jojek
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One application of the Hilbert Transform is to obtain a so-called Analytic Signal. For signal $s(t)$, its Hilbert Transform $\hat{s}(t)$ is defined as a composition: $$s_A(t)=s(t)+j\hat{s}(t)$$ The ...

We know that in general transfer function of a filter is given by: $$H(z)=\dfrac{\sum_{k=0}^{M}b_kz^{-k}}{\sum_{k=0}^{N}a_kz^{-k}}$$ Now substitute $z=e^{j\omega}$ to evaluate the transfer function ...

Just to make things clear - this property is not fundamental but important. It is the fundamental difference when it comes to using DCT instead of DFT for spectrum calculation. Why do we do Cepstral ...

Encouraged by Hilmar, I've decided to update the answer with all the steps necessary to calculate the Reverberation Time from a scratch. Presumably, it will be useful for others interested in this ...

This is the FIR filter, although it looks like an IIR. If you calculate the coefficients you get finite impulse response: $h=[1]$ This happens due to zero-pole cancellation: $Y(z)-0.5Y(z)z^{-1}=X(z)... View answer Accepted answer 18 votes Let me start from the beginning. The standard way of calculating cepstrum is following: $$C(x(t))=\mathcal{F}^{-1}[\log(\mathcal{F}[x(t)])]$$ In the case of the MFCC coefficients case is a bit ... View answer Accepted answer 18 votes This phenomenon has nothing to do with spectral leakage. What you are observing is the effect of zero padding. Given a number of samples$N$, there is a maximum possible frequency resolution$\Delta f$... View answer Accepted answer 16 votes By long shot it is doable - to what extend? You will see. This task of environmental sound classification is not very well studied. Also choice of machine learning paradigm is crucial - statistical ... View answer 14 votes Spectral Entropy describes the complexity of a system. It is defined as follows: Calculate the spectrum$X(\omega_i)$of your signal. Calculate the Power Spectral Density of your signal via squaring ... View answer Accepted answer 13 votes I can recommend you two books about DSP for C language. Embree P. M. - C Language Algorithms for Digital Signal Processing It is old and you can easily get it second-hand for a decent price. It ... View answer 12 votes It's not only about programming language but library you are using. I can think of the following: MATLAB - image processing capabilities are quite ok, but for more advanced and real time processing ... View answer Accepted answer 11 votes The way MFCC's are always used is by feeding them into the classifier. This can be done on a frame-by-frame basis (12x1 vector), or by concatenating (12xN) - same as a spectrogram. Thus for DTW, you ... View answer Accepted answer 11 votes There is only one correct way of scaling DFT when calculating PSD with RMS values. Given input signal$x$and its DFT$X$, the exact formula is: $$\mathrm{PSD}=\frac{2\cdot \hat{X}}{f_s\cdot S}$$ ... View answer Accepted answer 10 votes I think it is kind'a similar to soft and hard thresholding using in wavelet de-noising. Have you come across this topic? pywt has already an in-built function for this purpose. Please take a closer ... View answer Accepted answer 10 votes You should not be using the analog filter - use a digital filter instead. You want the filter to be defined in Z-domain, not S-domain. Also, you should define the time vector with known sampling ... View answer 10 votes Well, first of all the Sound Level Pressure decreases by$6 \; \mathtt{dB}$when doubling the distance - this plays a big role. We do also have sound attenuation coming from our medium - air. Let's ... View answer 10 votes Frequency bin at zero is simply mean value of your signal. Just take a look on definition of DFT, for zero frequency$k$we get:$$\left. X[k]=\sum_{n=0}^{N-1}x[n]e^{-i 2\pi n\cdot k} \right |_{k=0} ... View answer 9 votes If by "its" you mean the value of the fader, then yes - it's absolutely correct. Fader defines the attenuation of the signal with respect to the reference level. The units are in logarithmic scale. ... View answer Accepted answer 9 votes Definitely you will have to calibrate your system. You need to know what is the relationship between dBFS (Decibel Full-Scale) and dB scale you want to measure. In case of digital microphones, you ... View answer Accepted answer 9 votes Aside from reduction of spectral leakage, there is a one major trade-off to be made when choosing a window function. Below you can see a figure with various parameters. Two of them are most important: ... View answer Accepted answer 8 votes Probably you've noticed that primarities are$\mathbf{X}$,$\mathbf{Y}$,$\mathbf{Z}$, not$\mathbf{R}$,$\mathbf{G}$,$\mathbf{B}$(which are corresponding to the color values$R$,$G$,$B$). This is ... View answer 8 votes This plot depicts how to convert your digital signal back to the analog one, using$\mathrm{sinc}$functions. The nice property of these functions used in this process, is that maximum of each ... View answer Accepted answer 8 votes We always want to apply some kind of a window function in order to minimize the effect of leakage. This makes rectangular window (lack of any windowing) case never used, this is why: Any tapering ... View answer Accepted answer 8 votes Your code is bit unclear, especially generation of your signal. Python allows for vectorized operations so it is good to use it. What's more, it is good to clearly specify the sampling frequency of ... View answer Accepted answer 7 votes I don't really understand what do you mean by multiply them in the time domain and multiply them with window function. I think that you are trying to implement the Welch's PSD calculation. If so, ... View answer 7 votes From the ones I've been using I can recommend: YAAFE - very pleasant to work with in Python ESSENTIA - another one I like particularly due to Python integration aubio FEAPI Aquila - friend of mine ... View answer 7 votes If your signal is real-valued, then it's spectrum is conjugate symmetric. That means, that negative frequencies (or frequencies from$\frac{f_s}{2}$up to$f_s\$) are mirrored. Thus we can always ...

I believe that this "color graph" you are looking for is a spectrogram (although it looks to me more like a scalogram, but you did not mentioned wavelets). Let me give you an example in MATLAB of ...