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The difference between convolution and cross-correlation from a signal-analysis point of view

In signal processing, two problems are common: What is the output of this filter when its input is $x(t)$? The answer is given by $x(t)\ast h(t)$, where $h(t)$ is a signal called the "impulse ...
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19 votes

The difference between convolution and cross-correlation from a signal-analysis point of view

The two terms convolution and cross-correlation are implemented in a very similar way in DSP. Which one you use depends on the application. If you are performing a linear, time-invariant filtering ...
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12 votes

Scipy - Audio Processing

Personally I find Python one of the best choices out there and did myself some work in area of audio identification. You are welcomed to check for instance my software for automatic identification of ...
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9 votes

Fast pitch recognition

"Is there a way to measure frequency (detect pitch) better than FFT, that is, with better resolution in less acquisition time?" yes there is. or are. there are multiple better ways to do musical ...
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9 votes

Understanding the Difference Between MAP Estimation and ML Estimation

Maximium A Posteriori (MAP) and Maximum Likelihood (ML) are both approaches for making decisions from some observation or evidence. MAP takes into account the prior probability of the considered ...
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9 votes

A Machine Learning Based Algorithm as an Alternative to the Matched Filter

Sure, you can learn the matched filter, as convolution with a filter is just a function applied to a signal, and e.g. Neural Networks (through the universal approximation theorem) are good function ...
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8 votes

The difference between convolution and cross-correlation from a signal-analysis point of view

@MathBgu I have read all above given answers, all are very informative one thing I want to add for your better understanding, by considering the formula of convolution as follows $$f(x)*g(x)=\int\...
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Finding Reference Audio Signal in Test Audio Signal and Cropping Accordingly

If you have a reference signal you want to find in a different signal then your model matches almost perfectly (Up to the environment the signal to be found is in) to Matched Filter. So basically you ...
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7 votes
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Simple and efficient algorithm to detect frequency and phase of a sine signal

Note: I originally posted this answer for the Stack Overflow copy of this question, before realizing that it had also been asked here. It somewhat duplicates pichenettes' answer, but I felt it still ...
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7 votes
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What Are the Alternatives to FFT for Computing High Resolution Tone Power Levels?

Actually all those "Angle of Arrival" algorithms can be used for that. You can try: MUSIC. Pisarenko Harmonic Decomposition. Sensor Array (MVDR).
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7 votes

Estimators for improved spectral subtraction of noise

Maximum likelihood (ML) estimator Here will be derived a maximum-likelihood estimator of the power of the clean signal, but it doesn't seem to be improving things in terms of root mean square error, ...
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7 votes
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Signal Estimation after detection Part 2

After signal detection, how to estimate the clean signal $s(t)$? Matched filtering is used to detect the presence of a known signal in noise. There is no estimation part when you are talking about a ...
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7 votes
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A Machine Learning Based Algorithm as an Alternative to the Matched Filter

The idea is to have a simple experiment to see if we can get, for a known signal, a better results than the Matched Filter for time delay estimation. Experiment Objective Generate, using ML (DL) a ...
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6 votes

Good way to detect pulse with known width with background noise?

For peak detection a nice method is the following: apply a maximal filter to the data and find the places where the filtered data equals to the original one. A maximal filter is simply sliding ...
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What is the theoretical upperbound of information that could be transmitted by a device per second?

There are many factors involved in understanding the theoretical limits to communication. What follows is just a brief introduction that only scratches the surface. First, let's consider a simple ...
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6 votes
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How to Estimate Carrier Frequency & Amplitude for Several Overlapped Template Signal

If the auto correlation of the signal is sharp enough, you can do Matched Filter and search for local extreme points. Yet it seems the figure you'e displaying is in the frequency domain. But we can ...
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6 votes
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Detecting a Signal Inside a Time Series Using MATLAB's $ \tt xcorr() $

The function xcorr calculates the correlation of 2 signals. The correlation is known to be a good (The MLE) for delay estimation under Gaussian Noise. Yet, as ...
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6 votes
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How to Prove a System Is Invertible?

In general LTI System is invertible if it has neither zeros nor poles in the Fourier Domain (Its spectrum). The way to prove it is to calculate the Fourier Transform of its Impulse Response. The ...
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6 votes

Understanding the Difference Between MAP Estimation and ML Estimation

You have a set of message set $m_i$, $0 \le i \le N-1$. (For example, QPSK will be $N=4$). For the transmitted message $m_i$, the corresponding symbol vector is $\textbf{x}_i$, and the received symbol ...
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5 votes

Recovering signal for psk

To add to the excellent information given by Cassman in his response, here is a block diagram of a carrier recover loop for QPSK and QAM modems using a decision directed approach. I have detailed the ...
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Algorithm for detecting the time where the signal is above a threshold

There is a book by Basseville and Nikiforov called "Detection of Abrupt Changes : Theory and Application" that they released to the public as a PDF several years ago (it's out of print, now, I believe)...
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5 votes

The difference between convolution and cross-correlation from a signal-analysis point of view

There is a lot of subtlety between the meanings of convolution and correlation. Both belong to the broader idea of inner products and projections in linear algebra, i.e. projecting one vector onto ...
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5 votes

suppose if we send AM modulated message signal through space how the receiver will be knowing that we applied AM modulation?

Communications systems are always designed under the assumption that both emitter and receiver know what "language" they will be speaking to each other. AM modulation comms are standardized in ...
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Maximum Likelihood for Colored Noise

Let's have a look on the following model: $$ y \left[ n \right] = \left( h \ast x \right) \left[ n \right] + \left( g \ast w \right) \left[ n \right] $$ Where $ x \left[ n \right] $ is the signal of ...
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Isolate High Variance vs Low Variance Sections of Signals

What you did is the reasonable solution. From here you can do 2 things to mitigate your issues: Computation Efficiency You can use online calculation of the Mean and the STD. Remember when you move ...
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5 votes

Expectation of deterministic signals

If $x(t)$ is a deterministic signal, then you have $E[x(t)]=x(t)$. Furthermore, if $Y(t)$ is a random process you have $E[x(t)Y(t)]=x(t)E[Y(t)]$.
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How would you use machine learning for peak detection?

To be honest, I don't think CNNs, RNNs and LSTM are useful for this kind of problem – a bandpass filter followed by a threshold would be. Now, that would have three parameters: Lower cutoff ...
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The power of signal processing when faced with hardware constraints

That's a very broad question, but I'll give it a shot. 1 . ... how much could signal processing actually do to help us here ? ... That's highly dependent on the specific problem. Sometimes a lot, ...
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4 votes
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Need critical help: How to detect and distinguish two very similar looking signals?

As Conrad pointed out, a correlator is probably your best bet. The correlation of a signal with itself (also known as its self-similarity) is larger than its correlation with any other signal (except ...
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4 votes
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Create Matched Filter Reference Signal when Scaling Unknown

I think the problem is not as bad as you suspect it is. I wasn't around at the time, but from what I've read, early radar systems essentially connected the matched filter's output to an oscilloscope, ...
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