Kornfeld Miki Lustig Mishty Mou Dhekial Sebastian Arevalo Veeryan Bhatia Venkata Alapati: TuTh 09:30-10:59: Pimentel 1: 15998: EECS C106B: 001: LEC: Robotic Manipulation and Interaction: Kirthi Jan 16, 2024 · The course sequence provides a comprehensive introduction to core EECS topics in machine learning, circuit design, control, and signal processing while developing key linear-algebraic concepts motivated by application contexts. Designing Information Devices and Systems I. 5V. Roychowdhury and M. 6V. EECS 16B Designing Information Devices and Systems II Spring 2018 J. Please ask the current instructor for permission to access any restricted content. Solution: Veis a real number. EECS 16B Spring 2023 Lecture 1, Slide 3 Instructors: Prof. Catalog Description: This course is a follow-on to EECS 16A, and focuses on the fundamentals of designing and building modern information devices and systems that interface with the real world. No seats will be held for juniors and seniors. EECS 16B Queue EECS 16B Final Exam Review 2022-12-04 16:53:55-08:00 4. This means that there are a sequence of indices i ∈ Jean-Paul (JP) Tennant co-taught EECS 16B in Fall 2023, and is co-teaching it again in Spring 2024. The course sequence provides a comprehensive introduction to core EECS topics in machine learning, circuit design, control, and EECS 16B Homework 7 2022-03-08 20:14:06-08:00 3. You don't need to learn super deep about gram schmidt 16B Big Picture Themes and Story; EECS Student Climate & Incident Reporting Form. EECS 16B: 001: LEC: Designing Information Devices and Systems II: Clark Tu-Cuong Nguyen Ming-Chiang A Wu: TuTh 09:30-10:59: Wheeler 150: 28873: EECS C106A: 001: LEC Sign up for EECS 16B Sections! EECS 16B Midterm PRINT your name and student ID: 2023-10-11 15:34:25-07:00 (c)(5 pts. Final exam status: Written final exam conducted during the scheduled final exam period. This class is fucking egregiously difficult and needs to be reformed ASAP. EECS 16B is a heavily impacted course that students are expected to take within their first year and a half at Berkeley. So, it was hypothetically possible to not turn in the homework, wait for the solutions to come out after the deadline, copy A3: EECS 16A is designed to be taken without any prerequisites, so there is no need to take MATH 54 before EECS 16A. (If time) Gram Schmidt. The course sequence provides a comprehensive introduction to core EECS topics in machine learning, circuit design, control, and EECS 16B deepens the understanding of linear modeling and introduces dynamics and control, along with additional applications. Tu 11:00-13:59. As part of our band-pass filter, we will also build a first-order high-pass filter to isolate the frequencies above the desired cutoff frequency. Reading Material. (b)(8 pts. PROBLEM 1. Veis a real number. dVC dt = − VC RC − IL C + VS RC (7) dIL dt = VC L (8) (b) Using your answers from the previous part, create a vector differential equation with the state Was EECS 16B removed from LSCS degree requirements? Yes, see piazza. ) For all questions, fill in boxes for all answers that apply. Self-grades and HW Resubmissions are due on Saturday, October 21, 2023, at 11:59PM. When I took 16B my freshman year, I had Sahai whose homework policy was that for questions you got incorrect, you could resubmit on Gradescope to get 60% credit back on the given question. The problem is about system ID. The course sequence provides a comprehensive introduction to core EECS topics in machine See full list on inst. EECS 16B Discussion 1B 2024-01-20 19:35:55-08:00 circuit with an equivalent resistor and then redraw the circuit. Note that students wishing to study computer science at UC Berkeley have two different major options: The EECS major leads to the Bachelor of The instructors and TA will post announcements, clarifications, hints, etc. EECS 16b cheat sheet help. ) Suppose we have the 16B Big Picture Themes and Story; EECS Student Climate & Incident Reporting Form. Respectfully, fuck EECS 16B. Self-grades and HW Resubmissions are due the following Friday, February 24, 2023 at 11:59PM. ) You are given the graph in Figure1. EECS 16B is one of the most worthwhile classes you will take with lots of support available. ) Find the steady state value of vout(t) in terms of the component variables and input vin. Solution: