Channel Title: Mark Newman Channel Description: Are you a budding engineer dreaming of a career creating and inventing? Is the maths holding you back? I believe that mathematical concepts are more than just a set of abstract equations and I’m passionate about finding visual and intuitive ways of explaining them. I’m Mark Newman, an Electronics Engineer with 25 years of practical experience. I went through university in a haze of Greek letters and abstract formulae, doubting whether I'd chosen the right career. I'm determined that others shouldn’t have to suffer the same fate. On this channel, I use the power of video and animation to teach the core concepts of signals and systems, providing you with the tools you need to turn theory into practice. I can't produce a video a week, but I can promise you quality mini-series produced periodically which will help you ace your signals and systems course. Click subscribe and set the bell notification for updates on the next mini-series or email me at the address below. <video> Why do Discrete Time Signals Produce Repeating Frequency Spectra? Description: Why do discrete time signals exhibit a repeating pattern in their frequency spectra? When we sample a signal, turning it into a discrete-time signal, we are effectively throwing away some of the information about that signal. We only know what it is doing at the points we sampled it. But what is going on between two sampled points and why does it produce a repeating pattern in the frequency domain? For a comprehensive and visually intuitive exploration of the Fourier Transform and its workings, I invite you to explore my book series on the Fourier Transform available at: https://www.amazon.com/dp/B0BSJJ69Z1 </video> <video> How to use the FFT like a Pro, Understand the output Description: Feeling unsure how to use the FFT’s puzzling list of complex numbers that it gives you in its output? Don't worry, you're not alone! This video will show you how to make sense of all that gibberish. You’ll learn how to convert the position of each item in the output list into a frequency value in Hz and find out how you can increase the resolution of your results. You'll also discover how to calculate the true strength of each frequency component in your signal and unlock the phase information to gain deeper insights into its behavior. ️ Don’t let the output of the FFT baffle you anymore. Take control of your signal analysis with these easy tips. Understanding the Fourier Transform isn't just about using it – it's about unlocking its true potential. Imagine interpreting results with confidence, troubleshooting issues like a pro, and squeezing even more insights from your data. That's why I've created "How the Fourier Transform Works," an online course that breaks down the mathematical complexities of the Fourier Transform into clear, bite-sized lessons. No more feeling lost in equations! The official release is still a few months away, but you can be one of 50 early birds and get 50% off the course price, instant access to the first 15 lectures, and automatic updates as new lectures are added. Click the link below, and secure your spot as one of the lucky 50 today! https://the-fourier-transform.teachable.com/p/how-the-fourier-transform-works/?coupon_code=EARLYBIRD 00:00 Introduction 00:36 Ident 00:48 Where is the frequency information? 02:05 How to calculate the magnitude of each frequency 02:45 How to calculate the phase for each frequency 03:32 Master the Fourier Transform </video> <video> What is the Inner Butterfly in the FFT Description: The #FFT is so efficient because it breaks the problem down into little bits and performs the same 2-point #DFT calculation on each bit, using the output of one stage of calculations as the input to the next until the DFT for the entire signal is calculated. This repeating calculation can be represented using a Butterfly Diagram. A single calculation is sometimes referred to as the "Inner Butterfly". For a comprehensive and visually intuitive exploration of the Fourier Transform and its workings, I invite you to explore my book series on the Fourier Transform available at: https://www.amazon.com/dp/B0BSJJ69Z1 </video> <video> Calculating Twiddle Factors in the FFT Description: Twiddle Factors play a crucial role in the Fast Fourier Transform (FFT) algorithm by helping to combine and manipulate the complex numbers involved in the calculation of frequency spectra. In continuation to last week's short (https://youtube.com/shorts/LIOs__f8F44), in this video, we will demystify the complex (pun intended) world of Twiddle Factors and reveal what they do and how they are calculated. For a comprehensive and visually intuitive exploration of the Fourier Transform and its workings, I invite you to explore my book series on the Fourier Transform available at: https://www.amazon.com/dp/B0BSJJ69Z1 </video> <video> What is Convolution Description: Convolution plays a pivotal role in signal processing, allowing us to extract valuable information and uncover hidden patterns in various signals, ranging from audio and images to seismic data and beyond. But what is convolution and how does it work? For a comprehensive and visually intuitive exploration of the Fourier Transform and its workings, I invite you to explore my book series on the Fourier Transform available at: https://www.amazon.com/dp/B0BSJJ69Z1 #signalprocessing #fouriertransform #dataanalysis </video> <video> What is The Nyquist Rate? Description: Have you ever wondered how digital audio, images, and other data are accurately captured and reproduced? The Nyquist rate is a fundamental principle that underlies the flawless representation of analog signals in the digital realm. In this video, we explore what the Nyquist rate is and how it relates to the sampling process. For a comprehensive and visually intuitive exploration of the Fourier Transform and its workings, I invite you to explore my book series on the Fourier Transform available at: https://www.amazon.com/dp/B0BSJJ69Z1 </video> <video> Fourier and Napoleon: A Political and Scientific Alliance Description: Although we usually associate Jean Baptiste Joseph Fourier with mathematics and the Fourier Series, he was also very politically active and a keen supporter of the French Revolution. In this short, we examine the lesser-known historical connections between Fourier and the legendary French emperor Napoleon. For a comprehensive and visually intuitive exploration of the Fourier Transform and its workings, I invite you to explore my book series on the Fourier Transform available at: https://www.amazon.com/dp/B0BSJJ69Z1 </video> <video> Wave Composition and Transformation Description: Adding together (or compositing) a cosine wave and a sine wave at the same frequency but different amplitudes produces a sinusoid with the same frequency but a different amplitude and phase. This simple fact, based on a trigonometric identity has far-reaching implications in the world of telecommunications and signal analysis. In this video, we look at how to calculate the properties of the resulting sinusoid and what you can do with that information. For a comprehensive and visually intuitive exploration of the Fourier Transform and its workings, I invite you to explore my book series on the Fourier Transform available at: https://www.amazon.com/dp/B0BSJJ69Z1 </video> <video> Unraveling the Secrets of Twiddle Factors in the FFT Description: Twiddle Factors play a crucial role in the Fast Fourier Transform (FFT) algorithm. They are the workhorses of the algorithm, acting as weights and phase shifters. It is twiddle factors that enable the efficient computation of the Discrete Fourier Transform (DFT), vastly reducing the number of calculations needed. Grasping the significance of Twiddle Factors will enable you to optimize your FFT implementation, leading to faster and more accurate results in various signal processing applications. Therefore, understanding what they do and why they are there is essential. In this quick tutorial, I introduce the concept of Twiddle Factors and look at their function within the FFT. We look at how they are actually calculated in this video: https://youtube.com/shorts/FEI7FoEP3e4?feature=share For a comprehensive and visually intuitive exploration of the Fourier Transform and its workings, I invite you to explore my book series on the Fourier Transform available at: https://www.amazon.com/dp/B0BSJJ69Z1 </video> <video> An Introduction to the Fourier Transform Description: In this engaging introduction to the Fourier Transform, we use a fun Lego analogy to understand what the Fourier Transform is. Just as a toy car can be assembled from individual Lego bricks, each brick with properties like its color, its shape, and its position in the car, we'll see how signals can be built from individual sinusoids, each sinusoid with properties like its frequency, its amplitude, and its phase. Join us for a quick and intuitive introduction to the Fourier Transform, what it's all about, why it matters, and how it works. Get ready to unlock the power of this mathematical tool and gain a whole new perspective on the world of signals. Link to Books Series: https://howthefouriertransformworks.com/books.html 00:00 What is the Fourier Transform? 00:14 The Lego brick analogy 00:33 Building a signal out of sinusoids 01:46 Why is the Fourier Transform so useful? 02:20 The Fourier Transform book series 02:32 Book 1: How the Fourier Series Works 02:43 Book 2: How the Fourier Transform Works 02:58 Conclusion </video> <video> How to use the FFT on a signal of any size Description: Tired of having to make sure your signal contains a specific number of samples (power of 2)? Learn how to use the FFT with signals of any length! In this video, we’ll discover 3 powerful techniques to overcome the power of 2 limitation, discuss the pros and cons of each method, help you choose the right method for your application, and discover how to avoid data distortion and ensure accurate frequency analysis. Gain the knowledge and control to perform confident and accurate frequency analysis using the FFT. Understanding the Fourier Transform isn't just about using it – it's about unlocking its true potential. Imagine interpreting results with confidence, troubleshooting issues like a pro, and squeezing even more insights from your data. That's why I've created "How the Fourier Transform Works," an online course that breaks down the mathematical complexities of the Fourier Transform into clear, bite-sized lessons. No more feeling lost in equations! The official release is still a few months away, but you can be one of 50 early birds and get 50% off the course price, instant