jojek
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Meaning of Hilbert Transform
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44 votes

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 ...

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How do I manually plot the frequency response of a bandpass Butterworth filter in MATLAB without freqz function?
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28 votes

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 ...

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Cepstral Mean Normalization
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21 votes

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 ...

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Calculation of Reverberation Time (RT60) from the Impulse Response
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19 votes

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 ...

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What kind of filter is that? Is it IIR?
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19 votes

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)...

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Is this a correct interpretation of the DCT step in MFCC calculation?
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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 ...

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Why do I have frequency leakage in DFT after zero padding if frequency resolution is fine?
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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 $\Delta f$...

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Feature extraction for sound classification
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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 ...

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What is spectral entropy?
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 ...

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Recommendation for book - Writing DSP code in C
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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 ...

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Image processing coding
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 ...

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What's the correct graphical interpretation of a series of MFCC vectors?
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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 ...

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What should be the correct scaling for PSD calculation using $\tt fft$
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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: $$\mathrm{PSD}=\frac{2\cdot \hat{X}}{f_s\cdot S} $$ ...

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Feature extraction/reduction using DWT
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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 ...

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Apply Low pass Butterworth filter in Python
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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 ...

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If low frequency travels longer distance, why our speech is not travelling longer distance?
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 ...

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MATLAB - remove the frequency at zero in FFT
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} ...

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Is it accurate to say in digital audio that, when a fader is down, then its value is "-$\infty$"?
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. ...

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FFT to spectrum in decibel
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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 ...

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Why are there so many windowing functions?
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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: ...

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The small red peak in the CIE standard observer
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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 ...

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Sampling Theorem illustration
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 ...

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STFT: why overlapping the window?
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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 ...

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Why FFT does not retrieve original amplitude when increasing signal length
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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 ...

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Understanding the Windowing Method in PSD Calculation
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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, ...

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Are there libraries for extraction of sound wave features?
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 ...

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Under what condition is the available bandwidth $f_s$ instead of $\frac{f_s}{2}$?
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 ...

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Time-frequency representation of sound signal using Matlab
7 votes

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 ...

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DSP Concepts Visually Explained
6 votes

Personally, I very much like the interactive visualisations of filters that connect various bits together. There is a great website called MicroModeller DSP (I am not affiliated with it). You can ...

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Differences between soft knee and hard knee in Dynamic Range Compression (DRC)?
6 votes

Regarding advantages - there is only one I can think of... The soft knee makes the compressor less noticeable. It sounds more natural, especially when you are dealing with higher compression ratios (...

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