Podcasts about fourier transform

Intro topic:  Buying a CarNews/Links:Cognitive Load is what Mattershttps://github.com/zakirullin/cognitive-loadDiffusion models are Real-Time Game Engineshttps://gamengen.github.io/Your Company Needs Junior Devshttps://softwaredoug.com/blog/2024/09/07/your-team-needs-juniorsSeamless Streaming / Fish Speech / LLaMA OmniSeamless: https://huggingface.co/facebook/seamless-streamingFish: https://github.com/fishaudio/fish-speech LLaMA Omni: https://github.com/ictnlp/LLaMA-Omni Book of the ShowPatrick: Thought Emporium Youtubehttps://youtu.be/8X1_HEJk2Hw?si=T8EaHul-QMahyUvQJason: Novel Mindshttps://www.novelminds.ai/Patreon Plug https://www.patreon.com/programmingthrowdown?ty=hTool of the ShowPatrick: Escape Simulatorhttps://pinestudio.com/games/escape-simulator/Jason: Cursor IDEhttps://www.cursor.com/Topic: Vector Databases (~54 min)How computers represent data traditionallyASCII valuesRGB valuesHow traditional compression worksHuffman encoding (tree structure)Lossy example: Fourier Transform & store coefficientsHow embeddings are computedPairwise (contrastive) methodsForward models (self-supervised)Similarity metricsApproximate Nearest Neighbors (ANN)Sub-Linear ANNClusteringSpace Partitioning (e.g. K-D Trees)What a vector database doesPerform nearest-neighbors with many different similarity metricsStore the vectors and the data structures to support sub-linear ANNHandle updates, deletes, rebalancing/reclustering, backups/restoresExamplespgvector: a vector-database plugin for postgresWeaviate, Pinecone Milvus ★ Support this podcast on Patreon ★

Foundations of Amateur Radio Over the years you've heard me utter the phrase: "Get on air and make some noise!". It's not an idle thought. The intent behind it is to start, to do something, anything, and find yourself a place within the hobby of amateur radio and the community surrounding it. Since starting my weekly contribution to this community, thirteen years ago, almost to the day, I promise, this wasn't planned, you'll see why in a moment, I've been working my way through the things that take my fancy, things that are of interest to me, and hopefully you. From time-to-time I don't know where the next words are going to come from. Today they came to me five minutes ago when a good friend, Colin, VK6ETE, asked me what inspires me, after I revealed to him that I didn't know what I was going to talk about. That's all it took to get me rolling. There are times when getting to that point takes weeks, I do research, figure out how something works, explore how it might have been tackled before, if at all, and only then I might start putting my thoughts together, often I'll have multiple stabs at it and if I'm lucky, sometimes, something emerges that I'm astonished by. Today is much simpler than all that, since the only research required is to remember the people I've interacted with. Last week I met an amateur, Jess M7WOM, who was in town. Until last week, we'd never met and interacted only online. We discovered that we have a great many things in common. A joy for curiosity, exploration, technology, computers and a shared belief that we can figure out how to make things work. That interaction, over the course of a day, continues to fuel my imagination and provides encouragement to try new things. The same is true for a friend, Eric VK6BJW, who asked what they should do with the hobby after having been away for a long time with family, children, commitments and work. Just asking a few simple questions got the juices going and provided inspiration to start playing again. Another amateur was bored and claimed to have run out of things to do. A few of us started asking questions about their exposure to the hobby. Had they tried a digital mode, had they built an antenna, had they tried to activate a park, or as I have said in the past, any of the other 1,000 hobbies that are embedded within the umbrella that we call amateur radio. Right now I'm in the midst of working through, actually truth be told, I'm starting, Okay, actually, I've yet to start, reading the online book published at PySDR.org. Prompted by a discussion with Jess last week, I started exploring a known gap in my knowledge. I likened it to having a lamp-post in front of my face, I can see to either side, but in-between is this post, obscuring an essential piece of knowledge, how one side is connected to the other. In my case, on one side, I can see the antenna, how it connects to an ADC, or an Analogue to Digital Converter. On the other, I can also see how you have a series of bytes coming into your program that you can compare against what you're looking for, but the two are not quite connected, obscured by that .. post. I know there's a Fourier Transform in there, but I don't yet grok how it's connected. Recently I discussed using an RDS, or Radio Data Systems decoder, called 'redsea', connected to 'rtl_fm', in turn connected to an RTL-SDR dongle, that is, you connect an antenna to a cheap Digital TV decoder, tune to an FM broadcast station and use some software to decode a digital signal. It turns out that the PySDR book serendipitously uses this signal path as an end-to-end tutorial, complete with all the code and example files to make this happen. I actually read the chapter, but it's assuming some knowledge that I don't yet have, so I'm going to start on page one .. again. So, what has this got to do with Inspiration, you ask. Well, everything and nothing. Inspiration doesn't occur in a vacuum. It needs input. You cannot see light without it hitting something, radio waves don't exist and cannot be detected until it hits an antenna, the same is true for inspiration. It needs to hit something. You need to react, it needs to connect. That is why I keep telling you to get on air and make some noise. I'm Onno VK6FLAB

