This PDF 1.5 document has been generated by Acrobat PDFMaker 11 for Word / Adobe PDF Library 11.0, and has been sent on pdf-archive.com on 06/08/2016 at 17:36, from IP address 219.75.x.x.
The current document download page has been viewed 357 times.
File size: 405.12 KB (12 pages).
Privacy: public file
Chapters 7 & 8 – Online Revision Tutorial (Concise/Moderate/ Detailed)
i
Mind Map of Overall Picture
Recursive
/ Non-Recursive
Calculate y(n) by
substitution & iteration
Difference Eqn
y(n) = …
Calculate h(n) by
substituting
x(n)=δ(n)
System Block
Diagram
FIR / IIR
Unit Impulse
Response, h(n)
Calculate y(n) by
Z-transform
System Transfer
Function, H(z)
Order of filter
Freq Response, H(ejω)
by substituting z = ejω
Type of filter:
LPF / HPF
Mag Response or
Av at one given
frequency
-3 dB Cutoff
Freq
Mag Response,
|H(ejω)|
Chapters 7 & 8 – Online Revision Tutorial (Concise/Moderate/ Detailed)
Briefing
{A briefing video about using this interactive document}
ii
Chapters 7 & 8 – Online Revision Tutorial (Concise/Moderate/ Detailed)
iii
Contents
Mind Map of Overall Picture …………………………………………………………….……..…………………………………..…… i
Briefing …………………………………………………………………………………………………………………………………………. ii
Contents …………………………………………………………………………………………………………………….………..………. iii
1
System Block Diagram ↔ Difference Equation ..................................................................................... 1
3
System Transfer Function, (𝑧𝑧) ↔ Unit Impulse Response, ℎ(𝑛𝑛) ......................................................... 7
2
4
5
6
7
8
9
Difference Equation ↔ System Transfer Function, (𝑧𝑧) ......................................................................... 7
System Transfer Function, (𝑧𝑧) → Order of System .............................................................................. 7
Unit Impulse Response, ℎ(𝑛𝑛) → FIR / IIR .............................................................................................. 7
Recursive / Non-Recursive System ........................................................................................................ 8
Difference Equation → Calculate 𝑦𝑦(𝑛𝑛) by substitution & iteration ..................................................... 8
Difference Equation → Calculate ℎ(𝑛𝑛) by substituting 𝑥𝑥(𝑛𝑛) = δ(𝑛𝑛) ................................................... 8
System Transfer Function, (𝑧𝑧) → Calculate 𝑦𝑦(𝑛𝑛) by Z-transform ........................................................ 8
10 System Transfer Function, (𝑧𝑧) → Frequency Response, (ej𝜔𝜔) .............................................................. 9
11 Frequency Response, (ej𝜔𝜔) → Magnitude Response, |(ej𝜔𝜔)| ................................................................. 9
12 Magnitude Response, |(ej𝜔𝜔)| → Type of Filter (LPF/HPF)................................................................... 9
13 Magnitude Response, |(ej𝜔𝜔)| → Calculate Magnitude Response at a given frequency. ...................... 9
14 Magnitude Response, |(ej𝜔𝜔)| → Calculate −3 dB Cutoff Frequency .................................................... 9
15 Formula Sheet........................................................................................................................................... 9
Chapters 7 & 8 – Online Revision Tutorial (Concise/Moderate/ Detailed) M
1
1 System Block Diagram ↔ Difference Equation
1.1 System Block Diagram → Difference Equation
1.1.1 Worked Example
Example 1
What is the difference equation of the system?
0.5
Z -1
−0.7
Z -1
0.2
Solution
𝑦𝑦(𝑛𝑛) = 0.5𝑥𝑥(𝑛𝑛) − 0.7𝑥𝑥(𝑛𝑛 − 1) + 0.2𝑥𝑥(𝑛𝑛 − 2)
Explanation
Example 2
What is the difference equation of the system?
Z -1
3
Solution
Z -1
0.5
−0.1
𝑦𝑦(𝑛𝑛) = 3𝑥𝑥(𝑛𝑛) + 0.5𝑥𝑥(𝑛𝑛 − 1) − 0.1𝑥𝑥(𝑛𝑛 − 2)
Explanation
Chapters 7 & 8 – Online Revision Tutorial (Concise/Moderate/ Detailed) M
2
Example 3
Derive the difference equation of the system.
0.2
Z -1
Z -1
Z -1
0.5
0.6
−1.5
Z -1
Solution
𝑦𝑦(𝑛𝑛) = 0.2𝑥𝑥(𝑛𝑛) + 𝑥𝑥(𝑛𝑛 − 1) + 0.6𝑥𝑥(𝑛𝑛 − 2) + 0.5𝑦𝑦(𝑛𝑛 − 1) − 1.5𝑦𝑦(𝑛𝑛 − 2)
Explanation
Example 4
What is the difference equation of the system?
Z -1
Z -1
Solution
0.6
−0.3
Z -1
−0.1
𝑦𝑦(𝑛𝑛) = 𝑥𝑥(𝑛𝑛) + 0.6𝑥𝑥(𝑛𝑛 − 1) − 0.1𝑥𝑥(𝑛𝑛 − 2) − 0.3𝑦𝑦(𝑛𝑛 − 1)
Explanation
Chapters 7 & 8 – Online Revision Tutorial (Concise/Moderate/ Detailed) M
1.1.2 Problem
P1.
