Climmobile réversible Airwell MFR MAUI AW-MFR012-H41 - 3.52 kw 554.00 € TTC Clim WINDOW Airwell WFD AWWR-WFD009-C11 et AWWR-WFD012-C11 689.00 € TTC Clim mobile Airwell MFH MAUI AW-MFH010-C41 et AW-MFH012-C41 482.00 € TTC Console monobloc réversible inverter Airwell XDA AW-XDA009-N91 - 2.35 kw 1422.00 € TTC Clim mobile Wifi LG PA11WS Gainepour clim mobile. Gaine pour clim mobile : la sélection produits Leroy Merlin de ce mardi au meilleur prix ! Retrouvez ci-après nos 491 offres, marques, références et promotions en stock prêtes à être livrées rapidement dans nos magasins les plus proches de chez vous. Affiner. Quelest la meilleure clim mobile. janvier 29, 2021 janvier 29, 2021 Olivier .B. Read More . Climatisation. Quel est le meilleur Climatiseur mobile silencieux. janvier 29, 2021 février 8, 2021 Olivier .B. Lorsque la chaleur revient à la maison, vous avez besoin d’un peu de répit et vous ne voulez pas avoir à faire un travail pour installer. Read More . Climatisation. Quel est le meilleur Afinde se relaxer comme il faut, tout en remédiant aux problèmes, l’idéal serait d’utiliser ceux qui disposent à la fois d’un système sans évacuation et qui sont silencieux. voici pour vous un comparatif des 10 meilleurs climatiseurs mobiles silencieux sans évacuation de 2020 qui vous permettront d'en savoir un peu plus pendant cette période et de mieux faire le choix selon la Quevous ayez besoin de systèmes de chauffage fonctionnant au gaz, au fioul, au bois ou de systèmes de climatisation ou de ventilation, vous trouverez, accompagné de nos experts, la solution qui saura répondre aux besoins spécifiques de votre habitat. Consultez, également, le tableau de conversion en ligne pour le chauffage, mis à Climatiseurmobile Equation Silent 2 2600 W pas cher : retrouvez tous les produits disponibles à l'achat dans notre catégorie climatiseur En utilisant Rakuten, vous acceptez l'utilisation des cookies permettant de vous proposer des contenus personnalisés et de réaliser des statistiques. Hésitationentre deux modèles de clim mobiles. Je souhaite acheter un climatiseur mobile pour une surface de 25m2. Pouvez vous m'aider dans mon choix. Je voudrais le plus efficace dès deux modèles : TristarAC-5477 Mobile Climatizzazione – 7000 Btu – Benda Frigoriferi - Tipo di azionamento Cablato Marca Tristar Nome modello Ac Caratteristica speciale Telecomando Tipo di garanzia Limitata Colore Bianco Dimensioni articolo L x L x A 31,8 x 37,3 x 87,8 cm Peso 18 chilogrammi Metodo di controllo Telecomando Informazioni su questo articolo - Capacità di raffreddamento CaractéristiquesEquation 2600W - WAP-07EZ26. + Voir toutes les caractéristiques. - Fermer toutes les caractéristiques. Longueur du tuyau (min - max) 33 - 118 cm. Réversible (chauffage) Non. Puissance de refroidissement. SYNo. These are indeed strange days on planet Earth. For all of the technological genius of the human race, we have not even considered how to save ourselves from ourselves. The absolute epitome of human insanity is the ongoing decades long attempt to completely engineer Earth's climate system with countless variations of weather and biological warfare along the way. Even the U. S. National Academy of Sciences is trying to sound the alarm on the dangers of geoengineering though these scientists have not yet shown the courage to admit global geoengineering has long since been fully deployed. As the biosphere implosion continues to accelerate, the disaster capitalists have come from every dark corner with the goal of profiteering in the final hours of industrialized civilization. I have had my own confrontation with internationally recognized geoengineer David Keith, but there are many more in the camp of climate engineering capitalists. Who are these people? What are their individual parts in the planetary geoenigneering nightmare? Certainly those on the list below are only the lowest level pawns in the play, but it is still important to who they are and where they fit in. My most sincere gratitude to Jacob Brogan for assembling an excellent exposé of the geoengineering disaster capitalists. Dane Wigington Geoengineering describes the active transformation of our planet’s climate through human intervention. Here are some of the key players, major debates, and pop cultural landmarks shaping the ways that we understand this emerging field. Key Players Paul Crutzen Crutzen, a Nobel Prize–winning atmospheric chemist, helped legitimize scientific conversations about geoengineering with his 2006 paper about seeding the atmosphere with sulfur to reflect sunlight back into space. Peter Eisenberger Working to extract carbon dioxide from the air through his company Global Thermostat, Eisenberger is at the forefront of the still-developing business side of