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Basic Signal Generation Online Simulator (Sine, Cosine, Rectangular, and Triangular)


Basic Signal Generation Simulator

Signal Generation Simulator

Period 0
Power 0

Working & Mathematical Model

Simulator Workflow

  1. User selects waveform type (Sine, Cosine, Rectangular, Triangular)
  2. Adjusts parameters:
    • Amplitude (A)
    • Frequency (f)
    • Duty Cycle (for rectangular)
  3. Time axis is generated (t values)
  4. Signal equation is applied for each time point
  5. Graph is plotted using Chart.js
  6. Power and Period are calculated and displayed

Mathematical Representation

1. Sine Wave:

y(t) = A · sin(2Ï€ f t)

2. Cosine Wave:

y(t) = A · cos(2Ï€ f t)

3. Rectangular (Pulse) Wave:

The rectangular waveform is a periodic non-sinusoidal signal defined over one period T = 1/f. It alternates between two levels (typically 0 and A) based on the duty cycle D.

Duty Cycle (D): Fraction of one period for which the signal is HIGH
    D = Pulse Width / T

Pulse Width (Ï„): Ï„ = D · T

Mathematical Representation:
y(t) = { A,     0 ≤ (t mod T) < Ï„
  0,     Ï„ ≤ (t mod T) < T }

This waveform is widely used in digital systems, switching circuits, and pulse modulation techniques.


4. Triangular Wave:

The triangular waveform is a continuous, piecewise linear periodic signal characterized by linear rise and fall segments.

Standard Mathematical Form:
y(t) = (2A/Ï€) · sin-1(sin(2Ï€ f t))

Alternatively, it can be expressed as a Fourier series containing only odd harmonics with amplitudes decreasing as 1/n², which makes it smoother compared to a rectangular waveform.

The triangular wave is commonly used in signal processing, modulation schemes, and waveform synthesis due to its linearity.

Power Calculation

  • Sine / Cosine: P = A² / 2
  • Rectangular: P = A² × (Duty Cycle / 100)
  • Triangular: P = A² / 3

Summary

  • Amplitude (A): Controls height of the wave
  • Frequency (f): Controls how fast wave repeats
  • Period (T): Time for one cycle → T = 1/f
  • Duty Cycle: Percentage of ON time (rectangular only)
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