Chris and Elecia discuss the pros and cons of completing one project or starting a dozen.  Elecia's 2nd edition of Making Embedded Systems is coming out in March. (Preview is on O'Reilly's Learning System.) She's working on a companion repository that is already filled with links and goodies: github.com/eleciawhite/making-embedded-systems.  If you'd like to know more about signal processing, check out DSPGuide.com aka The Scientist and Engineer's Guide to Digital Signal Processing By Steven W. Smith, Ph.D. And as noted in last week's newsletter, there is an interesting overlap between smoothies and the Fourier Transform.  Giang Vinh Loc used  Charles Lohr's RISCV on Arduino UNO to boot Linux (in 16 hours).  We also talked a bit about Greg Wilson's recent episode with Elecia (Embedded 460: I Don't Care What Your Math Says). Transcript Thanks to Nordic for sponsoring this week's show! Nordic Semiconductor empowers wireless innovation, by providing hardware, software, tools and services that allow developers to create the IoT products of tomorrow. Learn more about Nordic Semiconductor at nordicsemi.com, check out the DevAcademy at academy.nordicsemi.com and interact with the Nordic Devzone community at devzone.nordicsemi.com.

В этом выпуске: очередная порция невероятных тем. Шоуноты: [00:04:11] Чему мы научились за неделю But what is the Fourier Transform? A visual introduction. — YouTube TodayTix | Theater Tickets to Musicals, Plays, Broadway, More [00:25:07] HiFiMan Sundara [00:41:09] 28 дней спустя: какова же судьба Сашиных репок на BitBucket? [00:47:49] Qdrant [01:02:10] Unity стреляет себе в… Читать далее →

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Short Remark on the (subjective) mathematical 'naturalness' of the Nanda--Lieberum addition modulo 113 algorithm, published by Spencer Becker-Kahn on June 1, 2023 on The AI Alignment Forum. These remarks are basically me just wanting to get my thoughts down after a Twitter exchange on this subject. I've not spent much time on this post and it's certainly plausible that I've gotten things wrong.In the 'Key Takeaways' section of the Modular Addition part of the well-known post 'A Mechanistic Interpretability Analysis of Grokking' , Nanda and Lieberum write: This algorithm operates via using trig identities and Discrete Fourier Transforms to map x,ycos(w(x+y)),sin(w(x+y)), and then extracting x+y(modp) And The model is trained to map x,y to z≡x+y(mod113) (henceforth 113 is referred to as p) But the casual reader should use caution! It is in fact the case that "Inputs x,y are given as one-hot encoded vectors in Rp ". This point is of course emphasized more in the full notebook (it has to be, that's where the code is), and the arXiv paper that followed is also much clearer about this point. However, when giving brief takeaways from the work, especially when it comes to discussing how 'natural' the learned algorithm is, I would go as far as saying that it is actually misleading to suggest that the network is literally given x and y as inputs. It is not trained to 'act' on the numbers x, y themselves. When thinking seriously about why the network is doing the particular thing that it is doing at the mechanistic level, I would want to emphasize that one-hotting is already a significant transformation. You have moved away from having the number x be represented by its own magnitude. You instead have a situation in which x and y now really live 'in the domain' (its almost like a dual point of view: The number x is not the size of the signal, but the position at which the input signal is non-zero). So, while I of course fully admit that I too am looking at it through my own subjective lens, one might say that (before the embedding happens) it is more mathematically natural to think that what the network is 'seeing' as input is something like the indicator functions t↦1x(t) and t↦1y(t). Here, t is something like the 'token variable' in the sense that these are functions on the vocabulary. And if we essentially ignore the additional tokens for | and =, we can think that these are functions on the group Z/pZ and that we would like the network to learn to produce the function t↦1x+y(t) at its output neurons.In particular, this point of view further (and perhaps almost completely) demystifies the use of the Fourier basis. Notice that the operation you want to learn is manifestly a convolution operation, i.e. And (as I distinctly remember being made to practically chant in an 'Analysis of Boolean Functions' class given by Tom Sanders) the Fourier Transform is the (essentially unique) change of basis that simultaneously diagonalizes all convolution operations. This is coming close to saying something like: There is one special basis that makes the operation you want to learn uniquely easy to do using matrix multiplications, and that basis is the Fourier basis. Thanks for listening. To help us out with The Nonlinear Library or to learn more, please visit nonlinear.org.