geoengineering. Russ George In 2012, the climate entrepreneur George attempted an unauthorized experiment in iron fertilization, dumping large quantities of metal into the ocean to stimulate the growth of carbon-consuming phytoplankton. Newt Gingrich The former speaker of the House, Gingrich is one of geoengineering’s most politically connected advocates, insisting that it’s an important weapon in the fight against climate change. David Keith Having literally written the book on solar radiation management, Harvard Kennedy School professor Keith also works to advance the science of CO2 reduction with his company Carbon Engineering. Marcia McNutt An oceanographer and editor-in-chief of Science, McNutt chaired the National Academy of Sciences’ comprehensive inquiry into geoengineering, which published its findings in February 2015. Nathan Myhrvold The former chief technology officer of Microsoft, Myhrvold has proposed a project he calls the Stratoshield, in which giant hoses would be lifted into the sky by balloons to spray aerosols into the upper atmosphere. Raymond Pierrehumbert A University of Oxford–based climatologist, Pierrehumbert has vocally argued against geoengineering by solar radiation management, famously calling such efforts “barking mad.” Alan Robock Rutgers University professor Robock’s widely discussed “Twenty Reasons Why Geoengineering May Be a Bad Idea” provided a sweeping response to the proposals of Crutzen and other geoengineering advocates. Lynn Russell An atmospheric scientist based at Scripps, Russell has led research into the potential impacts of geoengineering on ecosystems. Major Debates Further environmental degradation Though some geoengineering technologies may help cool the planet, it’s possible that they may release additional greenhouse gasses, harm the ozone layer, or otherwise advance the damage they aim to prevent. Is geoengineering an environmental dead end? Induced complacency Even geoengineering’s advocates acknowledge that it’s not a true solution to climate change. But if it’s successfully implemented, will it prevent us from doing more to save the planet? Will it simply give us permission to keep burning fossil fuels? International cooperation In the absence of treaties regulating geoengineering, there’s a risk that companies or countries will pursue projects without taking proper precautions—and the climate doesn’t respect national borders. Some commentators even worry that “rogue billionaires” might take matters into their own hands. Can we regulate geoengineering without restricting innovation? Long-term commitment Scientists such as Pierrehumbert argue that we’ll have to stick with geoengineering some technologies for thousands of years once we embrace them, lest we cause even worse catastrophes. Will civilization stay stable for long enough to make a difference? Price tag At present, the most effective geoengineering technologies are prohibitively expensive, often less cost-effective than converting to environmentally safe energies. Can scientists bring down the expense? Or should we pursue these avenues regardless? Unequal effects Most geoengineering proposals would have different and often unpredictable effects on different regions of the planet. Even as some benefit, others would potentially suffer colder winters, decreased rainfall, or other problems. How can we assure that it helps all? Unintended consequences We lack the technological sophistication to accurately model most geoengineering proposals on a global scale, making it difficult to anticipate their effects. Should we continue researching these consequences or try to aggressively push the technology ahead? Weaponization Many geoengineering proposals originate in Cold War technologies. As the science advances, will we be able to prevent their renewed use as weapons? How can we prevent climatological conflicts? Pop Culture The Brothers Vonnegut, by Ginger Strand Delving into the historical origins of climate technology, this biography demonstrates how weather-control technology shaped science fiction—and how science fiction helped shaped geoengineering in its wake. Green Earth, by Kim Stanley Robinson Collecting and condensing the three volumes previously known as the “Science in the Capital” trilogy into one novel, Robinson imagines attempts to resist the effects of climate change—and some of the disasters that could ensue. “Hypercane,” by Eric Holthaus In this short story published in Vice, Slate’s Holthaus shows how the promise of geoengineering could make things worse if we don’t aggressively investigate the technologies behind it. Ice Twisters, directed by Steven R. Monroe In this box office bomb, cloud seeding–based geoengineering creates an absurd disaster. But science can fix what