New answers tagged gaussian
1
I'll give this a shot.
The Fourier Transform of a Gaussian is also a Gaussian. The standard deviations in each domain are related as $\sigma_t \cdot \sigma_F = \frac{1}{2\pi}$ The time standard deviation, $\sigma_t$ has units of time and the frequency domain standard deviation $\sigma_F$ has units of Hz.
We can define the "bandwidth" of a gaussion ...
1
The fact that it's modulated with a sinusoid doesn't change the FWHM bandwidth of your pulse – the $e^{jx}$ function has $\left\lvert e^{jx}\right\rvert\equiv 1$ at every point. That doesn't change the amplitude, so the FWHM of a sinusoid-modulated gaussian is just the same as of the unmodulated gaussian.
1
No such thing as a single frequency of the noise. That's exactly why it's called white; it has power in all frequency ranges, but not at a single frequency.
Finally, is there a frequency-domain representation of Gaussian white noise?
Yes, a constant power spectral density for all frequencies. That's like white light (which contains also a continuum of all ...
Top 50 recent answers are included
Related Tags
gaussian × 274noise × 79
image-processing × 63
matlab × 39
filters × 31
digital-communications × 14
smoothing × 14
fourier-transform × 13
convolution × 13
power-spectral-density × 13
random-process × 12
signal-analysis × 11
fft × 10
discrete-signals × 10
filter-design × 9
statistics × 9
random × 9
autocorrelation × 8
kalman-filters × 7
snr × 7
scale-space × 7
sampling × 6
lowpass-filter × 6
stochastic × 6
blur × 6