Observe that R2 and R3 are in parallel. The course sequence provides a comprehensive introduction to core EECS topics in machine learning, circuit design, control, and EECS 16B Midterm PRINT your name and student ID: 2023-03-23 00:08:52-07:00 If you use any other method to solve the problem, you should find the same solution. Kannan Ramchandran Department of Electrical Engineering and Computer Sciences, UC Berkeley, niknejad@berkeley. For the rest of the problem, suppose that when we use the component values, we get the follow-ing differential equation: dvout(t) dt = 1 2 vout(t) 5 (1) Diagonalization. EECS 16B Designing Information Devices and Systems II Fall 2019 UC BerkeleyFinal Exam. Definition1(VectorDifferentialEquations) Designing Information Devices and Systems I. Jan 19, 2021 · Course Catalog Description section closed. EECS 16B Note 6: Bode Plots 2023-02-25 11:19:20-08:00 1. ago. If this is the case, we see the transistor hit the threshold The Berkeley Electrical Engineering and Computer Sciences major (EECS), offered through the College of Engineering, combines fundamentals of computer science and electrical engineering in one major. Miscellaneous (18 points) a) (6 pts) Assuming that for every inverter in the chain shown below, R on,n = R on,p = 1kΩ, and C g,n = C g,p = 20fF, what is the delay from V in transitioning from 0V to V dd to V out transitioning from V dd to 0V? V in 40fF Out +-+- EECS 16B Note 14: Symmetric Matrices and Spectral Theorem 2024-04-12 12:00:37-07:00 5 Example To recap what we have said before, the Spectral Theorem provides a powerful way to analyze matrices by decomposing them into components related to their eigenvalues and eigenvectors. Part 1: Caught in the Midrange First of all, we will be building a band-pass filter to isolate the mid-range frequencies. Finally, EECS 70, (which can be thought of as the third course in this sequence – except without any labs), introduces additional discrete structures for modeling problems, and brings in probability. Transistor Behavior For all NMOS devices in this problem, Vtn = 0. Then, use recognition of a design block to find an expression forVx. Hey dipshit, if 90% of the student body is out here doing the minimum 30% on homework assignments and relying on resubmissions, maybe you're not EECS 16B Designing Information Devices and Systems II Fall 2022 UC Berkeley Final Lab Report Introduction The final lab report tests your understanding of all EECS 16B Labs, with an emphasis on conceptual and analytical understanding. Maharbiz Discussion 4A 1 Transfer Function When we write the transfer function of an arbitrary circuit, it always takes the following form. EECS 16B Designing Information Devices and Systems II Spring 2022 UC Berkeley Hands-on Midterm Lab Report Introduction The midterm lab report tests your understanding of EECS 16B Labs 1-5, with an emphasis on conceptual and analytical understanding. The EECS 16 series also aims to provide students with real, hands EECS 16ADesigning Information Devices and Systems I4 Units. 8%. Diode System ID (10 pts. on Piazza. Circuit Potpourri (12 pts. The EECS 16 series labs aim to provide students with real, hands EECS 16B Midterm PRINT your name and student ID: 2024-02-22 16:38:47-08:00 3. But this class is on a different fucking level -- we are doing weekly homework assignments that EECS 16B Homework 0 2023-01-17 11:18:01-07:00 4. 16B Big Picture Themes and Story; EECS Student Climate & Incident Reporting Form. Part 2A: High-Pass Filter. Ali Niknejad and Prof. Option 1 C1 C2 Option 2 C1 C2 Option 3 C1 C2 C3 Option 4 C1 (a)A parallel plate capacitor with plate dimensions L and W, separated by a gap D, is filled with Course Catalog Description section closed. jVee 3 would be a valid phasor. Current ii. This ALSO used to be a topic covered in 16A but was cut. edu EECS 16B Designing Information Devices and Systems II. (2), as a system of differential equations. EECS 16B is the second part in the introductory electrical engineering series. ) Note: This problem does not require the use of your knowledge of circuits or diodes. Bounded-Input Bounded-Output (BIBO) Stability BIBO stability is a system property where bounded inputs lead to bounded outputs. Hambley P6. In this problem, you may use the atan2(b, a) function to compute the angle (phase) for the complex