it has wrought! Snowpiercer, directed by Bong Joon-ho This acclaimed film depicts a world driven into a new ice age by geoengineering gone wrong. Thunder & Lightning, by Lauren Redniss In this beautifully illustrated hybrid of comics and science journalism, Redniss visualizes some of the ways humans have attempted to regulate the weather, especially in the face of rapidly accelerating climate change. “Who Shot Mr. Burns?” The famous Simpsons whodunit began with Mr. Burns plotting to block out the sun so that Springfieldians would be forced to consume more energy. It’s kind of geoengineering! Read Up “20 Reasons Why Geoengineering May Be a Bad Idea,” by Alan Robock Despite its listicle format, this thoroughly annotated article offers one of the most comprehensive, rigorous challenges to geoengineering advocates. “Albedo Enhancement by Stratospheric Sulfur Injections,” by Paul Crutzen With this seminal paper, Crutzen helped to legitimize scientific conversations about geoengineering. A Case for Climate Engineering, by David Keith In this readable volume, climate scientist Keith makes a passionate case for albedo modification technologies, exploring their promise and the effort required to put them into practice. Climate Intervention Reports, by the National Academy of Sciences The product of years of research, this report comes close to offering the scientific consensus on both carbon dioxide removal and albedo modification. “The Ethics of Geoengineering,” by David Appell The first of a two-part series, this essay offers a thorough, balanced examination of geoengineering’s risks, as well as its possible rewards. The Planet Remade, by Oliver Morton Even as he discusses the science behind geoengineering technologies, Morton goes deep into the social and political anxieties that hover around them. Lingo Albedo The portion of sunlight that the Earth reflects back into space. The albedo is shaped by factors like cloud cover and snowfall. Biological pump Under ordinary circumstances, oceanic plankton naturally pull CO2 out of the atmosphere. By increasing plankton quantities, some geoengineers hope to reduce atmospheric CO2 levels. Carbon dioxide reduction A key geoengineering strategy, carbon dioxide reduction would involve removing pollutants directly from the air. Ocean fertilization The artificial stimulation of the ocean’s biological pump. Ocean fertilization might help pull CO2 out of the atmosphere, but it could also damage fisheries. Solar radiation management The second major geoengineering strategy, solar radiation management aims to cool the Earth by increasing its reflective properties see albedo. Source article by Jacob Brogan From Wave to MIDI In two easy steps and one hard step. A high-resolution spectrogram is made from a wave audio file. The constant-Q transform and the frequency reassignment algorithm are used for consistent high resolution. The user edits the image to erase overtones and echos. The edited image is then converted to MIDI. Dynamic programming and a nonlinear smoother remove noise and flutter. Greedy agglomeration merges frames into notes. Download source code - KB Table of Contents Introduction Part 1 Building a Better Spectrogram Constant-Q Transform Window Functions Frequency Reassignment Lanczos Interpolation Interlude Editing the Image Part 2 From Melody Line to MIDI Undoing Lanczos Interpolation with Root-finding Separating Sound from Silence with Dynamic Programming Trimming Outliers with a LULU Smoother Agglomerating the Notes The Formula for Expression Build Instructions Using the Code Release History References Appendix A Very Short Derivation of the Discrete Fourier Transform Introduction To transcribe recorded music to score notation is a difficult problem. Notes are hard to pick out from among the overtones and echos. On the other hand, converting solo audio to MIDI is fairly straightforward. One possible method is to convert the audio to an image by taking the spectrogram. The image is then hand-edited to erase overtones and echos, leaving the most subtle step for the human brain. The solo line of the edited image may be converted to MIDI. The SPECTR and SCRIBE programs are intended to serve as a MIDI voice controller, comparable to a keyboard or a breath controller. Program SPECTR produces a high-resolution spectrogram in the alto range, 32 notes in all, from F below treble clef to C above treble clef. Next, the user edits the image to remove the overtones. Because this is a standard image file, any editing operation which can be done on an image may be done at this step. Program SCRIBE converts the edited image to a standard MIDI file. The output of SCRIBE is made long by many changes in expression and pitch bend, at 240 frames per second. The