19
votes
Accepted
Why should an image be blurred using a Gaussian Kernel before downsampling?
An image "should not be blurred using a Gaussian Kernel" in general.
This however can be a safe bet for a lot of basic image processing needs, and a smoothing is almost mandatory when you ...
- 31.7k
14
votes
Why is Gaussian noise called so?
Noise is random, but like most random phenomena, it follows a certain pattern. Different patterns are given different names.
Consider rolling a die. This is clearly random. Roll the die 1000 times, ...
- 14.9k
14
votes
Capacity of AWGN channel
Assuming a channel whose input at each time is a continuous random variable $X$ and its output is $Y=X+Z$, where $Z\sim\mathcal{N}(0,N)$ and $Z$ is independent of $X$, then $$C_{\text{CI-AWGN}}=\frac{...
- 4,225
12
votes
Why is random noise assumed to be normally distributed?
Starting at an even more basic level than the other (much smarter) answers, I'd like to pick up on this part of the question:
This seems contradictory to me as on one side it is random then on the ...
- 221
10
votes
Accepted
Why does the separable filter reduce the cost of computing the operator?
Assume you have a $N\times M$ sized image.
If you know take what is classically used, a square filter kernel, of let's say size $L\times L$, you'd need to convolve that with the picture β which gives ...
- 29.6k
9
votes
Accepted
What is a $BT$ (Bandwidth-Time) product with reference to modulation?
The $BT$ product is the bandwidth-symbol time product where $B$ is the $-3\textrm{ dB}$(half-power) bandwidth of the pulse/filter and $T$ is the symbol duration. For different applications you will ...
- 3,366
9
votes
Why should an image be blurred using a Gaussian Kernel before downsampling?
According to (digital) sampling theorem, signals should be properly bandlimited, before they are (down) sampled.
A practical digital filter approximately limits the bandwidth of the signal and makes ...
- 28k
8
votes
Accepted
Correct way to add AWGN to a signal
Short answer
10*log(bw/fs) to take into account the oversampling operation because the awgn() function specifies the signal-to-...
- 6,080
8
votes
Why is random noise assumed to be normally distributed?
normal distribution (i like to call it "gaussian") remains normal after addition of normally distributed numbers. so if gaussian goes into an LTI filter, a gaussian distribution comes out. but because ...
- 20.1k
8
votes
PSD of complex white gaussian noise
With reference to $N_o$ this usually is the symbol for the power spectral density (PSD) of thermal noise, where $N_o = kT$, where k is Boltzmann's Constant and T is the temperature in Kelvin. With ...
- 48.9k
8
votes
Accepted
How to approximate gaussian kernel for image blur
The continuous Gaussian, whatever its dimension (1D, 2D), is a very important function in signal and image processing. As most data is discrete, and filtering can be costly, it has been and still is, ...
- 31.7k
7
votes
Gaussian Blur - Standard Deviation, Radius and Kernel Size
It turns out that the rows of Pascal's Triangle approximate a Gaussian quite nicely and have the practical advantage of having integer values whose sum is a power of 2 (we can store these values ...
- 243
7
votes
Capacity of AWGN channel
The capacity formula
$$C = 0.5 \log (1+\frac{S}{N}) \tag{1}$$
is for discrete time channel.
Assuming you have a sequence of data $\left\lbrace a_n \right\rbrace$ to send out, you need an orthonormal ...
- 6,080
7
votes
Accepted
The Distribution of Filtered Gaussian White Noise
If you filter a Gaussian random process with an LTI system, the output will also be Gaussian. You can make intuitive sense of this by considering that a linear combination (which is what filtering ...
- 89k
7
votes
Why is random noise assumed to be normally distributed?
I'll try to clear one possible source of confusion. If picking each sample value from a single distribution feels "not random enough", then let's try to make things "more random" by adding another ...
- 13.5k
7
votes
Accepted
The Effect of the Finite Radius of Gaussian Kernel
If 3π is enough for ignoring, why surely select β‘6πβ€ Γ β‘6πβ€ for size of kernel, and not β‘3πβ€ Γ β‘3πβ€ or β‘4πβ€ Γ β‘4πβ€?
It is 3π on either side of the middle, so the total width of the kernel is ...
- 2,359
6
votes
Is the discrete Gaussian kernel an eigenfunction of the DFT?
This answer complements @CedronDawg's answer which introduced this family of eigenvectors. More specifically, this answer presents three algorithms and a hybrid algorithm for generating for a given ...
- 13.5k
6
votes
Is the discrete Gaussian kernel an eigenfunction of the DFT?
I have made a tremendous amount of progress on this issue in the last few weeks.
The Zeroing Sine Family of Window Functions
I have discovered a previously unrecognized class of window functions. ...
- 7,520
6
votes
How Is Laplacian of Gaussian (LoG) Implemented as Four 1D Convolutions?
There are two ways to compute the Laplace of Gaussian operator:
As Royi suggests, by computing
$f * \nabla^2 * g$,where we take the operator $\nabla^2$ as a convolution kernel created using the ...
- 2,359
6
votes
Accepted
Gaussian filter: The best parameters for an implementation
The effect is in sidelobe level and is evaluated with consideration to number of samples per symbol used, waveform quality and the spectral mask. Increasing the length of the filter in total number of ...
- 48.9k
5
votes
How Does Gaussian Blur Affect Image Variance
In Gaussian blur the value of each output pixel is calculated as a weighted sum of all input pixels:
$$\text{out}(x, y) = \sum^\infty_{j = -\infty} \sum^\infty_{i = -\infty} \frac{1}{{2\pi \sigma_G^2}}...
- 13.5k
5
votes
Accepted
generating white gaussian noise in matlab using two different functions
A white noise sequence is one for which each (random) element is uncorrelated from every other element:
$$
E[y[n]y[m]] = \left \{ \begin{array}{ll}
0 & \mbox{for } n\not=m\\
\sigma_y^2 & \mbox{...
- 25.3k
5
votes
Accepted
Poles of an analog Gaussian filter
First of all, computing the poles of an (ideal) Gaussian filter is an impossible task, because its transfer function is not a rational function, and there are simply no poles. This is in contrast to ...
- 89k
5
votes
Accepted
Value of power spectral density $N_0$ or effect of scaling bandwidth to SNR
The noise power continues to be $N_0/2$, independent of bandwidth. The reason is that the noise variance at the output of a filter with frequency response $H(f)$ is $$\sigma_n^2=\int_{-\infty}^\infty \...
- 14.9k
5
votes
Why Does the Kalman Filter Remove Only Gaussian Noise?
First of all let us assure that a Kalman filter (estimator) does not only remove Gaussian noise, but can remove (with certain success) any other type of noise as long as it's designed accordingly.
...
- 28k
5
votes
Accepted
On coloured Gaussian noise
Colored Gaussian noise is by definition a wide-sense-stationary (WSS) process; that is, it has constant mean (all the random variables constituting the process have the same mean) and its ...
- 20.2k
5
votes
Accepted
How to generate random samples of Gaussian distribution directly in the frequency domain?
You can, but... you'll need to keep symmetry if your original time-domain signal is real-valued.
If a signal $x$ is real-valued, then its DFT $X$ will exhibit complex-conjugate symmetry:
$$
X[k] = X^*...
- 25.3k
Only top scored, non community-wiki answers of a minimum length are eligible