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16 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 ...
Mark Borgerding's user avatar
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 ...
Marcus Müller's user avatar
8 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 ...
jithin's user avatar
  • 2,263
8 votes
Accepted

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 ...
Engineer's user avatar
  • 3,042
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, ...
Olli Niemitalo's user avatar
7 votes

Amplifier Placement in a Wireless Receiver

Placing the amplifier first will result in a lower noise figure for the receiver and hence more sensitivity but the amplifier will be exposed to all of the ingested signals, including undesired ...
GrapefruitIsAwesome's user avatar
7 votes
Accepted

Identify abrupt changes in an audio waveform

Synchrosqueezed Wavelet Transform is an option. I have developed a complete algorithm for this task, which scores 100% train accuracy and 86% test accuracy with 0.05 sec tolerance, without machine ...
OverLordGoldDragon's user avatar
6 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 ...
orodbhen's user avatar
  • 511
6 votes
Accepted

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 ...
Marcus Müller's user avatar
6 votes

How to decide whether a recording contains a signal of interest?

Is it possible to decide based on the result of the cross-correlation whether a recording contains the signal of interest? Certainly. The easiest way would be look at the crest factor (peak to RMS ...
Hilmar's user avatar
  • 45.4k
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 ...
Dan Boschen's user avatar
5 votes
Accepted

Radar Pulse Compression Gain (PCR)

The answer is yes but one has to specify $B_n$ properly to avoide possible confusions. In case if one uses a pulse compression, the bandwidth through which the receiver collects the noise will ...
kda's user avatar
  • 66
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 $E[x(t)Y(t)]=x(t)E[Y(t)]$.
Matt L.'s user avatar
  • 90.4k
5 votes

Estimators for improved spectral subtraction of noise

Update: I'm sorry to have to say that testing shows the following argument seems to break down under heavy noise. This is not what I expected, so I have definitely learned something new. My prior ...
Cedron Dawg's user avatar
  • 7,570
5 votes
Accepted

Maximum likelihood estimation complexity computation

Ordinary Least Squares problem Your $$\hat x = \arg\min_x \sum_{n=1}^{N_r} \left\lvert y_n - h_n x\right\rvert^2$$ is just a way of saying $$\hat x = \arg\min_x \left\| y - Hx \right \|$$ and that is ...
Marcus Müller's user avatar
5 votes
Accepted

Testing if a signal contains a specific previously recorded signal

This does sound like a job for cross correlation. It's quite robust and some tweaking with the threshold value should give you the result you are looking for. It's calculated in the time domain, so no ...
Max's user avatar
  • 2,368
5 votes
Accepted

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, ...
Hilmar's user avatar
  • 45.4k
5 votes

Excitation signals for system identification - Applications

The basic principle of system identification is Fourier division (in one shape or another). If we excite with a signal spectrum $X[k]$ and receive the spectrum $Y[k]$ we can calculate the transfer ...
Hilmar's user avatar
  • 45.4k
4 votes
Accepted

Pulse Compression(Chirp) SNR Gain

It's often said that pulse compression gives you a gain proportional to the time-bandwidth product (otherwise known as the pulse compression ratio, or $PCR$). This is a really misleading statement, ...
Beepboop bebop's user avatar
4 votes
Accepted

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 ...
Royi's user avatar
  • 19.7k
4 votes

How Can Telecommunication System Know Which Part Is Signal and Which Is Noise?

To elaborate on MM's answer just a little bit. Unless the receiver has some sort of expectation of the nature of the signal there is no way to tell. With an expectation (for instance a pure tone), ...
Cedron Dawg's user avatar
  • 7,570
4 votes

Preamble Detection and Frequency Offset Estimation in radio packets

For maximum sensitivity preamble detection with time referencing, consider using a barker code, or for more choices with longer lengths a PRN (pseudo-random noise) sequence, or for even more choices ...
Dan Boschen's user avatar
4 votes

Understanding the Difference Between MAP Estimation and ML Estimation

A brief, non-mathy explanation: ML assumes that all hypothesis are equally likely. MAP does not make this assumption. MAP is the optimum criterion, but under some conditions ML is optimum too. When ...
MBaz's user avatar
  • 15.3k
4 votes
Accepted

SVD vs matched filter

That's not true, it's not better. The thing is: the matched filter just implements the projection in the signal vector space, onto the signal vector itself (or a multiple thereof). (You'll find ...
Marcus Müller's user avatar
4 votes

Autocorrelation function of a triangular wave

I couldn't quite follow your code (you calculate two different versions of the ACF?), but I believe the problem with the plot being shifted toward zero is that xcov ...
Engineer's user avatar
  • 3,042
4 votes
Accepted

Amplifier Placement in a Wireless Receiver

GrapefruitIsAwesome's answer is right in mentioning that Friis noise formula says to put the most amplification possible as far up front as possible to minimize overall noise figure, but I'd like to ...
Marcus Müller's user avatar
4 votes

Identify abrupt changes in an audio waveform

This is more meat-and-potatoes. An oft-used algorithm in audio is the pitch detector, which of course is attempting to accurately determine the instantaneous pitch of a note. The note is a waveform ...
robert bristow-johnson's user avatar
4 votes

Identify abrupt changes in an audio waveform

One domain where continuous (complex) wavelets (CWT) are especially efficient is when you expect the 1D signals to be piecewise regular. When a signal is $C^\alpha$ by pieces, then the $\alpha$ ...
Laurent Duval's user avatar
3 votes

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 ...
Royi's user avatar
  • 19.7k
3 votes
Accepted

How to interpret output of matched filter with complex input?

Yes, it is possible (at least on paper or code, since complex signal don't exist physically) to apply a matched filter to complex signals. This is one way to look at it that I think is illustrative. ...
MBaz's user avatar
  • 15.3k

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