shortcoming of the program is that it only transcribes solos, and it is a lot of work to hand-edit the images. This is a command-prompt program. It is free and in the public domain. Some subroutines are of interest in their own right. Subroutine FRAT implements the Frequency Reassignment transform, which offers greater precision than the Fourier transform. GLOM merges elements of a sequence into segments of similar value. SMOOTH is a nonlinear smoother for removing outliers from a data sequence. Also included in the distribution is some excellent legacy code SOLV and ZERORA are based on ZEROIN by L F Shampine and H A Watts for solving an equation. ISHELL by Alfred H. Morris, Jr. sorts an integer array. RORDER by Robert Renka applies a permutation to a floating-point array. Part 1 Building a Better Spectrogram A well-known graphical representation of a sound is the spectrogram. In this view, time is represented in the horizontal direction and frequency is represented in the vertical direction. Each vertical line in the image is a Fourier transform of a brief portion of the sound. Each pixel within that line is a coefficient of the Fourier transform. For more information on the Fourier transform, please refer to the CodeProject articles Discrete Fourier Transform for Frequency Analysis by pi19404, and Fourier Transform in Digital Signal Processing by Jakub Szymanowski The Constant-Q Transform The discrete Fourier transform takes a sequence and returns an array of coefficients see Appendix. The original signal is represented as a sum of sine and cosine waves at frequencies \f_o, 2f_o, \ldots, i f_o, \ldots, \frac{N}{2} f_o \ where \f_o\ is the fundamental frequency, that is, the sampling rate divided by the number of samples included in the transform. The design equation for setting up a Fourier transform is $MR = NF$ where M is an integer R is the sampling rate in cycles per second N is the number of samples in the transform F is the frequency to be measured The limitation of Fourier analysis is that in general, there is a tradeoff between time resolution and frequency resolution. To make the frequencies more closely spaced, \f_o\ must be made smaller. For a given sample rate, this requires N be made larger. The more precisely you seek the frequency of an event, the less precisely you can determine when it happened. By its nature, the Fourier transform finds amplitudes at a set of equally spaced frequencies. For the purposes of musical analysis, this is not optimal. The tones of the musical scale are spaced according to a geometric progression. Specifically, each tone has a frequency greater than the previous by a factor of \\sqrt[12]{2}\. The vertical bars in the graph represent the exponential growth of frequencies of musical tones. The horizontal lines represent the evenly spaced Fourier transform bins. A transform size adequate to separate notes of high frequency will not separate notes of low frequency. A transform size adequate to separate notes of low frequency has excess resolution for notes of high frequency. A large transform size must be chosen. This comes at the expense of diminished time resolution and increased computation. A straightforward solution [Brown, 1991] is to take transforms of different sizes to observe the different frequencies. This is the Constant-Q transform, which is not a new mathematical technique, but a targeted use of the Fourier transform. It allows the frequency-time resolution tradeoff to be chosen in an optimal way across the spectrum. In program SPECTR, M is chosen as 17, because the ratios 1617 and 1718 are approximately equal to the spacing between tones of the musical scale. The Discrete Fourier Transform DFT is not nearly as fast as the Fast Fourier Transform FFT to find all the coefficients from \1 \ldots \frac{N}{2}\. But the DFT can be used to find a single coefficient and the FFT always computes N coefficients. Many FFT implementations force N to be a power of 2 or a product of small prime numbers. The DFT places no restrictions on N. With suitable choices of M and N, the DFT permits any set of frequencies to be measured up to the Nyquist limit \\frac{R}{2}\. Window Functions Fourier analysis assumes that the signal to be analyzed is a perfectly periodic function, with a period equal to the transform size. Real signals to be analyzed never fulfill this assumption. To reduce the error introduced, it is necessary to taper off the beginning and end of the samples to be analyzed by multiplying them by a window function. Window functions are defined over \0 \ldots 2\pi\ and equal zero at their endpoints with a maximum at the center. Many window functions have been defined, but their shapes are much alike. The choice of window function has a definite