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Short Remark on the (subjective) mathematical 'naturalness' of the Nanda--Lieberum addition modulo 113 algorithm, published by Spencer Becker-Kahn on June 1, 2023 on LessWrong. These remarks are basically me just wanting to get my thoughts down after a Twitter exchange on this subject. I've not spent much time on this post and it's certainly plausible that I've gotten things wrong.In the 'Key Takeaways' section of the Modular Addition part of the well-known post 'A Mechanistic Interpretability Analysis of Grokking' , Nanda and Lieberum write: This algorithm operates via using trig identities and Discrete Fourier Transforms to map x,ycos(w(x+y)),sin(w(x+y)), and then extracting x+y(modp) And The model is trained to map x,y to z≡x+y(mod113) (henceforth 113 is referred to as p) But the casual reader should use caution! It is in fact the case that "Inputs x,y are given as one-hot encoded vectors in Rp ". This point is of course emphasized more in the full notebook (it has to be, that's where the code is), and the arXiv paper that followed is also much clearer about this point. However, when giving brief takeaways from the work, especially when it comes to discussing how 'natural' the learned algorithm is, I would go as far as saying that it is actually misleading to suggest that the network is literally given x and y as inputs. It is not trained to 'act' on the numbers x, y themselves. When thinking seriously about why the network is doing the particular thing that it is doing at the mechanistic level, I would want to emphasize that one-hotting is already a significant transformation. You have moved away from having the number x be represented by its own magnitude. You instead have a situation in which x and y now really live 'in the domain' (its almost like a dual point of view: The number x is not the size of the signal, but the position at which the input signal is non-zero). So, while I of course fully admit that I too am looking at it through my own subjective lens, one might say that (before the embedding happens) it is more mathematically natural to think that what the network is 'seeing' as input is something like the indicator functions t↦1x(t) and t↦1y(t). Here, t is something like the 'token variable' in the sense that these are functions on the vocabulary. And if we essentially ignore the additional tokens for | and =, we can think that these are functions on the group Z/pZ and that we would like the network to learn to produce the function t↦1x+y(t) at its output neurons.In particular, this point of view further (and perhaps almost completely) demystifies the use of the Fourier basis. Notice that the operation you want to learn is manifestly a convolution operation, i.e. And (as I distinctly remember being made to practically chant in an 'Analysis of Boolean Functions' class given by Tom Sanders) the Fourier Transform is the (essentially unique) change of basis that simultaneously diagonalizes all convolution operations. This is coming close to saying something like: There is one special basis that makes the operation you want to learn uniquely easy to do using matrix multiplications, and that basis is the Fourier basis. Thanks for listening. To help us out with The Nonlinear Library or to learn more, please visit nonlinear.org.

