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Results tagged with gaussian
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The gaussian function, an exponential function with a negative square of the argument in the exponent, is interesting in signal processing because the Fourier Transform of a gaussian function is also a gaussian function.
4
votes
Gaussian random generator
Dilip and pichenettes have already pointed out two methods for generating Gaussian random variables (the Box-Muller transform and the Ziggurat algorithm). … For the standard Gaussian distribution, $\mu = 0$ and $\sigma = 1$.
Invert the distribution's CDF to yield its inverse CDF $F^{-1}_x(x)$, sometimes called the quantile function. …
- 24.8k
19
votes
Accepted
How to Generate Band Limited Gaussian White Noise in MATLAB?
You would generate bandlimited Gaussian noise by first generating white noise, then filtering it to the bandwidth that you desire. … As an example:
% design FIR filter to filter noise to half of Nyquist rate
b = fir1(64, 0.5);
% generate Gaussian (normally-distributed) white noise
n = randn(1e4, 1);
% apply to filter to yield bandlimited …
- 24.8k
4
votes
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Determine the optimum receiver and the corresponding $P_{eM}$ for an AWGN channel
I will state without proof that the optimal decision rule (for minimum probability of bit error) for the case of equiprobable input symbols and white Gaussian noise is to pick the symbol value whose constellation … Assuming the noise process has variance $\sigma^2$, the above probabilities can be written in terms of the Gaussian distribution's tail probability function, known as the Q function:
$$
P(\text{error …
- 24.8k