agwn(x, snr_dB; rst = true)Adds a Gaussian White Noise (AGWN) to a signal x with a given SNR.
Inputs
x: Signal (Real or Complex)snr_dB: signal to noise ratio [dB]rst: Reset the random number generator - Bool
Output
y: Noisy signal
Noise models
In real-world applications, the noise is always present in the measured data. The noise can be due to various reasons such as the sensor noise, the environmental noise, the quantization noise, etc. The noise can be modeled as a random process. The package implements various type of noise in order to cover a wide range of practical situations.
1 Additive Gaussian White noise
When a signal, real or complex, \(x\) is corrupted by an additive Gaussian white noise \(n\), the measured signal \(y\) can be written as: \[ y = x + n \] where \(n \sim \mathcal{N}(n| 0, \sigma^2)\)
agwn
# Noiseless signal
Δt = 1e-4
t = 0:Δt:1
x = sin.(2π*5*t)
# Signal to noise ratio
snr_dB = 25.
# Noisy signal
y = agwn(x, snr_dB)
2 Additive Colored noise
When a signal, real or complex, \(x\) is corrupted by an additive colored noise \(n\), the measured signal \(y\) can be written as: \[ y = x + n, \] where \(n\) is a colored noise defined as in Excitation models - Colored noise.
acn - Real signal
acn(x, snr_dB, fs, color = :pink; band_freq = Float64[], rst = true)Adds a complex Colored Noise (ACN) to a signal x with a given SNR
Inputs
x: Signalsnr_dB: Signal to noise ratio [dB]fs: Sampling frequency [Hz]color: Color of the noise:white:pink(default):blue:brown:purple
band_freq: Frequencies used to defined the bandpass filter applied to the colored noiserst: Reset the random number generator
Output
y: Noisy signal
acn - Complex signal
acn(x, snr_dB, freq, color = :pink; rst = true)Adds a complex Random Colored Noise (ACN) to a signal x with a given SNR
Inputs
x::VecOrMat{Real}: Signalsnr_dB: Signal to noise ratio [dB]freq::AbstractVector: Frequency range of interestcolor: Color of the noise:white:pink(default):blue:brown:purple
rst::Bool: Reset the random number generator
Output
y: Noisy signal
acn(x, snr_dB, fs, color = :pink; band_freq = Float64[], rst = true)Adds a complex Colored Noise (ACN) to a signal x with a given SNR
Inputs
x: Signalsnr_dB: Signal to noise ratio [dB]fs: Sampling frequency [Hz]color: Color of the noise:white:pink(default):blue:brown:purple
band_freq: Frequencies used to defined the bandpass filter applied to the colored noiserst: Reset the random number generator
Output
y: Noisy signal
# Noiseless signal
Δt = 1e-4
fs = 1/Δt
t = 0:Δt:1
x = sin.(2π*5*t)
# Signal to noise ratio
snr_dB = 25.
# Noisy signal
y = acn(x, snr_dB, fs, :blue)
3 Multiplicative Gaussian White noise
When a signal, real or complex, \(x\) is corrupted by a multiplicative Gaussian white noise \(n\), the measured signal \(y\) can be written as: \[ y = (1 + n)x \]
mgwn
mgwn(x, snr_dB; rst = true)Adds a multiplicative Gaussian White Noise (MGWN) to a signal x with a given SNR
Inputs
x: Signalsnr_dB: Signal to noise ratio [dB]rst: Reset the random number generator
Output
y: Noisy signal
# Noiseless signal
Δt = 1e-4
t = 0:Δt:1
x = sin.(2π*5*t)
# Signal to noise ratio
snr_dB = 25.
# Noisy signal
y = mgwn(x, snr_dB)
4 Mixed noise
When a signal, real or complex, \(x\) is corrupted by a mixed noise \(n\), the measured signal \(y\) can be written as: \[ y = (1 + n_m)x + n_a \] where \(n_m\) is a multiplicative Gaussian white noise and \(n_a\) is an additive Gaussian white noise.
mixed_noise
mixed_noise(x, snr_dB; rst = true)Adds both additive and multiplicative Gaussian White Noise to a signal x with a given SNR
Inputs
x: Signalsnr_dB: Signal to noise ratio [dB]rst: Reset the random number generator
Output
y: Noisy signal
# Noiseless signal
Δt = 1e-4
t = 0:Δt:1
x = sin.(2π*5*t)
# Signal to noise ratio
snr_dB = 25.
# Noisy signal
y = mixed_noise(x, snr_dB)