MATLAB Implementation of Continuous Signals

Continuous signals and their MATLAB implementation are essential concepts in signal processing, covering fundamental waveforms like unit impulse signals and unit step functions. In signal processing, continuous signals represent analog phenomena that vary smoothly over time and can be expressed using mathematical functions. These signals typically model real-world analog data such as audio waves or light intensity. MATLAB provides powerful built-in functions and toolboxes for simulating, analyzing, and processing continuous signals efficiently. The unit impulse signal (Dirac delta function) is mathematically defined as having infinite amplitude at time t=0 while being zero elsewhere. In MATLAB implementation, we approximate this using the dirac() function or by creating a narrow pulse with high amplitude at t=0, often combined with plotting functions like plot() or stem() for visualization. The unit step function (Heaviside function) transitions from 0 to 1 at time t=0, maintaining a value of 1 for t>0. MATLAB's heaviside() function allows direct implementation, while alternative approaches involve logical operators or conditional statements to create step transitions. Both signals serve as building blocks for more complex signal operations, with the unit impulse being crucial for convolution operations and system response analysis, and the unit step for modeling system turn-on behaviors and ramp signals. Mastering continuous signal theory and their MATLAB implementation through functions like dirac(), heaviside(), and custom mathematical expressions is fundamental for signal processing education and practical applications in filter design, control systems, and communication engineering. Code implementation typically involves defining time vectors using linspace(), applying mathematical operations element-wise, and using subplot() for comparative visualization of multiple signals.