10

I will try to avoid math, because math and "how to do it" tutorials can be easily found. So, I start by pointing out one VERY important thing: One does not compute Harris for a single pixel, but for a vicinity (a patch of image) around that pixel! Let $I(i)_{xx}, I(i)_{xy} ...$ be your derivatives for a point $i_0$, then, $H = \left[ \begin{array}{cc} \...


8

From the (limited) description the uHz rotator algorithm sounds like one of the phase-weighted averages from this site, but it's not an algorithm I am familiar with. The Cramér–Rao lower bound$^1$ for estimating the frequency of sinusoid with amplitude $A$ in white noise with variance $\sigma^2$ is given by: $$ \mathrm{var}(\hat{f}) \ge \frac{12}{(2\pi)^2\...


8

I found the answer finally. I found a great article that explains many different libraries that can be utilized for peak detection. I now have the peaks I am really interested in, and can now create the output I am requiring. Finding Peaks in Python


7

I'll take an orthogonal tack to answering this question from what Peter K has (validly) already proposed. I assert that the 8-significant-figure claim is little more than marketing-speak; while the software may be able to provide you an estimate with that many digits on it, that doesn't mean that they carry any real information! It appears that the software ...


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

The first algorithm that springs to mind is the Goertzel Algorithm. That algorithm usually assumes that the frequency of interest is an integer multiple of the fundamental frequency. However, this paper applies the (generalized) algorithm to the case you are interested in. Another problem is that the signal model is incorrect. It uses 2*%pi*(1:siglen)*(Fc/...


4

If you use Flanagan [1] it is computed from the phase difference of successive phase spectra Δϕ (Instantaneous Frequency) and if you reconstruct the magnitude using a correct factor (Instantaneous Magnitude) [2] use a normalized sinc function: $$ \frac{\sin( \pi x ) }{ (\pi x)}$$ And at the end use Parabolic interpolation around the peak magnitude you can ...


4

If you are willing to use multiple neighboring FFT bins, not just 2, then windowed Sinc interpolation between the complex bin results can produce a very accurate estimate, depending on the width of the window. Windowed Sinc interpolation is commonly found in high quality audio upsamplers, so papers on that subject will have suitable interpolation formulas ...


4

Check out chapter 1.3 of this IRCAM paper on multi-F0 estimation. It discusses the difficulties in extracting multiple F0s from a recording, including the handling of overlapping partials, transients, and reverberation, as well as the modeling of domain-specific sources with varied spectral properties.


4

@Greyfrog. Here are the descriptions of four different kinds of averaging operations:


3

I had a lot of difficulty with this exact problem a couple of years ago. I posted this question: https://stackoverflow.com/questions/4633203/extracting-precise-frequencies-from-fft-bins-using-phase-change-between-frames I ended up doing the calculations from scratch, and posted an answer to my own question. I'm surprised that I was not able to find any ...


3

One method is to find the maximum and fit a parabola about it, and then use the parabola's maximum as the frequency and magnitude estimate. You can read all about here: https://ccrma.stanford.edu/~jos/sasp/Sinusoidal_Peak_Interpolation.html


3

OK Lets go! I consider HPS a very simple algorithm, this image representation show exactly how HPS work ! Yeah is highly recommended apply a hann window for every framed data ! What do you need to do is apply one window function over your framed signal, then apply FFT, you need just the first half absolute values from FFT, its give you the Magnitude, now ...


3

Maybe you could tell us more about the peak picking algorithm you are using! Some ideas: Use median filtering to remove noise (rather than a linear filter). If you have prior knowledge of the shape of the peaks you want to detect, use a correlator (matched filter) for this shape. Discriminate peaks according their amplitude.


3

Thought I should post my answer as it is bit different from other approaches. I tried this in Matlab. sum all channels and create an image, so all channels are weighted equally perform morphological closing and Gaussian filtering on this image for each column of the resulting image, find the local maxima and construct an image find the connected components ...


3

Here is yet an alternative solution to your problem by modelling your question as a 'path optimization problem'. Though it is more complicated than the simple binarization-and-then-curvefitting solution, it is more robust in practice. From the very high level, we should consider this image as a graph, where each image pixel is a node on this graph each ...


