9 votes
Accepted

Removing transients in highpass filtering with MATLAB

Your first order filter recursion for some real constants $a,b,c$ is $$ y[n] = a x[n] + b x[n-1] - c y[n-1] $$ with the two initial memory states $x[-1]$ and $y[-1]$ at $n=0$. Your "no transient" ...
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  • 4,314
8 votes

How to Calculate Gaussian Kernel for a Small Support Size?

Gaussian Kernel is made by using the Normal Distribution for weighing the surrounding pixel in the process of Convolution. Since we're dealing with discrete signals and we are limited to finite length ...
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6 votes

Optimal Level of Wavelet Decomposition for Denoising

I'd say it depends on the noise properties and of course the image itself. What you can think is that most Denoise Filters can handle only the High Frequencies of the noise. Hence the decomposition ...
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6 votes
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Does Higher Sampling Rate Increase SNR?

Sampling at a higher rate will distribute the quantization noise over a wider frequency, thus reducing the noise spectral density due to that quantization noise, with a lot of caveats. For more ...
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6 votes
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Extended Kalman Filter (EKF) for Non Linear (Coordinate Conversion - Polar to Cartesian) Measurements and Linear Predictions

Update If I understood your model, you have a model of Constant Velocity in 2D (Cartesian Coordinate System). While your measurement are in Polar Coordinate System. Pay attention that your measurement ...
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6 votes
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What is zero-phase filtering and forward-backward filtering?

Zero-phase filtering is a non-causal procedure, so it cannot be done in real time, only offline (or pseudo real-time, i.e., with a sufficient delay). A zero-phase filter needs to have a purely real-...
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6 votes
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Is There Any Filtering Technique with Element Wise Product Only Instead of Convolution?

Classic filteration is indeed done using convolution. Though I have seen broader definition of filtering as shaping the signal in its frequency domain which can be done in many other methods as well. ...
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6 votes
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Deconvolving a 1d Signal Using a Lookup Table

The way I understand the problem is each sample of the output is a linear combination of the samples of the input. Hence it is modeled by: $$ \boldsymbol{y} = H \boldsymbol{x} $$ Where the $ i $ -th ...
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5 votes
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Use Scale Space Representation to Filter Single Image

I used factor 5-6 going from the Standard Deviation (Std) of the Gaussian to the Kernel: radius = ceil(6 * STD); Though it means more computation power is required....
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5 votes
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Can the order of filtering and downsampling be exchanged?

Yes, the order does matter. In a real system with noise (as opposed to an idealized model) if you decimate before filtering, all the noise in the bands you aren't interested in will alias back in, ...
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5 votes
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Why Would Pre Filtering Measurement Data Affect the Least Squares Estimate?

I'm not sure what's you model is. Let's say it is something like: $$ y = H x + n $$ Now, using the Least Squares model is optimal (In the MSE sense) when $ n $ is AWGN (It is the linear optimal ...
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5 votes
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Interpolating/Decimating CIC Filter Group Delay

Consider an $D$-tap FIR filter with liner phase, the group delay (measured in samples) is $$g=\frac{D-1}{2}\tag{1}$$ and therefore, if it is measured in seconds it will be $$g=T_s\frac{D-1}{2}\tag{2}$$...
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  • 4,115
5 votes
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preprocessing raw ECG data

I need to preprocess raw ecg data in R, here is a sample already standardized. I'm not an expert in signal processing nor experienced in working with medical data,... Not being an expert on how the ...
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  • 10.1k
5 votes

Simple software low pass filter

A first order lowpass filter is usually implemented like this: $$p[n] = \alpha p[n-1] + (1-\alpha) pi[n]$$ Where $p[n]$ is your filtered power estimation, $p[n-1]$ is the previous result, $pi[n]$ is ...
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  • 4,721
5 votes

Filtering without using any transforms

You can achieve this result by using two combs filters : https://en.wikipedia.org/wiki/Comb_filter Put simply, the comb filter consists of adding a delayed version of the signal to itself, causing ...
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  • 196
5 votes
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How to Classify Image Filter as Low Pass Filter (LPF) or High Pass Filter (HPF)?