Link to original articleWelcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: Short Remark on the (subjective) mathematical 'naturalness' of the Nanda--Lieberum addition modulo 113 algorithm, published by Spencer Becker-Kahn on June 1, 2023 on LessWrong. These remarks are basically me just wanting to get my thoughts down after a Twitter exchange on this subject. I've not spent much time on this post and it's certainly plausible that I've gotten things wrong.In the 'Key Takeaways' section of the Modular Addition part of the well-known post 'A Mechanistic Interpretability Analysis of Grokking' , Nanda and Lieberum write: This algorithm operates via using trig identities and Discrete Fourier Transforms to map x,ycos(w(x+y)),sin(w(x+y)), and then extracting x+y(modp) And The model is trained to map x,y to z≡x+y(mod113) (henceforth 113 is referred to as p) But the casual reader should use caution! It is in fact the case that "Inputs x,y are given as one-hot encoded vectors in Rp ". This point is of course emphasized more in the full notebook (it has to be, that's where the code is), and the arXiv paper that followed is also much clearer about this point. However, when giving brief takeaways from the work, especially when it comes to discussing how 'natural' the learned algorithm is, I would go as far as saying that it is actually misleading to suggest that the network is literally given x and y as inputs. It is not trained to 'act' on the numbers x, y themselves. When thinking seriously about why the network is doing the particular thing that it is doing at the mechanistic level, I would want to emphasize that one-hotting is already a significant transformation. You have moved away from having the number x be represented by its own magnitude. You instead have a situation in which x and y now really live 'in the domain' (its almost like a dual point of view: The number x is not the size of the signal, but the position at which the input signal is non-zero). So, while I of course fully admit that I too am looking at it through my own subjective lens, one might say that (before the embedding happens) it is more mathematically natural to think that what the network is 'seeing' as input is something like the indicator functions t↦1x(t) and t↦1y(t). Here, t is something like the 'token variable' in the sense that these are functions on the vocabulary. And if we essentially ignore the additional tokens for | and =, we can think that these are functions on the group Z/pZ and that we would like the network to learn to produce the function t↦1x+y(t) at its output neurons.In particular, this point of view further (and perhaps almost completely) demystifies the use of the Fourier basis. Notice that the operation you want to learn is manifestly a convolution operation, i.e. And (as I distinctly remember being made to practically chant in an 'Analysis of Boolean Functions' class given by Tom Sanders) the Fourier Transform is the (essentially unique) change of basis that simultaneously diagonalizes all convolution operations. This is coming close to saying something like: There is one special basis that makes the operation you want to learn uniquely easy to do using matrix multiplications, and that basis is the Fourier basis. Thanks for listening. To help us out with The Nonlinear Library or to learn more, please visit nonlinear.org.

Complex math and models from all fields can often have an application to what we do as tastytraders. As we see today with the Fourier Transform concept that is more commonly used in Signaling Theory and musical analysis. Which reminds us of the value of deconstructing larger equations into their component parts to aid in decision making.Did you catch our recently on how to determine Delta/Theta levels for your portfolio?

Complex math and models from all fields can often have an application to what we do as tastytraders. As we see today with the Fourier Transform concept that is more commonly used in Signaling Theory and musical analysis. Which reminds us of the value of deconstructing larger equations into their component parts to aid in decision making.Did you catch our recently on how to determine Delta/Theta levels for your portfolio?

Episode: 2803 Fourier, the Fourier Transform, and Music.  Today, music in translation.

Foundations of Amateur Radio On the 12th of December 1961, before I was born, before my parents met, the first amateur radio satellite was launched by Project OSCAR. It was a 10 kilo box, launched as the first private non-government spacecraft. OSCAR 1 was the first piggyback satellite, launched as a secondary payload taking the space of a ballast weight and managed to be heard by over 570 amateurs across 28 countries during the 22 days it was in orbit. It was launched just over four years after Sputnik 1 and was built entirely by amateurs for radio amateurs. In the sixty years since we've come a long way. Today high school students are building and launching CubeSats and several groups have built satellites for less than a $1,000. OSCAR 76, the so-called "$50SAT" cost $250 in parts. It operated in orbit for 20 months. Fees for launching a 10cm cubed satellite are around $60,000 and reducing by the year. If that sounds like a lot of money for the amateur community, consider that the budget for operating VK0EK, the DXpedition to Heard Island in 2016 was $550,000. Operation lasted 21 days. I'm mentioning all this in the context of homebrew. Not the alcoholic version of homebrew, the radio amateur version, where you build stuff for your personal enjoyment and education. For some amateurs that itch is scratched by designing and building a valve based power amplifier, for others it means building a wooden Morse key. For the members of OSCAR it's satellites. For me the itch has always been software. Sitting in my bedroom in the early 1980's, eyeballs glued to the black and white TV that was connected to my very own Commodore VIC-20 was how I got properly bitten by that bug, after having been introduced to the Apple II at my high school. I'm a curios person. Have always been. In my work I generally go after the new and novel and then discover six months down the track that my clients benefit from my weird sideways excursion into something or other. Right now my latest diversion is the FPGA, a Field Programmable Gate Array. Started watching a new series by Digi-Key about how to use them and the experience is exhilarating. One way to simply describe an FPGA is to think of it as a way to create a virtual circuit board that can be reprogrammed in the field. You don't have to go out and design a chip for a specific purpose and deal with errors, upgrades and supply chain issues, instead you use a virtual circuit and reprogram as needed. If you're not sure how powerful this is, you can program an FPGA to behave like a Motorola 65C02 microprocessor, or as a RISC CPU, or well over 200 other open source processor designs, including the 64-bit UltraSPARC T1 microprocessor. I'm mentioning this because while I have a vintage HP606A valve based signal generator that I'm working on restoring to fully working. Homebrew for me involves all that the world has to offer. I don't get excited about solder and my hands and eyes are really not steady enough to manage small circuit designs, but tapping keys on a keyboard, that's something I've been doing for a long time. Another thing I like about this whole upgraded view of homebrew is that we as radio amateurs are already familiar with building blocks. We likely don't design a power supply from scratch, or an amplifier, or the VFO circuit. Why improve something that has stood the test of time? In my virtual world, I too can use those building blocks. In FPGA land I can select any number of implementations of a Fourier Transform and test them all to see which one suits my purpose best. In case you're wondering. My Pluto SDR is looking great as a 2m and 70cm beacon, transmitting on both bands simultaneously. It too has an FPGA on board and I'm not afraid to get my keyboard dirty trying to tease out how to best make use of that. What homebrew adventures have you been up to? I'm Onno VK6FLAB

