Examius
🇮🇳 GATE Electrical Engineering · flashcards
GATE Electrical Engineering Signals and Systems Flashcards
50 question-and-answer cards covering Signals and Systems as it is examined in GATE Electrical Engineering. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Signals and Systems deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
What is the definition of a discrete-time periodic signal?
$x[n]$ is periodic if there exists a positive integer $N$ such that $x[n]=x[n+N]$ for all $n$. The smallest such integer is the fundamental period $N_0$.
When is the DT sinusoid $x[n]=\cos(\Omega_0 n)$ periodic?
Only when $\dfrac{\Omega_0}{2\pi}$ is a rational number, i.e. $\Omega_0=2\pi\dfrac{k}{N}$ for integers $k,N$. Then the fundamental period is $N=2\pi k/\Omega_0$ (smallest integer $N$).
Find the fundamental period of $x[n]=\cos\!\left(\dfrac{3\pi}{4}n\right)$.
Set $\Omega_0=\frac{3\pi}{4}=2\pi\frac{k}{N}\Rightarrow \frac{N}{k}=\frac{2\pi}{\Omega_0}=\frac{8}{3}$. Smallest integers give $N=8$ (with $k=3$).
Why is the DT frequency $\Omega$ only unique over an interval of length $2\pi$?
Because $e^{j(\Omega+2\pi)n}=e^{j\Omega n}e^{j2\pi n}=e^{j\Omega n}$ for integer $n$. DT exponentials are periodic in frequency with period $2\pi$, so $\Omega$ and $\Omega+2\pi$ are indistinguishable.
If $x_1[n]$ has period $N_1$ and $x_2[n]$ has period $N_2$, what is the period of their sum?
$N=\operatorname{lcm}(N_1,N_2)$, the least common multiple of the individual periods.
If two CT periodic signals have periods $T_1$ and $T_2$, when is their sum periodic and with what period?
Their sum is periodic iff $T_1/T_2$ is rational. Then the period is the least value $T=k_1T_1=k_2T_2$, found as the LCM of the periods (smallest integers $k_1,k_2$).
Define even and odd parts of a CT signal $x(t)$.
Even part: $x_e(t)=\frac{1}{2}[x(t)+x(-t)]$ (satisfies $x_e(t)=x_e(-t)$). Odd part: $x_o(t)=\frac{1}{2}[x(t)-x(-t)]$ (satisfies $x_o(-t)=-x_o(t)$). Then $x(t)=x_e(t)+x_o(t)$.
Define the energy and power of a CT signal.
Energy: $E=\int_{-\infty}^{\infty}|x(t)|^{2}\,dt$. Power: $P=\lim_{T\to\infty}\dfrac{1}{2T}\int_{-T}^{T}|x(t)|^{2}\,dt$.
Define the energy and power of a DT signal.
Energy: $E=\sum_{n=-\infty}^{\infty}|x[n]|^{2}$. Power: $P=\lim_{N\to\infty}\dfrac{1}{2N+1}\sum_{n=-N}^{N}|x[n]|^{2}$.
How do you classify a signal as an energy signal vs a power signal?
Energy signal: $0<E<\infty$ (then $P=0$). Power signal: $0<P<\infty$ (then $E=\infty$). A signal cannot be both; periodic signals are power signals.
What is the average power of the periodic signal $x(t)=A\cos(\omega_0 t+\phi)$?
$P=\dfrac{A^{2}}{2}$ (independent of frequency and phase), and its energy is infinite, so it is a power signal.
For any general periodic waveform of period $T_0$, how is its average power computed over one period?
$P=\dfrac{1}{T_0}\int_{T_0}|x(t)|^{2}\,dt$ — integration over any one full period suffices because the signal repeats.
State the exponential (complex) Fourier series for any general periodic waveform $x(t)$ of period $T_0$.