impact on the results of the analysis. There is a tradeoff between removing noise and accuracy of amplitude measurements. This can be seen in a plot of some window functions in the frequency domain, computed according to the method in [Heinzel, Rudiger, & Schilling, 2002]. Visually, the difference between the functions may be described as a choice between flatness and sharpness of the center lobe. The Hann window has a fairly narrow center lobe, and it can better detect frequency. The Salvatore window has a flat center lobe, and it measures amplitude with greater accuracy. The Nuttall window has a flatness of < 1dB attenuation over the center bin, which means that it is flat enough for audio applications, since this is around the just-noticeable difference of human hearing. To not overburden the user with options, the Nuttall window has been selected for the project and is incorporated into subroutine FRAT. A different window function can be chosen by editing the parameter values in the source code. The practical effects of window functions can perhaps be shown by example. A very sharp window function like the Hamming has good resolution while a flattop window can be rather cloudy However, the comparison is not all in favor of the sharp windows. They seem to generate a forking artifact, where a single pitch splits falsely? into multiple frequencies The flattop window suffers much less from this effect Frequency Reassignment The frequency resolution obtained by the Fourier transform is the best possible in the general case. However, often there is only one frequency component present in an interval of the spectrum. In this case, the time-frequency tradeoff may be dodged and much better frequency resolution can be obtained. The idea is that since the sine and cosine coefficients of a component are known, the phase of the resultant wave is known. Frequency is the time derivative of phase. The derivation of the formula [Lazzarini, 2011] requires complex analysis which I don't pretend to understand, but the results are easy to use. Let \u_j\ denote the window function, \w_j\ denote the derivative of the window function with respect to index j, and \y_j\ denote the input signal. To find the energy \e\ and frequency \\hat{f}\, compute $\begin{aligned} a & = \frac{1}{N}\sum^N_{j=1} u_j y_j \cos\frac{2\pi}{N}Mj \\ b & = \frac{1}{N}\sum^N_{j=1} u_j y_j \sin\frac{2\pi}{N}Mj \\ c & = \frac{1}{N}\sum^N_{j=1} w_j y_j \cos\frac{2\pi}{N}Mj \\ d & = \frac{1}{N}\sum^N_{j=1} w_j y_j \sin\frac{2\pi}{N}Mj \\ e & = a^2 + b^2 \\ f & = \frac{MR}{N} \\ \hat{f} & = f + \left\frac{ad-bc}{e}\right\left\frac{R}{2\pi}\right \end{aligned}$ Amplitude is the square root of energy. Other Considerations For best results, the input signal should be passed through a high-pass filter to remove frequencies below the fundamental. For efficiency, the signal is downsampled to keep N ≤ 6000. Before downsampling, the signal should be low-pass filtered to half the reduced sample rate. Digital filters have been discussed in my earlier article Customizable Butterworth Digital Filter. Because there is a slight overlap of the frequency bins, there is a possibility that frequencies may be out of order. Insertion sort is efficient on almost sorted data. Subroutine ISORTR passively sorts on frequency. Subroutine RORDER by Robert Renka is then called to apply the ordering to the amplitudes and frequencies at each analysis frame. Interpolation The frequencies and amplitudes returned by FRAT must be used to set pixel intensities. That requires interpolation. There are several ways to do that, but Lanczos seems to be regarded as the best. That equation is $ Lx = \left\{ \begin{array}{cl} 1 & x = 0 \\ \frac{\sigma\sin\pi x\sin\frac{\pi x}{\sigma}}{\pi^2 x^2} & -\sigma < x < +\sigma, x \neq 0 \\ 0 & \mbox{otherwise} \\ \end{array}\right\}$ L is a factor that tells how much to scale down the amplitude according to the distance x between the pixel position and the estimated frequency both measured in pixels. Parameter is 2 or 3. It is chosen = 2 in SPECTR to avoid the halo effect that occurs for = 3. Finally, the logarithm of amplitude is taken, and the result is scaled into the range 0 to 255, the range of pixel intensities in a PGM file. Interlude Editing the Graphics Learning to read a spectrogram takes some practice. Horizontal lines are pure tones at a single frequency A stringed instrument like guitar produces a steady frequency. The human voice is not so steady. The vocal line is not nearly as straight, as seen in the above clip of "Delia's Gone" by Johnny Cash. Vertical lines are impulses. They sound like a click or a pop. An impulse is activity at every frequency at once. Here is a spectrogram of a handclap made with Sonic Visualiser Cloudy