Explore signals and systems by classifying continuous and discrete signals, periodic signals, and energy versus power. Examine system properties such as linearity, time invariance, causality, stability, memory, and invertibility.

Differentiate continuous and discrete signals by the independent variable, with continuous signals defined over time and discrete signals sampled at points, using parentheses for continuous and brackets for discrete time.

Explore how periodic signals repeat with a fundamental period in both continuous and discrete domains, and distinguish aperiodic signals in signals and systems.

Explain how to determine the fundamental period of continuous and discrete sinusoidal signals, using examples like x(t)=sin(7π/4 t), and discuss when discrete sinusoids are periodic or not.

Identify and classify signals as even or odd, based on symmetry about the y-axis or origin; illustrate with a continuous triangle and discrete impulses, and show their even-odd decomposition.

Explore the even and odd parts of a discrete-time signal by decomposing it into two terms, analyzing impulses at the origin, and visualizing left and right magnitudes.

Explore the unit step, unit impulse, and ramp signals in continuous and discrete time, and introduce sine and sign functions along with their key properties and relationships.

Explore the relationships between the unit step and unit impulse, including their derivative and integral connections, and the discrete-time identity u[n]-u[n-1]=δ[n].

Explore the relationships between continuous and discrete impulse functions, including delta functions, shifting, and signal multiplication. Understand how these properties govern integration and impulse behavior at the origin.

Learn how delta and unit impulse functions interact with signals, reducing multiplications to signal values at the impulse time, evaluating integrals, and deriving a and b with b ending zero.

Tackle a quiz on even and odd functions and the integral of sign(t) dt from negative to zero, and analyze the condition that delta t equals zero.

Analyze even and odd signal properties through the delta function and its derivative, showing that delta(t) is even, delta'(t) is odd, and t delta(t) = 0.

Plot plug-in signals by applying a linear transformation to a primary signal, first shift by b, then compress or expand by a, as in x(2t+3).

Explore plotting signals in electrical engineering: introduction to signals and systems, using time shifts, scaling, and reflections to illustrate right/left shifts and compression or expansion.

Explore discrete-time signal manipulation, including shifting its argument and scaling operations. See how compression by a factor reshapes the signal and how expansion creates zero-filled gaps, illustrated with impulses.

Plotting a discrete-domain signal under time scaling demonstrates compression by two and expansion by three, and how impulses shift with magnitudes like 1 and 1/4.

Learn how the integral of a signal from minus infinity to t accumulates the area under the curve, with examples using x1 through x4 and unit impulses.

Explore how energy and power describe signals, derive instantaneous power from voltage and current in a resistor, and define total energy and average power for continuous and discrete signals.

Defines average power for continuous and discrete signals over finite and infinite intervals, contrasts energy signals and power signals, and notes a signal cannot be both energy and power.

Compute energy and power for continuous and discrete signals. The continuous signal has infinite energy but power 1/2; the discrete signal has infinite energy and average power 5/12.

Define a system as a mapping from signal space to signal space that processes an input signal to produce an output signal, illustrated by a capacitor.

Explore continuous and discrete systems, where continuous inputs yield continuous outputs and discrete inputs yield discrete outputs, modeled with black box representations and mathematical notations x(t) and y(t).

Learn the linearity of systems by examining additivity and homogenize properties in continuous and discrete systems, ensuring combined inputs yield summed outputs and scaled inputs yield proportional outputs.

Explore linearity and nonlinearity in systems by verifying homogeneity and additivity through practical input-output examples, highlighting linear versus nonlinear behavior.

Highlight time invariant and time varying systems, demonstrating that time invariant systems shift outputs with inputs, whereas time varying systems may not, illustrated with unit step inputs.

Examine three examples to decide if a system is time-variant or time-invariant. A time-invariant system shifts output by the same amount as the input shift.

Explore capacitor memory: output voltage is the integral of past input current; compare with a resistor as a system without memory, relying only on present input.

Differentiate systems with memory from those without memory in signals and systems, using examples to show dependence on past or future inputs and instantaneous behavior.

Explore the causality of real-life systems, using a car and driver on snowy roads to show how past and present information guide actions, and how future data cannot determine outputs.

Analyze causality across four example systems to show that dependence on future input yields non-causal behavior, while dependence on past input yields causal output.

Explore the stability of systems, distinguishing stable and unstable behaviors through pendulum and op-amp examples. Learn the bounded input, bounded output principle and how feedback can enforce stability.

Apply bounded-input bounded-output criteria to assess stability across examples: a stable linear system; an integral system producing unbounded output; and unstable discrete and reciprocal/sinc-like systems.

Explore the invertibility of systems by examining when distinct inputs produce unique outputs; identify non-invertible cases where different inputs yield the same output.

Examine invertibility in signals and systems by showing how two distinct inputs can produce the same output, rendering a system noninvertible, with discrete and impulsive examples.

Explore linear time invariant systems and master convolution through discrete and continuous forms, visualize convolution concepts, and learn its key properties for solving signals and systems problems.

Explore convolution as the method to relate input and output in linear time invariant (LTI) systems using impulse response. Learn both discrete convolution sums and the continuous convolution integral.

Relate an lti system’s input and output in the discrete domain using the convolution sum and impulse response, by representing signals as sums of scaled, shifted unit impulse (delta) functions.

Derive the output of a discrete-time LTI system using linearity and time invariance to obtain the impulse response. Apply the convolution sum to compute y[n] for any input.

Compute the output of a linear time-invariant (lti) system via the convolution sum using a unit impulse input, its impulse response, and shifted responses to assemble y[n].

The lecture derives how both discrete and continuous signals can be represented through scaled unit impulses and their time shifts, leading to the input–output relation via the convolution integral.

Explore how continuous LTI systems use impulse response, linearity, and time invariance with the convolution integral to derive the input-output relationship.

Learn how to compute the output y(t) of LTI systems by convolving inputs with impulse responses delta(t), u(t), and delta'(t), demonstrating identity, ramp, and delta outputs.