A signal is a physical quantity that carries information. It can be continuous (analog) or discrete (digital), and can represent various phenomena like voltage, sound, temperature, etc.
Signals can be classified into various types based on their time and amplitude characteristics. Common examples include periodic, aperiodic, continuous-time, discrete-time, even, odd, energy, and power signals.
A system is a device or process that takes an input signal and produces an output signal. Systems can be linear or non-linear, time-invariant or time-varying, causal or non-causal.
Signals can be manipulated mathematically through various operations like addition, subtraction, scaling, shifting, and multiplications
Convolution is a mathematical operation used to determine the output of a linear system when the input is a known signal. It represents the impulse response of the system.
The Fourier Transform is applicable to both continuous-time and discrete-time signals, while the Fourier Series is only applicable to periodic continuous-time signals. The Fourier Series represents a periodic signal as the sum of sines and cosines of various frequencies.
The Laplace Transform is a mathematical tool used to analyze linear time-invariant systems in the frequency domain. It is useful for solving differential equations that describe system behavior
A system is linear if the principle of superposition holds true. This means that the weighted sum of multiple inputs produces a weighted sum of the corresponding outputs.
The characteristics of a time-invariant system do not change with time. The output for a given input remains the same regardless of when the input is applied.
A causal system only depends on the present and past values of the input signal to produce the output. It cannot anticipate future values.