regions are static noise Many musical instruments produce overtones at frequencies above the fundamental. These appear as parallel lines Sometimes there is an echo. This will show as a fainter line to the right of the original sound Identify the melody line, and erase the overtones, echoes, static, and clicks. It doesn't require a delicate touch. I recommend the black rectangle tool available in many editing programs. Fill in everything but the melody with solid black. If you miss a spot, program SCRIBE can handle a few stray pixels. Part 2 From Melody Line to MIDI Undoing Lanczos Interpolation After the edited .PGM file is read, the pixel positions and intensities must be converted back to frequencies and amplitudes. In the special case that there are only two active pixels at a time point, it is possible to do this precisely. Let xo,yo denote the original, unknown frequency and amplitude. Let x1,y1 and x2,y2 denote the pixel indices and intensities in the image, measured in linear light. Applying the Lanczos interpolation formula at each point gives $ y_1 = \frac{\sigma \sin\pix_1-x_o\sin\frac{\pi}{\sigma}x_1-x_o}{\pi^2 x_1-x_o^2}y_o \\ y_2 = \frac{\sigma \sin\pix_2-x_o\sin\frac{\pi}{\sigma}x_2-x_o}{\pi^2 x_2-x_o^2}y_o $ Solve for yo $ y_o = \frac{\pi^2 x_1-x_o^2}{\sigma\sin\pix_1-x_o\sin\frac{\pi}{\sigma}x_1-x_o}y_1 = \frac{\pi^2x_2-x_o^2}{\sigma\sin\pix_2-x_o\sin\frac{\pi}{\sigma}x_2-x_o}y_2 $ and so the problem has been reduced to solving an equation for a single unknown $ \frac{x_1-x_o^2}{\sin\pix_1-x_o\sin\frac{\pi}{\sigma}x_1-x_o}y_1 - \frac{x_2-x_o^2}{\sin\pix_2-x_o\sin\frac{\pi}{\sigma}x_2-x_o}y_2 = 0 $ Subroutine solv is based on ZEROIN by Shampine and Watts. It is called at this point to solve numerically for xo. Now substitute into the expression for yo $ y_o = \frac{\pi^2x_1-x_o^2}{\sigma\sin\pix_1-x_o\sin\frac{\pi}{\sigma}x_1-x_o} $ If more than two pixels are active in a frame, subroutine QWM is called for a fallback. It estimates frequency as a weighted average, and chooses amplitude as the maximum intensity. Separating Sound from Silence Next, it must be decided for each frame if a note is sounding or not. Setting a fixed threshold will not give good results. Tiny bright spots or dim spots will turn into many brief, unpleasant notes. A transition between sound and silence should only occur if it will last for a reasonable duration. The method of dynamic programming provides an optimal solution to these kinds of problems. [Temperley, 2001] The Viterbi algorithm is the simplest form of dynamic programming. It asks at each step in the sequence, for each possible event, what event was most likely at the prior step? The answers for each step are kept, and at the end of the sequence, the most likely chain of events may be traced back. Subroutine DYRB implements the Viterbi algorithm for the special case of binary states sounding or silent and a real-valued sequence of observations intensity. I don't know the correct statistical model for inferring the probability of a note as a function of pixel intensity. The normal distribution does not seem appropriate for this application. Under the normal model, taking zero intensity and full intensity as the extremes, half intensity is indifference between sound or silence. This is not what we want; the indifference value should be much closer to zero. Instead, the penalty function chosen is the logarithm of intensity divided by a reference value, added or subtracted for sound or for silence. The transition penalty is chosen by taking a small arbitrary unit of time. The value seconds is chosen to match that in program MELISMA [Sleator & Temperley, 2000], a unit they dub a "pip." The transition penalty is a equal to a duration of a pip of the maximum observation penalty. Thus the claim of optimality for dynamic programming must be hedged with a strong disclaimer. It is "optimal" given the assumed observation penalty and transition penalty. The LULU Smoother Next, outlier data is trimmed with a nonlinear smoother. Moving-averages have traditionally been used for this purpose. However, they are low-pass filters. As was shown above, an impulse contains all frequencies. Therefore, moving-average smoothers blur abrupt changes. Nonlinear smoothers can remove outlier points without blurring. [Jankowitz, 2007] Subroutine SMOOTH implements the Jankowitz "B" filter. It is based entirely on minimum and maximum operations, and does no arithmetic. Agglomerating the Notes Take the simple, greedy approach of merging the notes that will cause the least increase in variance within a segment. This is not an optimal algorithm, but it is efficient and has been shown to work well in practice. [Terzi & Tsaparas, 2006] As each segment grows, its frequency