3

It symbolizes the input-output characteristic of a half-wave rectifier, which only passes positive input signals: $$y(t)=\begin{cases}x(t),&x(t)>0\\0,&x(t)\le 0\end{cases}$$


3

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 frequency Upper cutoff frequency threshold value and what is usually called "Machine Learning" is nothing but finding local minima over some (loss) function with real ...


3

I would recommend a streaming RMS detector. The standard approach for computing a streaming RMS detector is to square the input samples and then apply these to a 1st-order lowpass filter. If you want the output in dB, take 10*log10() of this quantity. If you want the output in volts, take the square root of this quantity. If Logs and square-roots are too ...


3

is it ok to showcase this diagram ? Sorry, we can't tell you this. This is really a function of your specific application, the physics behind your signal, and how you exactly define "peak". DSP can offer you methods to suppress "near by" peaks or to de-noise multiple peaks but whether that's the right thing to do or not depends largely ...


2

There is an intuitive proof that upsampling before cross-correlation is equivalent to doing it afterwards: Cross-correlation is convolution with the other signal time-reversed. Time reversal does not affect the bandwidth. Convolution is multiplication in the frequency domain, which also does not increase the bandwidth. If the original signals are properly ...


2

If you come up with a set of criteria that define what makes a local maximum become a "peak of interest", then you could test whether each local maximum meets the criteria you set. For example: A local maximum at $X(f)$ is considered a peak of interest if for some chosen small value $\epsilon$ and some chosen height $\mu$ , we can satisfy the following $$\...


2

There are a few Matlab implementations of various frequency estimators here. However, they will probably be "tricked" by the higher harmonics. That you know a range, perhaps the best technique is one of Eric Jacobsen's estimators. Have a look at his page. In essence, Eric's estimators use the FFT bin at $X(k)$, and on either side of ($X(k+1), X(k-1)$) the ...


2

You could normalize the average amplitude, i.e. YData = YData / mean(abs(YData)); Or you could normalize the signal power to one, i.e. YData = YData / sqrt(mean(abs(YData).^2)); If just the peaks are bothering you, you could use dynamic range compression, but that would introduce nonlinear distortions. As Phonon hinted, please tell us why you are not ...


2

Hilmar's answer is perfectly correct though incomplete in some sense. For any two finite-energy signals both having the same energy, one criterion for measurement of how similar they are is the energy in the difference signal which energy is given by $$\sum_{n=-\infty}^\infty |x[n]-y[n]|^2 \qquad\text{or} \qquad \int_{-\infty}^\infty |x(t)-y|t)|^2$$ ...


2

As long as the two signals are simply delayed versions of each other the delay is simply given by the point in time where maximum of the cross correlation occurs. If the signals are uncorrelated, then the question is meaningless. The tricky part is when the two signals are partially correlated or are filtered versions of the same original signal. In ...


2

compute RMS from audio signal to get power do AGC (automatic gain control) perform "discrete differentiation" (the simplest is 1st order: $y[i] = x[i] - x[i-1]$) if the value is greater than certain threshold, it means we have an onset. You have to determinate the threshold experimentally or use adaptive algorithm. Obviously you also need some kind of ...


2

A few more comments in support of pichenettes' answer: the desired peaks seem to be equidistant. If you know this to be the case then you could use this knowledge in your peak detector. otherwise I also believe that median filtering should help a lot. don't try to solve everything by a super-smart pre-processing and a dumb peak-detector, but try to combine ...


2

This python code will give you a very accurate result (I used it for lots of musical notes and obtained errors less than 0,01% of semitone) with parabolic interpolation (method successfuly used by McAulay Quatieri, Serra, etc. in harmonic+residual separation techniques) import matplotlib.pyplot as plt import numpy as np from scipy.io.wavfile import read ...


2

You could try using the peak-to-sidelobe ratio, i.e. how many standard deviations above the mean is each point in the correlation output. psr = ${p - \mu }\over\sigma $ Typically you compute the mean and sigma in a window around each point excluding the region nearest to each point.


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