Signals & Systems: Fourier, Laplace & Z-Transform for ISRO / DRDO Interviews
Essential questions in signal transformations, LTI system properties, causality, and stability commonly grilled in ISRO Scientist SC and DRDO RAC boards.
In-Depth Interview Questions & Model Solutions
Q1What is the significance of the Region of Convergence (ROC) in Laplace and Z-Transforms?
The ROC defines the domain in the s-plane (Laplace) or z-plane (Z-transform) where the transform integral/sum converges. Key properties: (1) ROC cannot contain any poles. (2) For causal LTI systems, ROC lies to the right of the rightmost pole in s-plane (or outside outermost circle in z-plane). (3) For a stable LTI system, the ROC must include the imaginary axis (s = jω) for Laplace, or the unit circle (|z| = 1) for Z-transform.
- Poles determine the boundary of the ROC.
- Causality + Stability requires all poles to lie in Left Half of s-plane (or inside unit circle in z-plane).
Q2Explain Nyquist-Shannon Sampling Theorem and the phenomenon of Aliasing with anti-aliasing filter design.
The sampling theorem states that a continuous bandlimited signal with maximum frequency fm can be uniquely reconstructed from its samples if the sampling frequency fs >= 2*fm (Nyquist rate). If fs < 2*fm, spectral copies in the frequency domain overlap, causing high frequency components to impersonate lower frequencies (Aliasing). An analog low-pass Anti-Aliasing filter (AAF) is placed before the ADC to eliminate frequency components above fs/2.
- Nyquist Rate = 2 * fm.
- Aliasing causes irreversibly distorted reconstructed waveforms.
- Practically, oversampling (e.g. 4x - 16x Nyquist) is used to simplify analog filter roll-off.
Technical Panel Interview Strategy Tips
- Be ready to sketch frequency response plots and pole-zero diagrams on paper.