The Fourier Transform has made a huge contribution to almost every area of audio engineering. From individual filters to full mastering suites; from tuning your guitar to how we store and transmit sound, the Fourier Transform is there ferreting out every bit of frequency information from your time-based audio signal.In this episode, we look at a few examples of how the Fourier Transform has revolutionized the way engineers work with sound.Show Notes for this Episode:https://howthefouriertransformworks.com/podcast/audio-engineering/Course Home Page:https://howthefouriertransformworks.comPatreon Page:https://howthefouriertransformworks.com/patreonJoin the mailing list:https://howthefouriertransformworks.com/mailing-list

Preventative Maintenance is where we monitor the "health" of a system. If something in the system begins to wear out, we can take it offline for maintenance or repair BEFORE something goes seriously wrong.In this podcast, we'll investigate how the Fourier Transform can be used to listen to the health of an airplane's jet engine in much the same way a doctor uses a stethoscope to listen to your heart, a simple, non-invasive procedure that can save lives.I also answer a listener's question on how the Fourier Transform is used in Filter Banks, as well as giving an update on my progress on the "How the Fourier Transform Works" online course.Show Notes for this Episode:https://howthefouriertransformworks.com/preventative-maintenanceCourse Home Page:https://howthefouriertransformworks.comPatreon Page:https://howthefouriertransformworks.com/patreonJoin the mailing list:https://howthefouriertransformworks.com/mailing-list

The Fourier Transform is everywhere. Few are the days in your life where you won't pick up a piece of technology that implements it to provide you with pictures, videos, music, a phone call, and all manner of everyday applications. However, its very ubiquity means we take The Fourier Transform very much for granted and few are the people that really understand how it works. One of the reasons for this may be that, on the face of it, the maths can seem a little complicated.In this episode, we look at what the Fourier Transform is and I describe my own journey from mathematical ignoramus to actually understanding how the Fourier Transform works.Course Homepage: https://howthefouriertransformworks.com/ Podcast email: podcast@howthefouriertransformworks.comSupport the podcast: https://howthefouriertransformworks.com/patreonJoin the mailing list: https://howthefouriertransformworks.com/mailing-list

