24

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 $y(t)$...


17

What your distortion box does is apply a non-linear transfer function to the signal: output = function(input) or y = f(x). You're just applying the same function to every individual input sample to get the corresponding output sample. When your input signal is a sine wave, a specific type of distortion is produced called harmonic distortion. All of the ...


12

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. ...


10

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 ...


9

Mai, The length of the FFT depends on what application you are doing. A very course summary follows: Same size FFT: Analysis: This just means you want to 'analyse' the signal - look and see what type of spectrum it has, maybe patterns in the spectrums, etc. The 'usual' default is to simply use the FFT length equal to the length of your signal. Example: "...


9

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 ...


9

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 $...


9

"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] - ...


8

This is one of the oldest signal processing problems, and a simple form is likely to be encountered in an introduction to detection theory. There are theoretical and practical approaches to solving such a problem, which may or may not overlap depending upon the specific application. A first step toward understanding the approaches to the problem is ...


8

Time aligned If the signals are time aligned, you can conjugate-multiply the received signal with the reference signal divided by its magnitude-squared. Essentially dividing by the complex reference signal. Say the reference signal is $x(t)$, the frequency (i.e. time-varying phase) offset is $\theta(t) $ and noise is $N(t)$ Then the (time-aligned) ...


8

What you trying to achieve is called distortion. This techniques used when you want to add some harmonics to given signal. You have 2 basic methods to do this: waveshaping and ring modulation.I'll try to explain first one. Waveshaping Waveshaping allows you to make distortion via use of specially selected function. One of useful methods is Chebyshev ...


8

Two exact sine waves of the same frequency but different phases sum to another exact sine wave. That resultant sine wave can be decomposed into an infinite numbers of pairs (or any other greater number) of sine waves of the same frequency, not just the two original ones. Thus more information is required to reduce the possible solution space below infinite....


8

$E_1=E_{10}sin (\omega t)$ $E_2=E_{20}sin (\omega t + \delta)$ $E_{\theta} = E_1 + E_2 = E_{\theta0}sin (\omega t + \phi )$ This can be described as the figure below: Now given the $E_{\theta 0}$, you can rotate $E_1$ and $E_2$ arbitrarily as long as $E_1$ , $E_2$, and $E_{\theta 0}$ form the triangular. As a result, your given sine wave can be ...


7

A necessary (but not sufficient) conditions for $f_2$ to be a temporally scaled version of $f_1$ is that a spectral representation with a logarithmic frequency scale (such as the constant-Q transform) of $f_1$ is a translation of a log-frequency spectral representation of $f_2$. Practically, given two signals, you can perform the test and evaluate $a$ by ...


7

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 ($X$), ...


7

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 $m$ ...


6

My intuition is that it would be difficult to derive the right decision threshold you expect to find: $$\tau = \frac{1}{2}\left(\mu_0 + \mu_1\right) - \frac{\sigma^2}{\lVert\mu_0 - \mu_1\rVert^2} \log \frac{\pi}{1 - \pi}\left(\mu_0 - \mu_1\right)$$ From the global statistics you are considering (sample mean: $\pi \mu_0 + (1 - \pi) \mu_1$ ; standard ...


6

The measurement that is important to you will depend on the application. If you are looking for an over all measurement of all signal power to noise power then you define signal to be the power in all signal bands and the noise all of the powers in the noise bands. However, if you are trying to use an sub-band adaptive filter to correct for some sort of ...


6

What happens if I choose the length of signal L > NFFT? and what's about choosing L different form NFFT? Did you read the documentation? http://www.mathworks.com/help/techdoc/ref/fft.html Y = fft(X,n) returns the n-point DFT. fft(X) is equivalent to fft(X, n) where n is the size of X in the first nonsingleton dimension. If the length of X is less than ...


6

I assume here that your device is not in the feedback chain. If you can't afford a FFT or filter-bank decomposition (and then detect over successive frames the FFT bins in which the amplitude gets almost exactly multiplied by the same complex number over successive frames), I would suggest looking at these few parameters: Fit a line to the log of the RMS ...


6

In general, EEG, fMRI (and also MEG, SPECT and PET datasets -the so called "functional modalities") are obtained from a subject (e.g. a human being) while it is engaged in one or more "activities". This "activity" could even be "Stay at rest with your eyes closed" or "try to solve this equation" or "simply look at the images on this screen". Usually, ...


6

A synchronization sequence generally needs the property that its autocorrelation function resembles an impulse. There are two possible autocorrelation functions that can be considered. For a (real-valued) sequence $x$ of length $N$, the periodic autocorrelation function is $$R_x[n] = \sum_{k=0}^{N-1}x[k]x[k+n]$$ where the sequence is assumed to extend ...


6

A strong amplitude response at 0 Hz simply means that you have a very strong DC offset. In other words, it just means that the mean of your signal is not 0. If this is the only problem you have, then all you really need to do, is remove the mean of your signal. In other words: vp_sig_orig = vp_sig_orig - mean(vp_sig_orig);


5

When L>NFFT, the signal will be cropped before FFT; when NFFT>L, the signal will be zero padded before FFT. In your case, the window is used to surpress noise, and it will changes the spectrum of the signal so you cannot get the 'exact' amplitude spectrum. Actually, exact spectra can only be computed from infinte samples. Since the signal always has finite ...


5

on an ROC curve your plotting FP(x-axis) vs TP(y-axis) They are calculated by: True-positives = # of correctly detected positives/# of actual positives False-Positives = # of positives that are not true-positives/ number of positives Now on your ROC curve, because you did not mention incuding this into your question above, you most likely did not ...


5

HMM are useful for sequence modeling and classification - problems for which your observations unfold on a 1-D axis in time or space. Hence their usefulness for speech recognition, because a word is a sequence of heterogeneous states corresponding to its various phones. But the problem of recognizing whether a speaker is male or female doesn't really have ...


5

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)-...


5

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 ...


5

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 ...


5

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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