You are required to complete an individual assignment for the module Antennas and Wave Propagation (ELEC 20006.2). The work must be accurate, well-structured, and academically sound, as it will be evaluated based on understanding, analysis, and presentation.

### General Requirements:

– Answer all questions clearly and correctly.

– Show all steps in calculations.

– Use proper academic writing in English.

– Include suitable references using a standard referencing style (e.g., IEEE or Harvard).

– Ensure the report is neatly formatted with correct grammar and spelling.

– Include diagrams where required (especially for transmission lines and Smith Chart).

– Provide brief reflections where applicable.

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### Task Details:

#### 1. Quarter-Wave Line as an Impedance Inverter

Explain why a quarter-wave transmission line is called an impedance inverter.

– Include the mathematical expression.

– Explain the concept clearly.

– Provide real-life applications (e.g., RF circuits or antenna systems).

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#### 2. Copper and Insulators in Transmission Lines

Explain how copper and insulating materials are used in practical transmission lines.

– Describe their roles.

– Provide examples such as coaxial cables or twisted pair cables.

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#### 3. Propagation Velocity Calculation

Given:

– ( R = 40 , Omega/km )

– ( L = 0.7 , mH/km )

– ( C = 50 , nF/km )

– ( G approx 0 )

– Frequency = 1 MHz

You are required to:

– Calculate the propagation velocity using the correct formula.

– Show all steps clearly.

– Provide a short reflection on the result (compare with speed of light and explain).

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#### 4. Input Impedance Analysis

Apply the input impedance formula for transmission lines.

– Compare two different cases (e.g., short line vs quarter-wave line).

– Explain which case is suitable for impedance matching and why.

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#### 5. Quarter-Wave Transformer Design

Given:

– ( Z_0 = 300 , Omega )

– ( Z_L = 180 , Omega )

– Frequency = 400 MHz

– Length = 22.5 cm

You must:

– Calculate the required characteristic impedance of the quarter-wave transformer.

– Draw the equivalent circuit.

– Illustrate and explain the standing wave pattern.

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#### 6. Transmission Line Analysis using Smith Chart

For a lossless transmission line:

– Calculate the following:

1. Reflection coefficient

2. VSWR

3. Input impedance

4. Input admittance

5. Distance to first minimum

6. Distance to first maximum

– Solve analytically and verify using the Smith Chart.

– Include a scanned copy or clear image of the Smith Chart with proper markings.

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### Additional Requirements:

– The report must be logically structured with headings and subheadings.

– Include figures, equations, and explanations where necessary.

– Ensure all answers demonstrate clear understanding and correct application of theory.

– Add a reference list at the end of the report.

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### Submission Expectation:

The final work should be complete, accurate, and ready for submission without requiring further corrections.

You are required to complete and solve the Digital Signal Processing (ELEC 30001.3) assignment fully and accurately, ensuring all solutions meet academic standards and module requirements.

### General Instructions:

– Answer all questions in a clear, structured, and step-by-step manner.

– Show all derivations, calculations, and intermediate steps.

– Represent all signals in sequence form and provide proper sketches (stem plots) where required.

– Use correct mathematical notation throughout the solution.

– Ensure the final work is well-organized and ready for submission.

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### Task 1: Signal Analysis and Operations

#### (a)

– Evaluate the given radar signal for n = 0, 1, 2, 3, 4.

– Represent the result in sequence form and sketch the signal.

– Compute all required transformed signals step-by-step, showing full derivation.

– Perform sample-by-sample addition, tabulate results, and sketch the final signal.

– Provide a clear explanation of time-scaling by factor 2, and discuss its effect on radar resolution.

#### (b)

– Compute the required signal and represent it in sequence form with a sketch.

– Clearly explain how the signal is generated using time shifting and impulse multiplication.

– Perform convolution between the input and the system:

– Show each step of the convolution sum

– Present the final result in sequence form

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### Task 2: FFT Analysis

– Compute the 8-point DFT using DIT-FFT:

– Show the bit-reversed input sequence

– Draw a fully labeled 3-stage butterfly diagram

– Include all twiddle factors and intermediate values

– Compute the 8-point DFT using DIF-FFT:

– Draw the full signal flow graph with proper annotations

– Provide a comparison table including:

– Bit-reversal stage (input/output)

– Twiddle factor placement

– Butterfly structure

– Number of operations

– Suitability for hardware implementation

– Use an AI tool (e.g., MATLAB or ChatGPT) to verify results:

– Include the output

– Write a brief critical reflection (max 50 words) comparing manual and AI results

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### Task 3: System Analysis

– Derive the system function H(z) from the given difference equation.

– Determine and clearly state the poles and zeros.

– Sketch the pole-zero diagram accurately.

– Compute the impulse response h[n] using partial fraction expansion.

– Analyze BIBO stability and explain system behavior.

– Perform AI-assisted analysis:

– Include AI results (poles, zeros, stability)

– Provide a short comparison (max 50 words)

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### Task 4: Convolution and Critical Analysis

#### (a)

– Perform convolution using the tabulation (grid) method

– Show the complete table

– Present the output in sequence form and sketch it

#### (b)

– Provide a critical analysis (max 150 words) covering:

– Interaction between input and impulse response

– Significance of zero values in the system

– Effect of fractional inputs

– Practical interpretation in biomedical signals

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### Final Requirements:

– Ensure all answers are accurate, complete, and clearly presented

– Include all required diagrams, tables, and explanations

– The final solution must be submission-ready (report format)

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### Important Note:

The work must be completed with full understanding and originality, following academic integrity policies. AI tools should only be used where explicitly permitted.