Interactive Modulation Simulators
Visualize binary modulation techniques (ASK, FSK, BPSK) in real-time with adjustable carrier and sampling parameters.
Simulator for Binary ASK Modulation
Digital
Simulator for Binary FSK Modulation
Digital
Simulator for BPSK Modulation
Phase
๐ Technical Guide: Workflow & Mathematics
1. Modulation Equations
Let $m(k)$ be the $k$-th bit in the sequence, $f_c$ the carrier frequency, and $A_c$ the amplitude.
ASK (Amplitude Shift Keying)
s(t) = A_c · m(k) · cos(2ฯ f_c t)
*On-Off Keying: Carrier is present for '1', zero for '0'.
FSK (Frequency Shift Keying)
s(t) = A_c · cos(2ฯ f_i t)
*where f_i = f_1 if m(k)=1, and f_i = f_0 if m(k)=0.
BPSK (Phase Shift Keying)
s(t) = A_c · cos(2ฯ f_c t + ฯ_k)
*where ฯ_k = 0 for '1' and ฯ_k = ฯ for '0'.
⚠️ Simulation Constraints
To ensure a valid and visually clear simulation, the following digital signal processing (DSP) rules must be followed:
- • Nyquist Criteria: The Sampling Frequency ($f_s$) must be at least twice the Carrier Frequency ($2 \times f_c$). For a smooth visual curve, $f_s \ge 10 \times f_c$ is recommended.
- • Carrier vs. Message: The Carrier Frequency should be much higher than the Bit Rate ($f_c \gg R_b$). In these simulators, Bit Duration is fixed at 1s ($R_b = 1$ bps).
- • Aliasing Warning: If $f_s < 2f_c$, the output waveform will suffer from aliasing, appearing as a lower-frequency distorted wave.
- • Phase Continuity: These simulators use "Sudden Phase Transition" (Non-coherent) modeling for simplicity.
๐งช Experiment for Students:
"Try setting the Carrier Frequency to 50Hz and the Sampling Frequency to 40Hz in the ASK simulator. Observe the Aliasing Effect—the waveform will no longer resemble a sine wave because the Nyquist criteria is violated."