changes, and thus the potential change in variance from merging it with its neighboring segments also changes. These updates can be handled by putting the potential changes in variance into a heap and sifting the least change to the top. Subroutine GLOM takes as input a real-valued sequence and three parameters. ADPARM is the threshold difference between the average values of adjacent segments. MDPARM is the threshold value of range between the maximum and minimum values within a segment. K is a desired number of segments. Segments are merged until a stopping criterion is met. Either the difference between every pair of adjacent segments exceeds ADPARM, or no segments can be merged without exceed MDPARM, or the number of segments K has been reached. The Expression Formula In program SPECTR, the logarithm of the Fourier coefficients was taken and the result was scaled to the range of pixel intensities. According to the MIDI standard, note velocity is to have an exponential interpretation. Thus, the velocity may be taken directly proportional to maximum pixel intensity in a note, \ V = \frac{127}{255}Y \, where Y is intensity from 0 to 255 and V is velocity from 0 to 127. The situation for MIDI expression is more difficult. Expression is a maximum by default, and is set to create diminuendos within each note. See the source code for a derivation of the result $ E = 127 \sqrt{\epsilon}^{\scriptstyle \frac{V}{127} - \frac{Y}{255}} $ where \\epsilon = \frac{1}{1024}\, the resolution parameter in program SPECTR. Topics Not Covered Reading and writing the .WAV, .PGM, and .MID file formats is not very interesting. For information on them, please see the references. Build Instructions To compile the C code with gcc, do gcc -o spectr -O2 -lm gcc -o scribe -O2 -lm To compile the FORTRAN with gfortran, do gfortran -o spectr -O2 -fno-automatic gfortran -o scribe -O2 -fno-automatic That's a bit to type, but there are no dependencies, no makefiles, and no header files. Using the Code Usage is spectr scribe where .wav is standard Microsoft wave audio .pgm is Portable Grey Map image file .mid is your output You are free to attempt any kind of transform on the image except that it has to remain 640 pixels in height. Remember that SCRIBE transcribes solos only. Both programs have an option -tune to transpose. So you can do something like spectr -tune + scribe -tune That shifts a baritone voice up by two octaves and a quarter-tone into the range of the spectrogram, then transposes it back when writing the MIDI. Program SCRIBE has the options -patch, -text, -copyright, and -seqname so that scribe -patch 68 -seqname "Hacker's Blues" -copyright "C2021 Joe" -text "nobody reads the comments" sets the patch to oboe, gives the track a name, a copyright notice, and a comment. Program SPECTR has an option -swab which you might need if your .WAV is a 32-bit float with byte order backwards from the computer's default. Example Problems Vocal Consider this sample of singing by Katy, courtesy of digifishmusic. [Katy, 2007] An ordinary spectrogram made with sox is fairly blurry. A high-resolution spectrogram made with SPECTR shows the details of the tremolo. Next, edit the image with Windows paint or any similar program to remove the overtones. Erase all but one of the parallel lines Because this is a standard image file, any editing operation which can be done on an image may be done at this step. Now process the image with SCRIBE to produce the MIDI file. For comparison, the result from the free file converter at is available. This service is free and does not require you to install anything on your computer. Both MIDIs accurately capture the performance. The competitor's MIDI is very concise. On the other hand, it contains 167 notes. The output of SCRIBE is made long by many changes in expression, but there are only 28 notes. In this sense, it is a more accurate transcription. Instrumental A flute performance [kerri, 2007] was processed by the SCAT system. A detail of the spectrogram After editing the image The result is a reasonably good transcription, although some of the ornaments have been lost. Release History 2 30th April, 2022 Nonlinear smoothing, inverse interpolation, no .exe files 1 10th October, 2021 Add readme, FORTRAN source and .exe files 0 6th October, 2021 Original release to the MidKar group References "PGM Format Specification" by Jef Poskanzer, 1989. online "Calculation of a constant Q spectral transform," Judith C. Brown, Journal of the Acoustic Society of America January 1991. Available at researchgate. "Standard MIDI Files Specification", MIDI Manufacturers Association, 1996. online "Microsoft WAVE soundfile format", Craig Stuart Sapp, 1997. online The Cognition of Basic Musical Structures, David Temperley, MIT Press, 2001. First chapter available from the publisher. "Spectrum and spectral density estimation by the Discrete Fourier transform DFT, including a comprehensive list of window functions and some new flat-top windows," G. Heinzel, A. Rudiger and R. Schilling, Max-Planck-Institut fur Gravitationsphysik, February 15, 2002. Available at researchgate. "Cookbook formulae for audio EQ biquad filter coefficients," Robert Bristow-Johnson, [2005?]