$x(t)=\sum_{k=-\infty}^{\infty}c_k\,e^{jk\omega_0 t}$ with $\omega_0=\frac{2\pi}{T_0}$ and coefficients $c_k=\dfrac{1}{T_0}\int_{T_0}x(t)\,e^{-jk\omega_0 t}\,dt$.
State Parseval's relation (power) for a general periodic waveform in terms of its Fourier coefficients $c_k$.
$P=\dfrac{1}{T_0}\int_{T_0}|x(t)|^{2}\,dt=\sum_{k=-\infty}^{\infty}|c_k|^{2}$ — total power equals the sum of the powers in all harmonics.
What is the trigonometric Fourier series form for a general periodic waveform $x(t)$?
$x(t)=a_0+\sum_{k=1}^{\infty}\big[a_k\cos(k\omega_0 t)+b_k\sin(k\omega_0 t)\big]$, where $a_0$ is the DC (average) value and $\omega_0=\frac{2\pi}{T_0}$.
For a general periodic waveform, what symmetry makes all sine terms ($b_k$) vanish, and what makes all cosine terms ($a_k$) and DC vanish?
Even symmetry ($x(t)=x(-t)$) eliminates all $b_k$ (only cosines/DC remain). Odd symmetry ($x(-t)=-x(t)$) eliminates DC and all $a_k$ (only sines remain).
What does half-wave symmetry $x(t)=-x(t-T_0/2)$ imply about a periodic waveform's Fourier series?
Only odd harmonics are present; all even-harmonic coefficients (and the DC term) are zero.
What are the Dirichlet conditions for the Fourier series of a periodic waveform to converge?
Over one period: (1) $x(t)$ is absolutely integrable, $\int_{T_0}|x(t)|\,dt<\infty$; (2) finite number of maxima and minima; (3) finite number of finite discontinuities.
What is the difference between deterministic and random signals?
A deterministic signal can be described by an explicit mathematical expression (its future is exactly known), whereas a random (stochastic) signal can only be characterized statistically (probabilistically).
What is an anti-causal (non-causal) system in terms of its impulse response?
A system whose impulse response is nonzero only for negative time: $h(t)=0$ for $t>0$. Its output depends solely on future input values.
Distinguish an energy signal from a power signal regarding boundedness and time extent.
Energy signals have finite energy and are typically time-limited or decaying (e.g. $e^{-t}u(t)$). Power signals have finite nonzero average power and exist over all time (e.g. periodic signals, $u(t)$).
Is the unit step $u(t)$ an energy or a power signal? Give its power.
It is a power signal: $E=\infty$, and $P=\lim_{T\to\infty}\frac{1}{2T}\int_{0}^{T}1\,dt=\frac{1}{2}$.
How does the fundamental period of $x[n]=e^{j\Omega_0 n}$ compare to that of the CT signal $e^{j\omega_0 t}$ as frequency increases?
For CT, period $T_0=2\pi/\omega_0$ always decreases as $\omega_0$ increases. For DT it is not monotonic: the rate of oscillation increases only as $\Omega_0$ goes from $0$ to $\pi$, then decreases from $\pi$ to $2\pi$, and the signal may not even be periodic.
State the commutative and shift relationship: how does convolving a signal with a shifted impulse $\delta(t-t_0)$ act?
$x(t)*\delta(t-t_0)=x(t-t_0)$. Convolution with a shifted impulse simply shifts the signal; this combines the sifting and time-shift properties used throughout LTI analysis.
What this deck covers
The Signals and Systems deck follows the GATE Electrical Engineering Signals and Systems syllabus — 9 chapters and 8 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 5.6 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 153 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Signals and Systems flashcards FAQ
How many Signals and Systems flashcards are in this GATE Electrical Engineering deck?
50 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these GATE Electrical Engineering flashcards free?
Yes. The preview here is free to read with no signup, and the full 50-card deck is free inside the Examius app.
What do the Signals and Systems cards cover?
They follow the GATE Electrical Engineering Signals and Systems syllabus — 9 chapters and 8 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.