Welcome to DSP Community. General We assume 2 types of filters: LPF or HPF. Classifying Filter Type Usually, if it is a well planned LPF and well Planned HPF a simple test will do. Calculate the ...
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5 votes
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Filter before or after multiplication of two signals?

A personal rule: in general, it can be better to perform non-linear operations before linear ones. One reason behind that is that a lot of practical concerns are related to outliers or suspect ...
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5 votes
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Image Filtering by Averaging Similar Areas of the Same Image - Patch Based Processing

Those kind of algorithms are called Non Local algorithms. The most known algorithms of this family is the - Non Local Means which is a decent Noise Reduction (Denoising) algorithm. Until the Deep ...
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5 votes
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Derivation of the lowpass to bandpass transformation

You're right that the multiplication of a low pass and a high pass filter results in a band pass filter, as long as the cut-off frequency of the low pass is higher than the cut-off frequency of the ...
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  • 80.4k
5 votes

Deconvolution to Remove Gaussian Blur in 1D Signal (Wiener Filtering?)

Approaches There are many methods for Deconvolution (Namely the degradation operator is linear and Time / Space Invariant) out there. All of them try to deal with the fact the problem is Ill Poised in ...
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5 votes
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Deblurring 1D data using direct inverse filtering

Doing direct division in Frequency Domain means you are assuming cyclic / periodic boundary conditions for your data which I don't think is the proper assumption for your data. The model I'd pursue ...
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5 votes
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The Effect of Spatial or Temporal Averaging on Noise Properties

Let's model the data as: $$ {y}_{i} = {x}_{i} + {n}_{i} $$ So the the $ i $ -th pixel in the noisy image $ Y $ is composed by the noiseless image data and additive IID noise. Now assume we have 2 ...
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  • 41.4k
4 votes

Can the order of filtering and downsampling be exchanged?

In Short: The order does matter. Detailed: Downsampling by a factor of 2 without filtering, will cause aliasing in frequencies of 500Hz and more. Since your signal is bandlimited to 600Hz, the ...
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  • 1,440
4 votes

Discrete Sinusoidal to State Space

You may have a look on Paul Zarchan's lecture note about tracking a Sine Wave - Paul Zarchan - Fundamentals of Kalman Filtering: A Practical Approach - Tracking a Sine Wave. You also may have a look ...
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4 votes
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Undoing a filter operation in MATLAB

In general it's only possible to implement causal and stable filters. There are exceptions where marginally stable filters are used, but this doesn't apply here. So if you want to invert a given ...
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  • 80.4k
4 votes
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Smoothing a staircase

Looks like your data is virtually free of noise. That, combined with a very high sampling frequency would mean that at the jumps the data is exactly at the threshold between two quantized values. Set ...
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4 votes

Adaptive filtering: Optimum filter length and delay

In order to be able to choose an optimal value for the delay $\Delta$ it's important to understand how the system works. The purpose of the delay is to decorrelate the desired signal $s(n)$ and the ...
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  • 80.4k
4 votes

Laplacian Filter Implementation in MATLAB

You should use conv2() or imfilter() with your filter. Unless you want to implement it by hand,
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  • 41.4k
4 votes

Do integration/differentiation processes work as simple filters?

Yes, integration and differentiation can be linear filters. You can start from laplace properties that say: $ \int_{0}^{t} {x(t)dt} \longrightarrow \frac{X(s)}{s} \...
4 votes
Accepted

What are the advantages and disadvantages separability of Gaussian 2D filter?

Assuming the simplest case with a square image $x[n,m]$ of size $N \times N$ and a square filter kernel $h[n,m]$ of size $M \times M$, the raw 2D convolution to produce the, cropped, output image $y[n,...
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