. Available at musicsdp. "The Butterworth Low-Pass Filter," John Stensby, 19 Oct 2005. Available from the University of Alabama. "Efficient Algorithms for Sequence Segmentation," Evimaria Terzi and Panayiotis Tsaparas, Proceedings of the Sixth SIAM International Conference on Data Mining, April 2006. Available at researchgate. Some Statistical Aspects of LULU Smoothers, Maria Dorothea Jankowitz, Dissertation, Stellenbosch University, Dec. 2007. Available from Stellenbosch University. "Haunted Canyon Flute," by kerri, 2007. At freesound. "Katy Sings LaaOooAaa," by Katy, recorded by digifishmusic, 2007. At freesound. Bear File Converter, 2009. "Programming the Phase Vocoder" by Victor Lazzarini, in The Audio Programming Book, ed. Richard Boulanger and Victor Lazzarini. MIT Press, 2011. Appendix A Very Short Derivation of the Discrete Fourier Transform Suppose there is a discrete signal measured at N equally spaced intervals \y_0, y_1, y_2, \ldots, y_j, \ldots, y_n \ over some duration T. Assume that it is possible to represent this signal as a sum of sine and cosine waves $ y_j = \sum^{N/2}_{i=1} a_i \cos 2 \pi f_i t_j + b_i \sin2 \pi f_i t_j $ for \i = 1 \ldots \frac{N}{2} \ Substitute \t_j = \frac{j}{N}T\ and \f_i = i f_o = \frac{i}{T}\, thus $ y_j = \sum^{N/2}_{i=1} a_i \cos\frac{2\pi}{N}ij + b_i \sin\frac{2\pi}{N}ij $ Write out the tableaux $ \left[ \begin{array}{llllllllll} \cos\frac{2\pi}{N} & \sin\frac{2\pi}{N} & \cos\frac{2\pi}{N}2 & \sin\frac{2\pi}{N}2 & \cdots & \cos\frac{2\pi}{N}i & \sin\frac{2\pi}{N}i & \cdots & \cos\pi & \sin\pi \\ \cos\frac{2\pi}{N}2 & \sin\frac{2\pi}{N}2 & \cos\frac{2\pi}{N}22 & \sin\frac{2\pi}{N}22& \cdots & \cos\frac{2\pi}{N}2i & \sin\frac{2\pi}{N}2i & \cdots & \cos2\pi & \sin2\pi \\ \vdots & \vdots &\vdots &\vdots & \ddots & \vdots & \vdots & \cdots & \vdots & \vdots \\ \cos\frac{2\pi}{N}j & \sin\frac{2\pi}{N}j & \cos\frac{2\pi}{N}2j & \sin\frac{2\pi}{N}2j &\cdots & \cos\frac{2\pi}{N}ij & \sin\frac{2\pi}{N}ij & \cdots & \cos\pi j & \sin\pi j \\ \vdots & \vdots &\vdots & \vdots& & \vdots & \vdots & \ddots &\vdots & \vdots \\ \cos2\pi & \sin2\pi & \cos2\pi2 & \sin2\pi2 & \cdots & \cos2\pi i & \sin2\pi i & \cdots & \cos\pi N & \sin\pi N \\ \end{array} \right] \left[ \begin{array}{l} a_1 \\ b_1 \\ a_2 \\ b_2 \\ \vdots \\ a_i \\ b_i \\ \vdots \\ a_\frac{N}{2} \\ b_\frac{N}{2} \\ \end{array} \right] = \left[ \begin{array}{l} y_1 \\ y_2 \\ \vdots \\ y_j \\ \vdots \\ y_N \\ \end{array} \right] $ The sine and cosine terms form a square matrix, because there are \\frac{N}{2}\ pairs \a_i, b_i\. It is also an orthogonal matrix, so its inverse is the same as its transpose. Note that frequencies beyond \\frac{N}{2}\ cannot be obtained, because there would be more unknowns than equations. Thus, $ \left[ \begin{array}{l} a_1 \\ b_1 \\ a_2 \\ b_2 \\ \vdots \\ a_i \\ b_i \\ \vdots \\ a_\frac{N}{2} \\ b_\frac{N}{2} \\ \end{array} \right] = \left[ \begin{array}{llllll} \cos\frac{2\pi}{N} & \cos\frac{2\pi}{N}2 & \cdots & \cos\frac{2\pi}{N}j & \cdots & \cos2\pi \\ \sin\frac{2\pi}{N} & \sin\frac{2\pi}{N}2 & \cdots & \sin\frac{2\pi}{N}j & \cdots & \sin2\pi \\ \vdots & \vdots & \ddots & \vdots & & \vdots \\ \cos\frac{2\pi}{N}i & \cos\frac{2\pi}{N}i2 & \cdots & \cos\frac{2\pi}{N}ij & \cdots & \cos2\pi i \\ \sin\frac{2\pi}{N}i & \sin\frac{2\pi}{N}i2 & \cdots & \sin\frac{2\pi}{N}ij & \cdots & \sin2\pi i \\ \vdots & \vdots &\vdots &\vdots & \ddots & \vdots \\ \cos\pi & \cos2\pi & \cdots & \cos\pi j &\cdots & \cos\pi N \\ \sin\pi & \sin2\pi & \cdots & \sin\pi j & \cdots & \sin\pi N \\ \end{array} \right] \left[ \begin{array}{l} y_1 \\ y_2 \\ \vdots \\ y_j \\ \vdots \\ y_N \\ \end{array} \right] $ in summation notation $ a_i = \sum^N_{j=1} \cos\frac{2\pi}{N} ij y_j\\ b_i = \sum^N_{j=1} \sin\frac{2\pi}{N} ijy_j $ for \i = 1 \ldots \frac{N}{2} \ Since the sample rate \R = \frac{N}{T}\, these coefficients correspond to frequencies \f_i = i \frac{R}{N}\ To make the amplitudes independent of the length of the transform, the coefficients must be divided by N, yielding the formulae $ a_i = \frac{1}{N}\sum^N_{j=1} \cos\frac{2\pi}{N} ij y_j\\ b_i = \frac{1}{N}\sum^N_{j=1} \sin\frac{2\pi}{N} ijy_j $ Notice that the Discrete Fourier Transform has been obtained without the use of any imaginary numbers. 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