Continuous Signals - Unit Impulse, Unit Step, and Sine Functions with MATLAB Implementations

Unit impulse, unit step, and sine functions represent fundamental examples of continuous signals in signal processing. In MATLAB, these signals can be implemented using the following expressions and approaches:

- Unit Impulse Function: The `dirac(t)` function generates a Dirac delta function, which is mathematically infinite at t=0 and zero elsewhere. For practical implementations, use `t==0` to create a discrete approximation or the Control System Toolbox's `impulse()` function for system response analysis.

- Unit Step Function: Implement using `heaviside(t)` which returns 0 for t<0, 0.5 for t=0, and 1 for t>0. Alternatively, create a custom implementation with `double(t>=0)` for a basic step function without the 0.5 value at origin.

- Sine Function: Use `sin(t)` for standard sinusoidal signals, where 't' represents the time vector. For complete signal generation, combine with frequency and amplitude parameters: `A*sin(2*pi*f*t + phase)` where A is amplitude, f is frequency, and phase determines the initial angle.