Wrap up study notes for this sem

README.md

@@ -48,6 +48,7 @@ along with this program. If not, see <http://www.gnu.org/licenses/>.
   - 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.
 
 <details>
 <summary>Listing of examination papers on OneSearch</summary>
@@ -67,6 +68,16 @@ along with this program. If not, see <http://www.gnu.org/licenses/>.
 - 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.
 
 <div style="page-break-after: always;"></div>
 </div>
@@ -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