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Signal and Control MCQs: Fourier Series Period, ROC, Modulation, LTI, Transfer Function

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What are the correct answers to these signals-and-systems, control, and DSP MCQs?

These MCQs are mostly answered in the thread as: 1) c for infinite period, 2) a / origin for the ROC question, 3) d (QPSK) for the highest data rate, 5) a for transfer function, 6) b, 7) c (critically damped) for the fastest response without overshoot, 8) A (system stable), and 9) b [#21674295][#21674296][#21674297][#21674314][#21674348][#21674357] The ROC is also stated to be around the origin [#21674314][#21674357] The replies do not clearly settle question 4.
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  • #1 21674294
    John Carter
    Anonymous  
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  • #2 21674295
    EMMR EMMR
    Anonymous  
  • #3 21674296
    EMMR EMMR
    Anonymous  
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  • #4 21674297
    John Carter
    Anonymous  
  • #5 21674298
    engridrees Aslam
    Anonymous  
  • #6 21674299
    engridrees Aslam
    Anonymous  
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    engridrees Aslam
    Anonymous  
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    engridrees Aslam
    Anonymous  
  • #9 21674302
    engridrees Aslam
    Anonymous  
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    engridrees Aslam
    Anonymous  
  • #11 21674304
    John Carter
    Anonymous  
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  • #12 21674305
    engridrees Aslam
    Anonymous  
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    engridrees Aslam
    Anonymous  
  • #14 21674307
    Ali Waqas
    Anonymous  
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    Ali Waqas
    Anonymous  
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    Ali Waqas
    Anonymous  
  • #17 21674310
    Ali Waqas
    Anonymous  
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    John Carter
    Anonymous  
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    John Carter
    Anonymous  
  • #20 21674313
    Ali Waqas
    Anonymous  
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    John Carter
    Anonymous  
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    John Carter
    Anonymous  
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    engridrees Aslam
    Anonymous  
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    engridrees Aslam
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  • #25 21674318
    John Carter
    Anonymous  
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    John Carter
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    John Carter
    Anonymous  
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    Ali Waqas
    Anonymous  
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    Ali Waqas
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    Ali Waqas
    Anonymous  

Topic summary

✨ The discussion centers on multiple-choice questions (MCQs) related to signals and systems, control engineering, and digital signal processing (DSP), primarily for electrical power engineering test preparation. Key topics include the period of infinite continuous Fourier series, region of convergence (ROC) in Z-transform, modulation schemes with higher data rates, characteristics of linear time-invariant (LTI) systems, and definitions and properties of transfer functions. Participants debated correct answers, such as the Fourier series period being infinite, ROC convergence related to poles and zeros inside the origin, and quadrature amplitude modulation (QAM) offering higher data rates compared to AM and FM. LTI systems are characterized by impulse response, and transfer functions serve as mathematical models derived from differential equations. The importance of the ROC including the unit circle for Fourier transform convergence was highlighted. Additional questions touched on RLC circuit resonance properties, power calculations, and stability criteria in control systems. The conversation also referenced practical test contexts like FESCO and LESCO electrical utility exams, with users requesting and sharing MCQs and answers. Some technical clarifications included the role of poles in the s-plane, Nyquist sampling criteria, and amplifier classes (Class A). The discussion reflects a collaborative effort to clarify fundamental concepts in signal processing and control theory relevant to power engineering assessments.
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FAQ

TL;DR: Typical DAC modules span 6–24 bits, and as one user noted, “ideal voltage source he hy.” This FAQ compiles thread‑proven answers on Fourier, ROC, modulation, LTI, damping, and RLC to speed up test prep. [Elektroda, iqbal sayed, post #21674351]

Why it matters: If you’re cramming for signal/control/DSP MCQs, these concise, sourced checkpoints cut confusion fast and reduce last‑minute errors.

Quick Facts

What’s the period of an infinite continuous Fourier series?

Infinite. For MCQs, when options include N, N+M, infinity, or 2π/n, choose “infinite” for an infinite continuous Fourier series. [Elektroda, EMMR EMMR, post #21674295]

Which modulation in the list has higher data rates: AM, FM, QPSK, or QAM?

QAM. It maps multiple bits per symbol and, within the given options, supports the highest raw data throughput for a fixed symbol rate. [Elektroda, Ali Waqas, post #21674307]

How is an LTI system uniquely characterized for analysis?

By its impulse response. Measure or model h(t) or h[n], and use convolution with the input to predict the output. [Elektroda, EMMR EMMR, post #21674295]

What exactly is a transfer function in control/signal problems?

A mathematical model that relates input to output in the transform domain (Laplace or z). It abstracts physical details into poles and zeros. [Elektroda, EMMR EMMR, post #21674296]

What’s the fastest achievable step response without overshoot?

Critically damped. It reaches the target quickly with zero overshoot; underdamped is faster initially but overshoots. “Pick critically damped when ‘no overshoot’ is stated.” [Elektroda, John Carter, post #21674297]

Does stability hold if the system’s z-transform is within the ROC?

Yes. If the system’s response lies in the ROC, the MCQ key flags it as stable; choose “system is stable.” [Elektroda, EMMR EMMR, post #21674295]

At resonance, what happens to net reactance in an RLC circuit?

Net reactance becomes zero; impedance equals R. Current peaks for a given applied voltage, enabling maximum real power in the resistor. [Elektroda, iqbal sayed, post #21674329]

Which theorem is often used for quick fault or network analysis in MCQs?

Superposition theorem. It simplifies multi-source circuits by summing individual source effects with others turned off appropriately. [Elektroda, iqbal sayed, post #21674336]

What sampling period avoids distortion per Nyquist criteria in the given MCQ?

Half the maximum signal period (i.e., sample at least twice the highest frequency). Select “half the max period.” [Elektroda, iqbal sayed, post #21674349]

Which amplifier class do preamps use for high linearity?

Class A. “Class A is highly linear” for small-signal stages, trading efficiency for distortion performance. [Elektroda, iqbal sayed, post #21674351]

Which system demands more stability margin among typical options?

A motor with position control. Precision positioning is sensitive to instability, so it needs higher stability margins. [Elektroda, iqbal sayed, post #21674349]

Quick how-to: check an MCQ on LTI stability using ROC/unit circle

  1. Read if the ROC includes the unit circle (discrete-time).
  2. If the stated response lies inside the ROC, select “stable.”
  3. If “no unit circle in ROC” appears, beware: it flags instability in many keys. [Elektroda, EMMR EMMR, post #21674295]
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