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13 votes
Accepted

Bandwidth of an entire song

First of all, kudos to you: I appreciate the effort and thinking you've managed to articulate in your question. The DFT is a mathematical tool. As such, the parameters used to compute it can hide or ...
Jdip's user avatar
  • 6,265
9 votes
Accepted

Which transform most closely mimics the human auditory system?

In designing such transformations, one should take into account competing interests: fidelity to the human auditory system (that varies with people), including non-linear or even chaotic aspects (...
Laurent Duval's user avatar
8 votes
Accepted

Intuitive explanation of subspace

TL;DR: Subspaces are low-dimensional, linear portions of the entire signal space that are expected to contain (or be close to) a large part of the observable and useful signals or transformations ...
Laurent Duval's user avatar
7 votes
Accepted

Slow Down Music Playing While Maintaining Frequency

Yeah some of us can do it, you can speed up or slow down without affect the pitch, some guys call this applications of Time Stretch, there different ways to do it, you can do in frequency domain or ...
ederwander's user avatar
  • 2,038
7 votes

Intuitive explanation of subspace

Subspaces are a Linear Algebra concepts. The best representative example I can think of is the relationship of the XY plane to XYZ space, The former is a subspace of the latter. Any vector in the ...
Cedron Dawg's user avatar
  • 7,560
7 votes
Accepted

Synthesizing piano

Physical Audio Signal Processing by Julius Smith is probably something you'd be interested in! The full book is available online, and there's a whole chapter devoted to piano synthesis.
Jdip's user avatar
  • 6,265
7 votes

Can one use MUSIC algorithm to estimate DOA for a circular microphone array with a small radius?

Problem Summary You have a couple of difficulties with this problem: The microphone array isn't a uniform linear array (ULA), which is the most straightforward to model steering vectors for. Unless ...
Gillespie's user avatar
  • 1,797
6 votes

Is a recording of a chord merely a superposition of recordings of its constituent notes?

Depends to some degree on the instrument: electronic versus mechanical, string versus reed versus pipe, etc. Typical electronic keyboards have no coupling between keys, and the DSP mixer is usually ...
hotpaw2's user avatar
  • 35.4k
6 votes
Accepted

Spectral plot shows more notes than there really should be

Since the notes from a guitar are no pure sinusoids, you should expect to see some harmonics, even when analyzing the dry signal without effects. E.g., the note E is the perfect fifth of the note A, i....
Matt L.'s user avatar
  • 90.3k
6 votes
Accepted

MUSIC implementation in Pyroomacoustics library

Why the Code Works It's important to note that the MUSIC algorithm works on the microphone array dimension only. So it doesn't care how the data on the receive channels (microphones in this case) has ...
Gillespie's user avatar
  • 1,797
4 votes

Slow Down Music Playing While Maintaining Frequency

The tool/theory you describe is really a large area of research in music technology, broadly called audio time-scale modification. A large component of this field is how you might prevent audible ...
Speedy's user avatar
  • 436
4 votes

Intuitive explanation of subspace

A subspace is just a vector space that's included in a bigger vector space. Separating a random signal space into two statistically uncorrelated subspaces, a desired signal space and a noise space, ...
Fat32's user avatar
  • 28.3k
4 votes
Accepted

MUSIC algorithm terminology

Yeah, notation is not ideal. It is not - he assumes that each of the $M$ antenna elements is connected to its own RF chain, i.e., there are also $M$ receivers available. If you have fewer receivers ...
Florian's user avatar
  • 2,463
4 votes

FFT seems more accurate than MUSIC algorithm?

I created a signal with two sinusoids and added increasing amounts of random noise to it. The results of running the FFT and MUSIC on this signal are shown in the image below. You are using ...
havakok's user avatar
  • 682
4 votes

Why mixing two sines sounds like a triangle?

I tried looking at what your libraries output as just a sine wave by modifying your code: ...
Peter K.'s user avatar
  • 25.8k
4 votes
Accepted

Why is the null of an adaptive beamformer narrower than antenna beam-width?

Super-resolution techniques such as MUSIC can be used for creating higher resolution nulls (see MUSIC-based steering vector used in adaptive nulling suppression for example), but what I think may be ...
Dan Boschen's user avatar
  • 51.9k
4 votes

Can one use MUSIC algorithm to estimate DOA for a circular microphone array with a small radius?

The paper 2D DOA estimation with sparse uniform circular arrays in the presence of mutual coupling suggests that the steering vectors are given by: For your array, it looks like there are 4 sensors ...
Peter K.'s user avatar
  • 25.8k
4 votes
Accepted

Smallest Eigenvalue in the Derivation of the MUSIC Algorithm

This is a simple consequence of previous insights. As was observed that $APA^H$ is positive semi-definite, this means that also $S-\lambda S_0$ has to be the same. Now if $\lambda$ is not the smallest ...
Lutz Lehmann's user avatar
  • 1,195
3 votes
Accepted

Weird note structure on guitar audio waveform

Here are some possibilities: Transverse waves on a guitar string have two polarized components, one parallel and one perpendicular to the guitar's soundboard. User hotpaw2 mentioned energy exchange. ...
Olli Niemitalo's user avatar
3 votes
Accepted

DOA estimation; Music (Multiple Signal Classification) algorithm

The receive-signals covariance matrix $\mathbf R$ is by its definition $$\DeclareMathOperator{\expect}{E}\newcommand{\E}[1]{\expect\left[#1\right]}\DeclareMathOperator{\diag}{diag}$$ $$\mathbf R= \E{\...
Marcus Müller's user avatar
3 votes

what are the Pros and Cons of ESPRIT and MUSIC algorythms?

The prime thing such algorithms aim to do is to make use of more information that you may have about the signal. In this case, the extra information is that you know the number of signals (sinusoids) ...
Peter K.'s user avatar
  • 25.8k
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 ...
Fat32's user avatar
  • 28.3k
3 votes

What is difference between frequency and pitch?in nutshell and simple words?

Frequency is mathematically defined as the number of cycles per second. So it is a more strict word mathematically. It is represented numerically by the unit called Hertz. $f=1/T$, where $T$ ...
micropyre's user avatar
  • 161
3 votes

MUltiple SIgnal Classification (MUSIC) Implementation

I'm going to group number 1 and 3 as related. For a high level description of MUSIC, you can take a look at MATLAB's overview here. One of the main steps in the algorithm is to find the eigenvectors ...
Envidia's user avatar
  • 2,546
3 votes

What are features in signal processing using a more tangible or less abstract description

A feature is a number that describes one aspect of a signal. Signals can be very complex, and the simplest analysis tools (like a time plot, a spectrum, or an energy measurement) don't tell you ...
MBaz's user avatar
  • 15.3k
3 votes
Accepted

Audio compressor delay/lookahead

What is typical delay times for a compressors or limiters delay/lookahead time? I don't think there is "typical": it depends a lot on the bandwidth, frequency content and what specifically ...
Hilmar's user avatar
  • 45.3k
3 votes

Audio compressor delay/lookahead

In another life, maybe about 25 years ago, I did a few simple compressors in DSP code and I did toss in a delay on the audio, which is equivalent to a lookahead on the audio envelope. The delay was ...
robert bristow-johnson's user avatar
3 votes

Relation of pitch to frequency?only with fundamental frequency or also with harmonics?

For a single note (as compared to a chord) there is only one pitch. The sound typically consists of a fundamental and some harmonics. For example, you play the open A string (note = "A2") on ...
Hilmar's user avatar
  • 45.3k

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