From cb6b3bb35128163075eea37831234eccde307366 Mon Sep 17 00:00:00 2001 From: Peter Tanner Date: Fri, 15 Nov 2024 05:28:26 +0800 Subject: [PATCH] Wrap up study notes for this sem --- README.md | 88 +++++++------------------------------------------------ 1 file changed, 11 insertions(+), 77 deletions(-) diff --git a/README.md b/README.md index 286a543..525950c 100644 --- a/README.md +++ b/README.md @@ -48,6 +48,7 @@ along with this program. If not, see . - ENGT4301 Digital Communications and Networking - ELEC3302 Communications Systems - Note that ELEC5501 Advanced Communications is a different unit. +- To be honest, you select (relevant) questions from these for class test study as well.
Listing of examination papers on OneSearch @@ -67,6 +68,16 @@ along with this program. If not, see . - This formula sheet will attempt to condense all processes/formulas you may need in this unit. - **You do not get given a formula sheet**, so you are entirely dependent on your own notes (except for some exceptions, such as the $\text{erf}(x)$ table). So bring good notes. - Doing this unit after signal processing is a good idea. +- Try to practice questions from the exam papers on OneSearch mentioned above before class test, since you don't get past questions for the tests. + +### Final exam 2024 + +As quoted from the lectures: + +- No short questions +- 10 calculation questions +- From exam front page: Any printed or written material (e.g. dictionaries, textbooks, statutes, cases, legislation, annotations, lecture notes, tutorials with solutions, notes) except UWA Library books. Photocopied or printed eBook of a textbook is permitted. + - So yes you can still bring as many papers as you want to the final, unlike in signals and systems/signal processing where the final only allowed two pages.
@@ -834,83 +845,6 @@ Bit error rate (BER) from matched filter outputs and filter output noise ### $Q(x)$ function -You should use [$\text{erf}$ function table](#function-1) instead in exams using the identity $Q(x)=\frac{1}{2}-\frac{1}{2}\text{erf}\left(\frac{x}{\sqrt{2}}\right)$. Use this for validation. - -| $x$ | $Q(x)$ | $x$ | $Q(x)$ | $x$ | $Q(x)$ | $x$ | $Q(x)$ | -| ------ | ---------- | ------ | ----------------------- | ------ | ------------------------ | ------ | ------------------------ | -| $0.00$ | $0.5$ | $2.30$ | $0.010724$ | $4.55$ | $2.6823 \times 10^{-6}$ | $6.80$ | $5.231 \times 10^{-12}$ | -| $0.05$ | $0.48006$ | $2.35$ | $0.0093867$ | $4.60$ | $2.1125 \times 10^{-6}$ | $6.85$ | $3.6925 \times 10^{-12}$ | -| $0.10$ | $0.46017$ | $2.40$ | $0.0081975$ | $4.65$ | $1.6597 \times 10^{-6}$ | $6.90$ | $2.6001 \times 10^{-12}$ | -| $0.15$ | $0.44038$ | $2.45$ | $0.0071428$ | $4.70$ | $1.3008 \times 10^{-6}$ | $6.95$ | $1.8264 \times 10^{-12}$ | -| $0.20$ | $0.42074$ | $2.50$ | $0.0062097$ | $4.75$ | $1.0171 \times 10^{-6}$ | $7.00$ | $1.2798 \times 10^{-12}$ | -| $0.25$ | $0.40129$ | $2.55$ | $0.0053861$ | $4.80$ | $7.9333 \times 10^{-7}$ | $7.05$ | $8.9459 \times 10^{-13}$ | -| $0.30$ | $0.38209$ | $2.60$ | $0.0046612$ | $4.85$ | $6.1731 \times 10^{-7}$ | $7.10$ | $6.2378 \times 10^{-13}$ | -| $0.35$ | $0.36317$ | $2.65$ | $0.0040246$ | $4.90$ | $4.7918 \times 10^{-7}$ | $7.15$ | $4.3389 \times 10^{-13}$ | -| $0.40$ | $0.34458$ | $2.70$ | $0.003467$ | $4.95$ | $3.7107 \times 10^{-7}$ | $7.20$ | $3.0106 \times 10^{-13}$ | -| $0.45$ | $0.32636$ | $2.75$ | $0.0029798$ | $5.00$ | $2.8665 \times 10^{-7}$ | $7.25$ | $2.0839 \times 10^{-13}$ | -| $0.50$ | $0.30854$ | $2.80$ | $0.0025551$ | $5.05$ | $2.2091 \times 10^{-7}$ | $7.30$ | $1.4388 \times 10^{-13}$ | -| $0.55$ | $0.29116$ | $2.85$ | $0.002186$ | $5.10$ | $1.6983 \times 10^{-7}$ | $7.35$ | $9.9103 \times 10^{-14}$ | -| $0.60$ | $0.27425$ | $2.90$ | $0.0018658$ | $5.15$ | $1.3024 \times 10^{-7}$ | $7.40$ | $6.8092 \times 10^{-14}$ | -| $0.65$ | $0.25785$ | $2.95$ | $0.0015889$ | $5.20$ | $9.9644 \times 10^{-8}$ | $7.45$ | $4.667 \times 10^{-14}$ | -| $0.70$ | $0.24196$ | $3.00$ | $0.0013499$ | $5.25$ | $7.605 \times 10^{-8}$ | $7.50$ | $3.1909 \times 10^{-14}$ | -| $0.75$ | $0.22663$ | $3.05$ | $0.0011442$ | $5.30$ | $5.7901 \times 10^{-8}$ | $7.55$ | $2.1763 \times 10^{-14}$ | -| $0.80$ | $0.21186$ | $3.10$ | $0.0009676$ | $5.35$ | $4.3977 \times 10^{-8}$ | $7.60$ | $1.4807 \times 10^{-14}$ | -| $0.85$ | $0.19766$ | $3.15$ | $0.00081635$ | $5.40$ | $3.332 \times 10^{-8}$ | $7.65$ | $1.0049 \times 10^{-14}$ | -| $0.90$ | $0.18406$ | $3.20$ | $0.00068714$ | $5.45$ | $2.5185 \times 10^{-8}$ | $7.70$ | $6.8033 \times 10^{-15}$ | -| $0.95$ | $0.17106$ | $3.25$ | $0.00057703$ | $5.50$ | $1.899 \times 10^{-8}$ | $7.75$ | $4.5946 \times 10^{-15}$ | -| $1.00$ | $0.15866$ | $3.30$ | $0.00048342$ | $5.55$ | $1.4283 \times 10^{-8}$ | $7.80$ | $3.0954 \times 10^{-15}$ | -| $1.05$ | $0.14686$ | $3.35$ | $0.00040406$ | $5.60$ | $1.0718 \times 10^{-8}$ | $7.85$ | $2.0802 \times 10^{-15}$ | -| $1.10$ | $0.13567$ | $3.40$ | $0.00033693$ | $5.65$ | $8.0224 \times 10^{-9}$ | $7.90$ | $1.3945 \times 10^{-15}$ | -| $1.15$ | $0.12507$ | $3.45$ | $0.00028029$ | $5.70$ | $5.9904 \times 10^{-3}$ | $7.95$ | $9.3256 \times 10^{-16}$ | -| $1.20$ | $0.11507$ | $3.50$ | $0.00023263$ | $5.75$ | $4.4622 \times 10^{-9}$ | $8.00$ | $6.221 \times 10^{-16}$ | -| $1.25$ | $0.10565$ | $3.55$ | $0.00019262$ | $5.80$ | $3.3157 \times 10^{-9}$ | $8.05$ | $4.1397 \times 10^{-16}$ | -| $1.30$ | $0.0968$ | $3.60$ | $0.00015911$ | $5.85$ | $2.4579 \times 10^{-9}$ | $8.10$ | $2.748 \times 10^{-16}$ | -| $1.35$ | $0.088508$ | $3.65$ | $0.00013112$ | $5.90$ | $1.8175 \times 10^{-9}$ | $8.15$ | $1.8196 \times 10^{-16}$ | -| $1.40$ | $0.080757$ | $3.70$ | $0.0001078$ | $5.95$ | $1.3407 \times 10^{-9}$ | $8.20$ | $1.2019 \times 10^{-16}$ | -| $1.45$ | $0.073529$ | $3.75$ | $8.8417 \times 10^{-5}$ | $6.00$ | $9.8659 \times 10^{-10}$ | $8.25$ | $7.9197 \times 10^{-17}$ | -| $1.50$ | $0.066807$ | $3.80$ | $7.2348 \times 10^{-5}$ | $6.05$ | $7.2423 \times 10^{-10}$ | $8.30$ | $5.2056 \times 10^{-17}$ | -| $1.55$ | $0.060571$ | $3.85$ | $5.9059 \times 10^{-5}$ | $6.10$ | $5.3034 \times 10^{-10}$ | $8.35$ | $3.4131 \times 10^{-17}$ | -| $1.60$ | $0.054799$ | $3.90$ | $4.8096 \times 10^{-5}$ | $6.15$ | $3.8741 \times 10^{-10}$ | $8.40$ | $2.2324 \times 10^{-17}$ | -| $1.65$ | $0.049471$ | $3.95$ | $3.9076 \times 10^{-5}$ | $6.20$ | $2.8232 \times 10^{-10}$ | $8.45$ | $1.4565 \times 10^{-17}$ | -| $1.70$ | $0.044565$ | $4.00$ | $3.1671 \times 10^{-5}$ | $6.25$ | $2.0523 \times 10^{-10}$ | $8.50$ | $9.4795 \times 10^{-18}$ | -| $1.75$ | $0.040059$ | $4.05$ | $2.5609 \times 10^{-5}$ | $6.30$ | $1.4882 \times 10^{-10}$ | $8.55$ | $6.1544 \times 10^{-18}$ | -| $1.80$ | $0.03593$ | $4.10$ | $2.0658 \times 10^{-5}$ | $6.35$ | $1.0766 \times 10^{-10}$ | $8.60$ | $3.9858 \times 10^{-18}$ | -| $1.85$ | $0.032157$ | $4.15$ | $1.6624 \times 10^{-5}$ | $6.40$ | $7.7688 \times 10^{-11}$ | $8.65$ | $2.575 \times 10^{-18}$ | -| $1.90$ | $0.028717$ | $4.20$ | $1.3346 \times 10^{-5}$ | $6.45$ | $5.5925 \times 10^{-11}$ | $8.70$ | $1.6594 \times 10^{-18}$ | -| $1.95$ | $0.025588$ | $4.25$ | $1.0689 \times 10^{-5}$ | $6.50$ | $4.016 \times 10^{-11}$ | $8.75$ | $1.0668 \times 10^{-18}$ | -| $2.00$ | $0.02275$ | $4.30$ | $8.5399 \times 10^{-6}$ | $6.55$ | $2.8769 \times 10^{-11}$ | $8.80$ | $6.8408 \times 10^{-19}$ | -| $2.05$ | $0.020182$ | $4.35$ | $6.8069 \times 10^{-6}$ | $6.60$ | $2.0558 \times 10^{-11}$ | $8.85$ | $4.376 \times 10^{-19}$ | -| $2.10$ | $0.017864$ | $4.40$ | $5.4125 \times 10^{-6}$ | $6.65$ | $1.4655 \times 10^{-11}$ | $8.90$ | $2.7923 \times 10^{-19}$ | -| $2.15$ | $0.015778$ | $4.45$ | $4.2935 \times 10^{-6}$ | $6.70$ | $1.0421 \times 10^{-11}$ | $8.95$ | $1.7774 \times 10^{-19}$ | -| $2.20$ | $0.013903$ | $4.50$ | $3.3977 \times 10^{-6}$ | $6.75$ | $7.3923 \times 10^{-12}$ | $9.00$ | $1.1286 \times 10^{-19}$ | -| $2.25$ | $0.012224$ | | | | | | | - -Adapted from table 6.1 M F Mesiya - Contemporary Communication Systems - -### $\text{erf}(x)$ function - -```math -Q(x)=\frac{1}{2}-\frac{1}{2}\text{erf}(\frac{x}{\sqrt{2}}) -``` - -| $x$ | $\text{erf}(x)$ | $x$ | $\text{erf}(x)$ | $x$ | $\text{erf}(x)$ | -| ------ | --------------- | ------ | --------------- | ------ | --------------- | -| $0.00$ | $0.00000$ | $0.75$ | $0.71116$ | $1.50$ | $0.96611$ | -| $0.05$ | $0.05637$ | $0.80$ | $0.74210$ | $1.55$ | $0.97162$ | -| $0.10$ | $0.11246$ | $0.85$ | $0.77067$ | $1.60$ | $0.97635$ | -| $0.15$ | $0.16800$ | $0.90$ | $0.79691$ | $1.65$ | $0.98038$ | -| $0.20$ | $0.22270$ | $0.95$ | $0.82089$ | $1.70$ | $0.98379$ | -| $0.25$ | $0.27633$ | $1.00$ | $0.84270$ | $1.75$ | $0.98667$ | -| $0.30$ | $0.32863$ | $1.05$ | $0.86244$ | $1.80$ | $0.98909$ | -| $0.35$ | $0.37938$ | $1.10$ | $0.88021$ | $1.85$ | $0.99111$ | -| $0.40$ | $0.42839$ | $1.15$ | $0.89612$ | $1.90$ | $0.99279$ | -| $0.45$ | $0.47548$ | $1.20$ | $0.91031$ | $1.95$ | $0.99418$ | -| $0.50$ | $0.52050$ | $1.25$ | $0.92290$ | $2.00$ | $0.99532$ | -| $0.55$ | $0.56332$ | $1.30$ | $0.93401$ | $2.50$ | $0.99959$ | -| $0.60$ | $0.60386$ | $1.35$ | $0.94376$ | $3.00$ | $0.99998$ | -| $0.65$ | $0.64203$ | $1.40$ | $0.95229$ | $3.30$ | $0.999998$\*\* | -| $0.70$ | $0.67780$ | $1.45$ | $0.95970$ | | | - \*\*The value of $\text{erf}(3.30)$ should be $\approx0.999997$ instead, but this value is quoted in the formula table. ### $Q(x)$ fast reference