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

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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  • 10.5k
9 votes
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Why is each window/frame overlapping?

Why is each window/frame overlapping? Windowing is a means to stationarize signals. Inside a small enough window, you can expect that the properties of the signal chunk do not vary too fast. And you ...
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9 votes

What are i-vectors and x-vectors in the context of Speech Recognition?

The i-vectors and x-vectors share the ability to represent speech utterance in a compact way (as a vector of fixed size, regardless of length of the utterance). The extraction algorithms of i-vectors ...
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  • 231
8 votes
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Signal processing for audio and speech

In line with a previous similar question here are my suggestions: There are so many nice books but I believe you should first have a look at the science of sound from Rossing for getting the most ...
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  • 26.9k
7 votes

Confusion Regarding Bi Linear Transform

The bi linear transform is the transform from the Laplace Transform Domain to the Z Transform. The Laplace Transform Domain is a regular plane. This transform transforms vertical lines in the Laplace ...
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  • 41.5k
7 votes

Why is each window/frame overlapping?

More overlap means you end up with more windows (of a given length) per second of audio. More windows (of a given length) requires more FFTs which requires more MACs or FLOPs which generally requires ...
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  • 34k
6 votes

Is There a Sparse Representation for Noise?

Let's think about it in a different way - Generate Noise from a Dictionary. Let's create a Dictionary $ A \in \mathbb{R}^{m \times n} $ where each of its rows is normalized (Has Euclidean Norm of $ 1 ...
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6 votes
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What Is the Point of Doing the Zero Padding?

You may think of it as efficient way to apply Dirichlet Window Based interpolation in the Fourier Domain. The advantage of applying the interpolation using Zero Padding in the Time Domain is very ...
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6 votes
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Audio Processing Glossary

My own interpretation: Sound: a mechanical wave that propagates through the air or water. Audio: sound in the 20 Hz to 20 kHz range; in other words, sound that is (at least in theory) audible to a ...
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6 votes
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Which Programming Language Should Be Used for Deep Learning (Deep Neural Network [DNN])?

The language choice depends on many factors. For instance, are you after developing low level features of DNN or using existing building blocks? Most advanced and popular Deep Neural Networks (DNN) ...
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5 votes
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Confusion Regarding Bi Linear Transform

As already mentioned by other people, the bilinear transform is often used to map a continuous-time system described in the $s$-domain to a discrete-time system described in the $z$-domain. However, a ...
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  • 80.4k
5 votes
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Harmonics to Noise Ratio Estimation

For large number of samples both will be indistinguishable. The Biased Version is the Maximum Likelihood Estmator (MLE) of the problem. It means it has many nice properties for $ N \to \infty $. ...
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5 votes
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Modelling Unwanted Signal in a LMS Adaptive Filter

The LMS and many of the variants of Adaptive Filters (In the Linear System context) work in the following settings (Intuitive): You have access to 2 signals. One signal is the result of the other one ...
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5 votes

Converting speech audio to telephone audio

Band-pass filtering with cut-off frequencies of 300 Hz and 3400 Hz should result in a good approximation. Try with a Chebychev filter or order not more than 6. Then you may need to downsample your ...
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4 votes
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What is best practice to remove static noise?

The standard method to remove stationary noise is spectral subtraction, where the magnitudes of the short-time Fourier transform of the noisy signal are modified based on an SNR estimate in the ...
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4 votes
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In framing of audio samples', what is need of frame shift while giving frame size??

By performing the windowing with overlap we are artificially increasing our time resolution (larger granularity of features in time). This is especially useful when frame duration is long (bad time ...
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4 votes

Signal processing for audio and speech

But which features of signals reveal differences between piano and guitar Look at things like timbre; basically, most things when excited to oscillate will not only produce a single tone, but a set ...
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4 votes

Cepstrum calculus disambiguation

A common technique for computing the inverse fft is to invert the imaginary part of the input array, perform a forward fft and then invert the imaginary part of the output array. In the case of the ...
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  • 486
4 votes

What is a "pitch period"?

The pitch period of a perfectly periodic function, $x(t)$, is the smallest positive value $P>0$ such that $$ x(t+P) = x(t) \qquad \forall t \in \mathbb{R} $$ Now, simply because a function is ...
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3 votes
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When should we using moving average in algorithm design?

So when will you think you need moving average in an algorithm design? If you mean moving average filters; moving averages as the name suggest are computed as averages of samples say, $M-1$ ...
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  • 3,282
3 votes

Calculation of SNR

I have a suggestion for you. Compute the mean power of the signal at the input of the filter without any signal applied at the input. You should only receive noise. This will be the noise power $ P_{...
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3 votes

Signal processing for audio and speech

Here is a series of tutorial videos on Speech and Audio Processing by Professor E. Ambikairajah; about 1 hour each. They can serve as a basis to focus on more specific topic. Speech and Audio ...
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3 votes
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Logarithmic Spacing

Let's note $x_k$ and $x_{k+1}$ two successive samples. In the usual case of uniform sampling, the spacing between two successive samples is independent of $k$ and is given by $T$, the sampling period. ...
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  • 927
3 votes

Parseval's Theorem for discrete series

You are right, but you have mistaken the DTFTs... Considering the Parseval's relation for real discrete-time sequences to be: $$ \sum_{n} x[n]y[n] = \frac{1}{2\pi} \int_{-\pi}^{\pi} X(e^{j\omega})Y(...
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  • 26.9k
3 votes
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How to edit audios so that they have the same length

ImageMagick is a great tool to edit multiple images in the command line. Thanks to your question, I just discovered SoX, or Sound eXchange: SoX is a cross-platform (Windows, Linux, MacOS X, etc.) ...
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3 votes

Audio Quality Assessment

Audio quality assessment is one of the most critical pieces of audio coding and enhancing applications. The task requires an accurate and objective (mathematical) modeling of human auditory system ...
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3 votes

Negative Signal to Noise Ratio

Signal to Noise ratio (SNR) is a ratio of powers and hence it is always greater than or equal to zero, it cannot be negative. On the other hand, very commonly SNR is expressed in decibel (dB) ...
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  • 26.9k
3 votes

Mel Cepstral Distortion

Ok so here is what I found. The distance is dependent on the way that the mfccs are calculated. This makes sense to me and also explains why cepstral mean normalization affects the values of the MCD. ...
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  • 81
3 votes

Is there any way that we can perform speech recognition without using Fourier transforms?

All recognition tasks (doesn't even have to be speech recognition) are reductions of a very high-dimensional signal (your speech recording's dimension is the number of audio samples!) to a low-...
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