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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 $y(t)$...


20

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 ...


13

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. ...


11

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 ...


10

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

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 ...


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

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

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

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);


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

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

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 ...


6

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

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

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

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 ...


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=...


5

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.


5

@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(...


5

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 ...


4

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 ...


4

Here's an attempt to answer your first question: "An example of a 94% overlap transform processing could be demonstrated by a 279 sample frame with 262 samples overlapped from each frame into the next. A spectrogram is really just a sequence of spectra. In this case, each individual spectrum is taken of 279 time samples (which I will call a frame). ...


4

How can I get the exact value of amplitude of input signal? If your signal is stationary and perfectly periodic, then you can get the amplitude by using a data and FFT length that are exactly an integer multiple of the signal's period, and using no window function. A non-rectangular window function and an FFT length longer than the data length are useful ...


4

First, you need to precisely define what you mean by starting point of the cycle. What exactly is your reference that determines t=0 and what exactly determines the start of the cycle Your signal is comprised of the fundamental and a lot of odd harmonics. The fundamental is the strongest. You can easily determine the "start of the fundamental as follows: ...


4

Have a look at the acoustic scale website for some inspiration http://www.acousticscale.org/wiki/index.php/Main_Page You can estimate age based on a combination of vocal tract length (vtl) and pitch. Both of these attributes can be extracted from vowel sounds. Children will have short vtls and high pitch, adult males will have low pitch and long vtl, adult ...


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