EECS 16B Homework 1 2022-01-22 17:54:56-08:00 5. g. The topics of controls and robotics will be introduced in detail in 16B, but once you have 16B and want more, 106AB and 128 are where you can go. This is known as a homogeneous differential equation. For a symmetric matrix EECS 16B Designing Information Systems and Devices II UC Berkeley Fall 2022 Homework 5 This homework is due on Friday, February 25, 2022, at 11:59PM. Python 4. (b)(3 pts. Modeling is emphasized in a way that deepens mathematical maturity, and in both labs and homework, students will Course Catalog Description section closed. LAB. 1. Hi! I'm stressin stressing for the 16b midterm coming up, and don't feel confident in a lot of the math/content even though I've been going to lecture and trying to do the homeworks. The course sequence provides a comprehensive introduction to core EECS topics in machine learning, circuit design, control, and Final Exam @ 2021-01-12 12:51:19-08:00. The course provides a continuation of the material learned in EECS 16A, with an applications based focus. Class Schedule (Fall 2024): EECS 16A – MoWe 18:30-19:59, Pimentel 1 – Babak Ayazifar, Jean-Paul Tennant. There can be more than one correct an- EECS 16B Spring 2023 Lecture 1, Slide 32 Instructors: Prof. 1 Low-Pass Filter As a reminder, our low-pass filter has the following form: HLP(jω) = 1 1 +jω/ωc (1) 1. EECS 16B Designing Information Devices and Systems II Spring 2021 UC Berkeley Final Exam There is a total of 126 points on this exam and 106 points will be counted as a full score. Link to the Form; EECS Department Message: It is very important to the EECS Department that every student in the EECS community feels safe, respected and welcome. •What if we use a “low pass” filter to get rid of high-pitched parts? EECS 16B Designing Information Devices and Systems II Spring 2021 Note 6: Bode Plots Overview Having analyzed our first order filters and gone through a design example in the previous Note to show why filter-design is important, we will now plot their transfer functions H(w) (or frequency responses) using Bode Plots. RLC Circuit In this question, we will take a look at an electrical systems described by second order differential equations EECS 16B Designing Information Devices and Systems II Summer 2022 UC Berkeley Lab Note 5 Lab 5: Sensing Part 2 In this part of lab, we will explore cascade design, one of the most popular methods for designing filters. Anthro/Art Practice Bldg 155. This course is a follow-on to EECS 16A, and focuses on the fundamentals of designing and building modern information devices and systems that interface with the real world. Students interested in only studying computer science should consider the Computer Science Minor. 1 "Homogeneous" Differential Equations Next, we work to extend this reasoning beyond d dt x(t) = b to more general differential equations of the form d dt x(t) = ax(t) where a ∈R is a constant. Controllable Canonical Form (Fall 2019 Final) Suppose that we have a two-dimensional continuous time system governed by: d dt ~x(t) = " 1 1 0 4 # ~x(t)+ " 1 1 # u(t) (7) We would like to put this system into Controllable Canonical Form (CCF) to use state feedback to place the eigenvalues at EECS 16B deepens the understanding of linear modeling and introduces dynamics and control, along with additional applications. Module 1: Capacitors. Aug 23, 2023 · This course is a follow-on to EECS 16A, and focuses on the fundamentals of designing and building modern information devices and systems that interface with the real world. The course sequence provides a comprehensive introduction to core EECS topics in machine learning, circuit design, control, and Circuits Review @ 2020-08-13 11:27:24-07:00 EECS 16B Designing Information Devices and Systems II Summer 2020 UC Berkeley Circuits Review 1. These will be useful in plotting a filter’s frequency response by hand, and also help us better understand Course Catalog Description section closed. In the lab ipynb, there is a schematic of how to make a simple RC high-pass filter. EECS 16B Designing Information Devices and Systems II Fall 2022 UC Berkeley Midterm Lab Report Overview The midterm lab report tests your understanding of EECS 16B Labs 1-5, with an emphasis on conceptual and analytical understanding. eecs. is kx ca mc yj nf dh ru mi kr