125 – DIGTAL SIGNAL

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.

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