#fnet #attention #fourier Do we even need Attention? FNets completely drop the Attention mechanism in favor of a simple Fourier transform. They perform almost as well as Transformers, while drastically reducing parameter count, as well as compute and memory requirements. This highlights that a good token mixing heuristic could be as valuable as a learned attention matrix. OUTLINE: 0:00 - Intro & Overview 0:45 - Giving up on Attention 5:00 - FNet Architecture 9:00 - Going deeper into the Fourier Transform 11:20 - The Importance of Mixing 22:20 - Experimental Results 33:00 - Conclusions & Comments Paper: https://arxiv.org/abs/2105.03824 ADDENDUM: Of course, I completely forgot to discuss the connection between Fourier transforms and Convolutions, and that this might be interpreted as convolutions with very large kernels. Abstract: We show that Transformer encoder architectures can be massively sped up, with limited accuracy costs, by replacing the self-attention sublayers with simple linear transformations that "mix" input tokens. These linear transformations, along with simple nonlinearities in feed-forward layers, are sufficient to model semantic relationships in several text classification tasks. Perhaps most surprisingly, we find that replacing the self-attention sublayer in a Transformer encoder with a standard, unparameterized Fourier Transform achieves 92% of the accuracy of BERT on the GLUE benchmark, but pre-trains and runs up to seven times faster on GPUs and twice as fast on TPUs. The resulting model, which we name FNet, scales very efficiently to long inputs, matching the accuracy of the most accurate "efficient" Transformers on the Long Range Arena benchmark, but training and running faster across all sequence lengths on GPUs and relatively shorter sequence lengths on TPUs. Finally, FNet has a light memory footprint and is particularly efficient at smaller model sizes: for a fixed speed and accuracy budget, small FNet models outperform Transformer counterparts. Authors: James Lee-Thorp, Joshua Ainslie, Ilya Eckstein, Santiago Ontanon Links: TabNine Code Completion (Referral): http://bit.ly/tabnine-yannick YouTube: https://www.youtube.com/c/yannickilcher Twitter: https://twitter.com/ykilcher Discord: https://discord.gg/4H8xxDF BitChute: https://www.bitchute.com/channel/yann... Minds: https://www.minds.com/ykilcher Parler: https://parler.com/profile/YannicKilcher LinkedIn: https://www.linkedin.com/in/yannic-ki... BiliBili: https://space.bilibili.com/1824646584 If you want to support me, the best thing to do is to share out the content :) If you want to support me financially (completely optional and voluntary, but a lot of people have asked for this): SubscribeStar: https://www.subscribestar.com/yannick... Patreon: https://www.patreon.com/yannickilcher Bitcoin (BTC): bc1q49lsw3q325tr58ygf8sudx2dqfguclvngvy2cq Ethereum (ETH): 0x7ad3513E3B8f66799f507Aa7874b1B0eBC7F85e2 Litecoin (LTC): LQW2TRyKYetVC8WjFkhpPhtpbDM4Vw7r9m Monero (XMR): 4ACL8AGrEo5hAir8A9CeVrW8pEauWvnp1WnSDZxW7tziCDLhZAGsgzhRQABDnFy8yuM9fWJDviJPHKRjV4FWt19CJZN9D4n

In this explorative episode we ask the material universe might be created as a type of Fourier Transform and how that could relate to more "New Age" types of ideas.We also ask about the atemporal types of experiences that people who experience near death circumstances go through and how they might be connected to the ideas of a frequency space.If the material universe is based on something like a Fourier Transformation, then all that is is created from a sort of primordial "sound".It would be interesting to know what the primordial frequencies are.  And so, physics explorations may be fruitful.  If we choose to explore a more spiritual path, then quieting the mind may provide us greater access to the frequency space, from which timelines originate.If you are interested in more physics oriented types of explorations of the Holographic Order, based on as few suppositions as possible, then you may enjoy "Physics from Wholeness: Dynamical Totality as a Conceptual Foundation for Physical Theories".If you have any comments, questions, or suggestions for the podcast you can contact me on Instagram @BasiasThoughts.  And, of course, if you would like to see more content from me do sponsor me on https://www.patreon.com/basia because that will allow me to focus more on content creation. 

בפרק זה, נשוחח על מהי התמרת פורייה. מוטיבציות, שימושים, Time Series והקשר ללמידה עמוקה.קישורים רלוונטיים: But what is the Fourier Transform? A visual introduction Fourier Convolutional Neural Networks

Link to bioRxiv paper: http://biorxiv.org/cgi/content/short/2020.09.05.284141v1?rss=1 Authors: Shakya, B. R., Teppo, H.-R., Rieppo, L. Abstract: Among skin cancers, melanoma is the lethal form and the leading cause of death in humans. Melanoma begins in melanocytes and is curable at early stages. Thus, early detection and evaluation of its metastatic potential are crucial for effective clinical intervention. Fourier transform infrared (FTIR) spectroscopy has gained considerable attention due to its versatility in detecting biochemical and biological features present in the samples. Changes in these features are used to differentiate between samples at different stages of the disease. Previously, FTIR spectroscopy has been mostly used to distinguish between healthy and diseased conditions. With this study, we aim to discriminate between different melanoma cell lines based on their FTIR spectra. Formalin-fixed paraffin embedded samples from three melanoma cell lines (IPC-298, SK-MEL-30 and COLO-800) were used. Statistically significant differences were observed in the prominent spectral bands of three cell lines along with shifts in peak positions. Partial least square discriminant analysis (PLS-DA) models built for the classification of three cell lines showed accuracies of 96.38 %, 95.96 % and 99.7 %, for the differentiation of IPC-298, SK-MEL-30 and COLO-800, respectively. The results suggest that FTIR spectroscopy can be used to differentiate between genetically different melanoma cells and thus potentially characterize the metastatic potential of melanoma. Copy rights belong to original authors. Visit the link for more info

