Kit Library / Engineering / Signals and Systems
⚡ Topic Learning KitShared by a Veda learner · Generated with Veda AI
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. Here's a taste from this kit; the app has the full deck.
Shift, flip, and scale systematically.
To sketch transformed signals like $x(at+b)$, always factor the argument first: $x(a(t + b/a))$. Then apply operations in this order: scale (multiply $t$ by $a$), shift (add/subtract $b/a$), and flip (if $a$ is negative). This prevents common sketching...
↳ Factor the argument first; then scale, shift, and flip in that order.
The on/off switch for signals.
The continuous-time unit step $u(t)$ is 0 for $t<0$ and 1 for $t\geq 0$. The discrete-time step $u[n]$ is 0 for $n<0$ and 1 for $n\geq 0$. It is used to gate or truncate other signals.
↳ The step function turns signals on at a specified time.
The step's integral — a linear rise.
The unit ramp $r(t)$ equals $t$ for $t\geq 0$ and 0 for $t<0$. It is the integral of the step function. Ramp signals increase linearly with time after they turn on.
↳ A ramp is a linearly increasing signal that starts at zero.
This topic covers sketching basic continuous-time and discrete-time signals (step, ramp, pulse) under transformations like shifting, scaling, and flipping. It also covers determining periodicity and fundamental periods f...
~8 min · full explanation, examples & memory tricks in the app
15 questions laddered from warm-up to topper-level, each with an explanation. A taste:
For the signal $x(t) = u(-t + 4)$, what is the value of $x(t)$ for $t > 4$?
Beginner0
The argument $-t+4$ is negative for $t > 4$. The unit step $u(\text{negative}) = 0$, so $x(t)=0$ for $t > 4$.
The signal $x(t) = \Pi\left(\frac{t-2}{4}\right)$ is a rectangular pulse. What is its time duration?
Beginner4 seconds
The standard rectangular pulse $\Pi(t)$ has duration 1. Scaling the argument by $\frac{1}{4}$ stretches the duration by a factor of 4, so the duration is 4 seconds.
Which of the following is the correct expression for the signal $x(t) = r(t) - 2r(t-2) + r(t-4)$ for $2 \le t < 4$?
Intermediate$x(t) = -t + 4$
For $2 \le t < 4$, $r(t) = t$ and $r(t-2) = t-2$, while $r(t-4) = 0$. So $x(t) = t - 2(t-2) = t - 2t + 4 = -t + 4$.
Given $x(t)$ is a triangular pulse with peak amplitude 2 at $t=0$ and zero outside $[-1, 1]$, what is the peak amplitude of $3x(5t)$?
Beginner6
Amplitude scaling by 3 multiplies the peak amplitude by 3. The original peak is 2, so the new peak is $3 \times 2 = 6$.
17 flashcards in this kit — the app reviews them with spaced repetition so the right card returns on the right day.
Every game is built from this kit's own content — scores feed your mastery, so playing counts as studying.
The full Veda Bites deck, complete notes, spaced-repetition flashcards, leveled MCQs, tests and games for this kit — plus Daily Facts and the Arena, every day.
