Here is a combined Markdown table summarizing the question patterns from the uploaded question papers:
| Question No. | Description | Skills Tested | Marks |
|---|---|---|---|
| Q1.a | Sketch signals or calculate even/odd components, such as unit step, impulse, or triangular signals. | Signal sketching, understanding basic components, time-domain analysis. | 5 |
| Q1.b | Analyze system properties: Time invariance, linearity, and causality. | System analysis: Understanding and applying definitions to given systems. | 5 |
| Q1.c | Apply Laplace Transform to given signals and compute ROC. | Transform techniques and ROC understanding. | 5 |
| Q1.d | Compute Z-transform and determine ROC for given sequences. | Mastery of Z-transform properties, ROC calculation, and stability conditions. | 5 |
| Q2.a | Test systems for linearity, such as y(t) = tx(t) or y(t) = x(t²). | Understanding system response properties and algebraic manipulation. | 10 |
| Q2.b | Compute convolution of given signals using graphical or analytical methods. | Time-domain signal operations, convolution properties. | 10 |
| Q3.a | Derive Fourier series for periodic signals or compute exponential Fourier series. | Fourier series expansion, periodic signal properties, and harmonic analysis. | 10 |
| Q3.b | Check time invariance or compute inverse Z-transform for given ROCs. | System property analysis, inverse transforms, and interpretation of ROCs. | 10 |
| Q4.a | Determine initial and final values from Laplace Transform using respective theorems. | Application of Laplace Transform properties, stability, and asymptotic behavior. | 10 |
| Q4.b | Compute inverse Laplace Transform or list properties of ROCs. | Analytical transform techniques and understanding causality/stability from ROCs. | 10 |
| Q5.a | List Fourier Transform properties or derive FT for given signals like sin(ω₀t). | Fourier Transform techniques and conceptual understanding of frequency-domain behavior. | 10 |
| Q5.b | Compute Z-transform and ROC for sequences or derive exponential Fourier series for signals. | Advanced Z-transform applications, Fourier spectra, and frequency analysis. | 10 |
| Q6.a | Compute Fourier Transform of signals like x(t) = e^(-at)u(t) and plot magnitude/phase spectrum. | Fourier Transform properties, frequency-domain representation, and spectrum interpretation. | 10 |
| Q6.b | Explain ROC properties for Laplace Transform or discuss system interconnection types. | Fundamental ROC understanding and interconnection modeling of systems (serial, parallel, feedback). | 10 |
| Q7.a | Compute impulse response for LTI systems using differential equations or find system output for given inputs. | Differential equation solving, impulse response calculation, and input-output relationships. | 10 |
| Q7.b | Compute Laplace Transform and ROC for advanced signals like x(t) = te^(-4t)u(t). | Mastery of Laplace Transform for complex signals and their regions of convergence. | 10 |
This table integrates the patterns, highlighting how each part tests your conceptual and computational skills in Signals and Systems. Let me know if you’d like further refinements or study suggestions!