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AWGN Online Simulator



Theory: Sine Wave, Noise, Variance, and SNR

In our simulation, we generate a noisy sinusoidal signal: 


x[n] = A * sin(2Ï€ f n / N) + w[n]

Where:

  • A = amplitude of the sine wave
  • f = frequency of the sine wave
  • N = total number of samples
  • w[n] = additive noise with zero mean and variance σ²

The variance of the noise determines how strong the noise is compared to the sine wave: 


σ² = P_signal / (10^(SNR_dB / 10))

The Signal-to-Noise Ratio (SNR) in decibels is given by: 


SNR_dB = 10 * log10(P_signal / σ²)

For a pure sinusoid of amplitude A, the average signal power is: 


P_signal = A² / 2

Using these formulas, we can interconvert between variance and SNR, allowing us to control the noise strength and quality of the generated signal.

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