access to the first 15 lectures, and automatic updates as new lectures are added. Click the link below, and secure your spot as one of the lucky 50 today! https://bit.ly/3vhS3z2 Link to the Cubic Spline and Linear Interpolation JavaScript code featured in the video: https://howthefouriertransformworks.com/Interpolation.js 00:00 Introduction 00:46 Ident 00:58 The big limitation of the FFT 02:21 Zero Padding 02:48 Resampling 03:57 Overlap-Add 06:18 Master the Fourier Transform </video> <video> How to use the FFT like a pro, 3 essential signal prep tips Description: Unsure how to use the FFT to get meaningful results from your data? Join me as I unveil 3 crucial signal preparation tips to ensure accurate frequency analysis. In this video, you'll discover: 1. How to find the perfect sampling rate to avoid aliasing and capture all the frequencies in your signal. 2. How low-pass filters prevent high-frequency noise from distorting your signal and messing up your FFT results. 3. How windowing functions smooth out signal edges and minimize spectral leakage for cleaner FFT output. Stop feeding garbage into your FFT and start getting the insights you deserve! Understanding the Fourier Transform isn't just about using it – it's about unlocking its true potential. Imagine interpreting results with confidence, troubleshooting issues like a pro, and squeezing even more insights from your data. That's why I've created "How the Fourier Transform Works," an online course that breaks down the mathematical complexities of the Fourier Transform into clear, bite-sized lessons. No more feeling lost in equations! The official release is still a few months away, but you can be one of 50 early birds and get 50% off the course price, instant access to the first 15 lectures, and automatic updates as new lectures are added. Click the link below, and secure your spot as one of the lucky 50 today! https://the-fourier-transform.teachable.com/p/how-the-fourier-transform-works/?coupon_code=EARLYBIRD 00:00 Introduction 00:31 Ident 00:50 Tip 1: Set the optimum sampling rate 02:38 Tip 2: Use an antialiasing filter 03:51 Tip 3: Use a windowing function 07:16 Master the Fourier Transform </video> <video> Why the DFT is necessary Description: This video looks at the differences between the DFT (Discrete Fourier Transform) and the FT (Fourier Transform) and why the DFT is crucial for practical signal processing. The DFT is specifically designed for discrete signals making it the go-to tool for most everyday applications. For a comprehensive and visually intuitive exploration of the Fourier Transform and its workings, I invite you to explore my book series on the Fourier Transform available at: https://www.amazon.com/dp/B0BSJJ69Z1 </video> <video> What is negative Frequency? Description: Negative frequency is a confusing but important concept in signal analysis, especially when it comes to radio modulation techniques. Far from being simply a quirk of the math, it is a totally physical phenomenon that has to be taken into account when considering the total bandwidth of a signal. In this video, we try to understand what negative frequency is in a more intuitive way. For a more in-depth video on the subject, check out one of my longer videos at: https://youtu.be/_3-qntJ12q4 For a comprehensive and visually intuitive exploration of the Fourier Transform and its workings, I invite you to explore my book series on the Fourier Transform available at: https://www.amazon.com/dp/B0BSJJ69Z1 </video> <video> Why do Discrete Frequency Signals Repeat in the Time Domain Description: The frequency spectrum of a repeating time-domain signal is discrete due to the repeating nature of the sinusoids that make them up. Adding two or more sinusoids together causes them to interfere with each other. Adding together sinusoids at similar frequencies and carefully controlled amplitudes can even produce a periods of silence in the signal. In this video, we investigate the relationship between frequency resolution and how often signals repeat in the time domain. For a comprehensive and visually intuitive exploration of the Fourier Transform and its workings, I invite you to explore my book series on the Fourier Transform available at: https://www.amazon.com/dp/B0BSJJ69Z1 </video>

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Are you a budding engineer dreaming of a career creating and inventing? Is the maths holding you back? I believe that mathematical concepts are more than just a set of abstract equations and I’m passionate about finding visual and intuitive ways of explaining them.

I’m Mark Newman, an Electronics Engineer with 25 years of practical experience. I went through university in a haze of Greek letters and abstract formulae, doubting whether I'd chosen the right career. I'm determined that others shouldn’t have to suffer the same fate.

On this channel, I use the power of video and animation to teach the core concepts of signals and systems, providing you with the tools you need to turn theory into practice. I can't produce a video a week, but I can promise you quality mini-series produced periodically which will help you ace your signals and systems course. Click subscribe and set the bell notification for updates on the next mini-series or email me at the address below.

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