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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 response" of the filter, and $\ast$ is the convolution operation.
Given a noisy signal $y(t)$, is the signal $x(t)$ somehow present in $y(t)$? In other words, is $y(t)$...
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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 operation, you convolve the signal with the system's impulse response.
If you are "measuring the similarity" between two signals, then you cross-correlate them.
...
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Depends on what you are controlling. For DC-motors it is the inertia of the device that acts as a low-pass filter of the PWM modulated signal resulting in a continuous motion. For most LEDs it is the human eyes that do the apparent low-pass filtering.
If the PWM-frequency is not very high you can actually see this by moving your head from left to right ...
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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 birds from noisy audio recordings: Ornithokrites. The program is used by Department of Conservation of New Zealand and they are happy about it. Based on this ...
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The two channels exist only inside a transmitter or a receiver; the channels are physically combined in a single signal (or channel) in the physical medium (wire, coax cable, free space, etc). At the transmitter, two signals $s_I(t)$ and
$s_Q(t)$ (called the I (or inphase) signal and Q (or quadrature) signal
respectively) are combined into a single signal $...
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"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 pitch detection in real time that are far, far better than running an FFT.
consider :
Average Magnitude Difference Function (AMDF)
$$ Q_x[k] = \sum_n |x[n] - ...
answered Nov 13 '15 at 9:08
robert bristow-johnson
14.9k3 gold badges26 silver badges61 bronze badges
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When you say that the "information content may remain the same," do you mean the information in the total signal, or the information of the desired signal? Hopefully this will answer both cases. I know Shannon entropy much better than Kolmogorov so I'll use that, but hopefully the logic will translate.
Let's say $X = S + N$ is your total signal ($X$), ...
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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, for any SNR, compared to spectral power subtraction.
Introduction
Let's introduce the normalized clean amplitude $a$ and normalized noisy magnitude $m$ ...
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At the end what has proven to be the best solution was onset detection based on either high frequency or energy content. Before it could work I had to use high-pass filter to cut out first 1 kHz, since it contained too much noise.
Once I had noise-only area I could use its profile to reduce noise from rest of the sample.
One library I found particularly ...
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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 worth (re)posting here, since it includes some extra details. (Whether those details are useful or not, I'll leave for you and the OP to judge.)
If you know ...
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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 through the data and selecting the maximal element from the sliding window. Formally:
$$g_w[x] = \max\left(f[x-w], f[x-w+1], \dots , f[x+w-1], f[x+w]\right)$$
where ...
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@MathBgu I have read all above given answers, all are very informative one thing I want to add for your better understanding, by considering the formula of convolution as follows
$$f(x)*g(x)=\int\limits_{-\infty}^{\infty}f(\tau)g(x-\tau)\,d\tau$$
and for the cross correlation
$$(f\star g)(t)\stackrel{\text{def}}{=}\int\limits_{-\infty}^{\infty}f^*(\tau)g(...
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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 matched filter. The estimate part comes after you have done the matched filter and need to estimate the symbols.
It looks like you are talking about a ...
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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 decision directed phase detector in this post Phase synchronization in BPSK and this one How to correct the phase offset for QPSK I-Q data, while the block ...
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Though the Matched Filter is the best tool detection of a known signals under AWGN it should work well here as well.
To say something about the probabilities the question is, do you know something about the energy of the received signals?
If you do, you should easily say something about the probabilities.
Pay attention that if the assumption is a signal ...
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There are several things missing/extra in your diagram.
What you are using is
rectangular PAM pulses of duration $T$ to send data across the channel, and so
you really don't need the multiplier. It is necessary only if $s_1(t)$ and $s_2(t)$
are different from rectangular pulses (though they are still of duration $T$,
and in that case, the input $s_1(t)-...
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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 scenario: there is no noise and no distortion of the signal being transmitted. We do allow for attenuation. Under these circumstances, you can transmit up to $R_p=...
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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).
That book looks at the basic CUSUM (cumulative sum) algorithm and how to choose appropriate thresholds for it.
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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 frequency, channel width for example. So each receiver is materially designed to demodulate AM signals with the appropriate hardware.
When people start trying to ...
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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 vector is $\textbf{y} = \textbf{x} + \textbf{w}$, where $\textbf{w}$ is the AWGN at the receiver. The above is a simplified baseband model assuming a simple ...
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The FFT is much better at detecting a sinusoid than a DWT. The FFT is approximating a periodic signal with a series of periodic signals. The coefficients of the FFT will be maximum in the frequency bins (could be a single bin with sufficient resolution) where the component of the FFT series best matches the periodic signal to be detected. The noise will ...
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Assume noise is not a serious issue in your problem. I guess you can get pretty clear speech signal. If you have speech recognition part implemented in your system, I think you should be able to take advantage over the language model in your recognition system. According to the transition probabilities, you shall get some confidence to say at what moment ...
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Assuming you're looking for symmetry around $x=0$, you can decompose any function into a symmetric and an antisymmetric part:
$$ f(x) = \frac{1}{2}\left(f(x)+f(-x)\right) + \frac{1}{2}\left( f(x) - f(-x) \right)$$
Calling $f_+(x):=\frac{1}{2}\left( f(x) + f(-x) \right)$ and $f_-(x):=\frac{1}{2}\left( f(x) - f(-x) \right)$ you can easily verify that $f_+$ ...
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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, and a trained operator would look at the phosphor and decide, from experience and intuition, when the signal raised above the noise ("the grass") indicating a ...
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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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The Goertzel algorithm allows you to sample the DTFT of a signal with slightly lower complexity than direct computation (still $\mathcal{O}(N^2)$ to produce the DFT but with a smaller coefficient). I think of it as being advantageous in two ways:
If you know the frequency you are looking for (like in telephone dialing systems)
If you only want a small ...
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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, and it had me confused enough to sit down and think about it for awhile. I thought I'd share some of my findings that I pieced together from both reading the ...
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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 normally be $B_n = \beta_c$. Then, the "new" signal-to-noise ratio should be written as:
$SNR = \dfrac{P_TG_TG_R\lambda^2\sigma{P_g}}{(4\pi)^3R^4(kT_{sys}\beta_c)} = \...
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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 need to do cross correlation between the Test Signal and the Reference Signal.
Find the point of maximum correlation and create a cropping zone around it ...
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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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