Link to bioRxiv paper: http://biorxiv.org/cgi/content/short/2020.07.19.210609v1?rss=1 Authors: Lopez, G.-D., Suesca, E., Alvarez-Rivera, G., Rosato, A., Ibanez, E., Cifuentes, A., Leidy, C., Carazzone, C. Abstract: Staphyloxanthin (STX) is a saccharolipid derived from a carotenoid in Staphylococcus aureus involved in oxidative-stress tolerance and antimicrobial peptide resistance. In this work, a targeted metabolomics and biophysical study was carried out on native and knock-out S. aureus strains to investigate the biosynthetic pathways of STX and related carotenoids. Identification of 34 metabolites at different growth phases (8, 24 and 48h), reveal shifts of carotenoid populations during progression towards stationary phase. Six of the carotenoids in the STX biosynthetic pathway and three menaquinones (Vitamin K2) were identified in the same chromatogram. Furthermore, other STX homologues with varying acyl chain structures reported herein for the first time, which reveal the extensive enzymatic activity of CrtO/CrtN. Fourier Transform infrared spectroscopy show that STX increases acyl chain order and shifts the cooperative melting of the membrane indicating a more rigid lipid bilayer. This study shows the diversity of carotenoids in S. aureus, and their influence on membrane biophysical properties. Copy rights belong to original authors. Visit the link for more info

The Fourier transform is one of the handiest tools in signal processing for dealing with periodic time series data. Using a Fourier transform, you can break apart a complex periodic function into a bunch of sine and cosine waves, and figure out what the amplitude, frequency and offset of those component waves are. It's a really handy way of re-expressing periodic data--you'll never look at a time series graph the same way again.

Is grey ‘real’? Is all discretization perspectival? Can there be absolute notions of discreteness and continuity? Is time eternal? Is the world continuous but we perceive it as discrete? Are micro and macro objects continuous, but the meso discrete? Can real numbers be ‘made’ from integers? Are real numbers continuous (analog), & integers discrete (digital)? Do we don’t have access to ‘most’ of the real numbers? Did God make integers – or only 1 (& 0?)? What does Fourier Transform imply? What is the most fundamental signal? When does sampling not lead to loss of information? Can the sense of touch be discretized? Can surgeries be performed remotely? Does discretization happen in Nature? Is noise always continuous? Is speech predictable even if the underlying phonemes seem discrete? Do all manifolds lie on a continuum? Is making linear (analog) circuits difficult? Are higher order infinities deeper forms of ‘silence’? Does mathematics understand the ‘ambiguous’ ways in which things are (sometimes…) equal? Would a world without continuity (& community) be doomed? SynTalk thinks about these & more questions using concepts from logic & philosophy (Prof. Mihir K. Chakraborty, ex-University of Calcutta, Kolkata), mathematics (Prof. Kiran S. Kedlaya, University of California San Diego, La Jolla, California), & electrical engineering (Prof. D. Manjunath, IIT Bombay, Mumbai). Listen in...

Did George Harrison "cheat" the solo to A Hard Day's Night?

No one’s sure exactly how the most famous chord in popular music was played. Until now.

The concept of the Fourier series can be applied to aperiodic functions by treating it as a periodic function with period T = infinity. This new transform has some key similarities and differences with the Laplace transform, its properties, and domains.

This lecture covers rearrangements of the basic decimation-in-frequency algorithm and discuss the relation between decimation-in-time and decimation-in-frequency through the transposition theorem. It also covers more general arbitrary radix FFT algorithms.

This lecture discusses interpretation of the FFT flow graph and bit-reversed data ordering. It also discusses other decimation-in-time FFT algorithms by rearranging the flow graph and the decimation-in-frequency FFT algorithm.

This lectures covers different methods of computation of the discrete Fourier transform, including direct computation, successive decimation of the sequences, the decimation-in-time form of the FFT algorithm, and basic butterfly computation.