Derive the difference equation of the system.
5
Z
-1
−2
Z -1
P2.
Answer
0.7
What is the difference equation of the system below?
Answer
Z -1
Z -1
P3.
3
0.5
What is the difference equation of the system below?
1.5
Z
Z
-1
-1
2.3
Z -1
P4.
−0.4
Answer
Z -1
What is the difference equation of the system below?
Z -1
−0.3
Z -1
0.6
−0.1
Z
-2
Answer
Chapters 7 & 8 – Online Revision Tutorial (Concise/Moderate/ Detailed) M
4
1.1.3 Related Past Examination Question
15/16 s2 B5, 15/16 s1 B5, 14/15 s1 B6, 13/14 s2 B5, 12/13 s2 B5, 10/11 s2 B6
1.2 System Block Diagram ← Difference Equation
1.2.1 Worked Example
Example 1
The difference equation of a dicrete-time system is
𝑦𝑦(𝑛𝑛) = 2.5𝑥𝑥(𝑛𝑛) + 0.5𝑥𝑥(𝑛𝑛 − 1) − 0.2𝑥𝑥(𝑛𝑛 − 2)
Draw the system block diagram of the system.
Solution
2.5
Z -1
Z -1
0.5
−0.2
Explanation
Example 2
The difference equation of a dicrete-time system is
𝑦𝑦(𝑛𝑛) = 0.2𝑥𝑥(𝑛𝑛) − 2𝑥𝑥(𝑛𝑛 − 1) + 0.5𝑦𝑦(𝑛𝑛 − 1)
Draw the system block diagram of the system.
Solution
0.2
Z -1
−2
0.5
Z -1
Explanation
Chapters 7 & 8 – Online Revision Tutorial (Concise/Moderate/ Detailed) M
1.2.2 Problem
P1.
P2.
P3.
The difference equation of a system of a system is
𝑦𝑦(𝑛𝑛) = 0.5𝑥𝑥(𝑛𝑛) − 0.7𝑥𝑥(𝑛𝑛 − 1) + 0.2𝑥𝑥(𝑛𝑛 − 2)
Draw the system block diagram of the system.
Answer
The difference equation of a system of a system is
𝑦𝑦(𝑛𝑛) = 0.2𝑥𝑥(𝑛𝑛) + 0.6𝑥𝑥(𝑛𝑛 − 1) + 0.5𝑦𝑦(𝑛𝑛 − 1) − 1.5𝑦𝑦(𝑛𝑛 − 2)
Draw the system block diagram of the system.
Answer
The difference equation of a system of a system is
𝑦𝑦(𝑛𝑛) = 𝑥𝑥(𝑛𝑛) + 0.5𝑥𝑥(𝑛𝑛 − 1) − 1.2𝑦𝑦(𝑛𝑛 − 1)
Draw the system block diagram of the system.
Answer
1.2.3 Related Past Examination Question
08/09 s2 B3, 07/08 s2 B3
1.3 Answer
1.3.1 Answer of Section 1.1.2
Go back to Problem
P1. 𝑦𝑦(𝑛𝑛) = 5𝑥𝑥(𝑛𝑛) − 2𝑥𝑥(𝑛𝑛 − 1) + 0.7𝑥𝑥(𝑛𝑛 − 2)
P2. 𝑦𝑦(𝑛𝑛) = 𝑥𝑥(𝑛𝑛) + 0.5𝑥𝑥(𝑛𝑛 − 2)
P3. 𝑦𝑦(𝑛𝑛) = 1.5𝑥𝑥(𝑛𝑛) + 2.3𝑥𝑥(𝑛𝑛 − 1) + 𝑥𝑥(𝑛𝑛 − 2) + 𝑦𝑦(𝑛𝑛 − 1) − 0.4𝑦𝑦(𝑛𝑛 − 2)
P4. 𝑦𝑦(𝑛𝑛) = 𝑥𝑥(𝑛𝑛) − 0.3𝑥𝑥(𝑛𝑛 − 1) + 0.6𝑥𝑥(𝑛𝑛 − 2) − 0.1𝑦𝑦(𝑛𝑛 − 2)
1.3.2 Answer of Section 1.2.2
Go back to Problem
P1.
5
Z -1
−0.2
Z -1
0.7
Alternative Answer
5
Z -1
Z -1
−0.2
0.7
5
Chapters 7 & 8 – Online Revision Tutorial (Concise/Moderate/ Detailed) M
P2.
0.2
Z -1
0.6
Z -1
0.5
−1.5
Z -1
P3.
Z -1
0.5
Z -1
−1.2
6
Chap 7 & 8 Online Revision Tutorial (Moderate).pdf (PDF, 405.12 KB)
Use the permanent link to the download page to share your document on Facebook, Twitter, LinkedIn, or directly with a contact by e-Mail, Messenger, Whatsapp, Line..
Use the short link to share your document on Twitter or by text message (SMS)
Copy the following HTML code to share your document on a Website or Blog