This lecture includes more demonstrations of sampling and aliasing with a sinusoidal signal, sinusoidal response of digital filters, dependence of frequency response on sampling period, and the periodic nature of the frequency response of a digital filter.

This lecture covers generalization of the frequency response representation of sequences and the inverse Fourier transform relation. It also covers the properties of and the relationship between continuous-time and discrete-time Fourier transforms.

To view this content, you must be a member of Mark's Patreon at $5 or more - Click "Read more" to unlock this content at the source The post What is The Discrete Fourier Transform (DFT)? appeared first on How the Fourier Transform Works.

. TWTS – Episode 21. – Biological Fourier Transform Peak Experiences! http://www.blooomy.org/podcast/BiologicalFourierTransform.mp3 DOWNLOAD (right click to save linked file): TWTS Biological Fourier Transform Peak Experiences! . What matters? Our more “metaphorical” and poetic language turns out to be an excellent clue as to the more scientific processes of what’s going on unconsciously with our more […]

This video gives a summary of relationships between continuous-time and discrete-time Fourier series and Fourier transforms.

This video covers many uses and applications of Fourier transforms in signal processing. We will derive the Fourier transform representation of aperiodic signals, and examine the relationship between Fourier series and Fourier transforms.

This video covers Fourier transofrm properties, including linearity, symmetry, time shifting, differentiation, and integration. We will also cover convolution and modulation properties and how they can be used for filtering, modulation, and sampling.

We find the Fourier transform of a simple piecewise function with values 0 and e^(-kt).

We find the Fourier transform of a simple piecewise function with values 0 and t.

We find the Fourier transform of a simple piecewise function with values 0 and 1.

E. Hitzer

T. Batard and M. Berthier

Siltanen, S (U. of Helsinki) Tuesday 22 November 2011, 14:00-15:00

revised Fall 2011

It is very important to understand how to perform direct convolution, as well as to have a picture in your mind about graphical convolution and how it works. However, there is a vitally important theorem that relates the convolutional of two functions to their Fourier transforms. Consider the system that we’ve put together in Fig. 1. Our picture of linear systems tells us that we can compute the output in one of two ways. Either we can break up the input into a superposition of shifted and weighted delta functions, pass each one through the system to get a superposition of shifted and weighted impulse responses h(x − x0), and then add them up through a convolution integral. Alternately, we can break up our input into a superposition of weighted complex sinusoids via the Fourier transform, pass each one through our system using the transfer function H(ξ), and then add them back up again through the inverse Fourier transform. We might ask ourselves, “what is the relationship between h(x) and H(ξ)? Given the notation we’ve chosen, we might guess that they are related by a Fourier transform.

We have discussed the Fourier series and its relative, the Fourier integral. There are many specific forms that the Fourier integral can take, but the one that we are most interested in is known as the Fourier Transform.

The question is analysed if the human cerebral cortex is self similar in a statistical sense, a property which is usually referred to as being a fractal. The presented analysis includes all spatial scales from the brain size to the ultimate image resolution. Results obtained in two healthy volunteers show that the self similarity does take place down to the spatial scale of 2.5 mm. The obtained fractal dimensions read D=2.73±.05 and D=2.67±.05 correspondingly, which is in good agreement with previously reported results. The new calculational method is volumetric and is based on the fast Fourier Transform of segmented three dimensional high resolved magnetic resonance images. Engagement of FFT enables a simple interpretation of the results and achieves a high performance, which is necessary to analyse the entire cortex.

Fluorescence and initiation of photoreactions are problems frequently encountered with resonance Raman spectroscopy of photobiological systems. These problems can be circumvented with Fourier-transform Raman spectroscopy by using the 1064-nm wavelength of a continuous wave neodymium-yttrium/aluminum-garnet laser as the probing beam. This wavelength is far from the absorption band of most pigments. Yet, the spectra of the investigated systems--bacteriorhodopsin, rhodopsin, and phycocyanin--show that these systems are still dominated by the chromophore, or that preresonant Raman scattering is still prevalent. Only for rhodopsin were contributions of the protein and the membrane discernible. The spectra of phycocyanin differ considerably from those obtained by excitation into the UV-absorption band. The results show the usefulness of this method and its wide applicability. In addition, analysis of the relative preresonant scattering cross sections may provide a detailed insight into the scattering mechanism.