 Ever used an FFT in languages like Python, C or JavaScript, expecting perfect results? I did, but when different libraries gave me slightly different frequency spectra, I knew something was wrong. Much research led me to discover that it was the way I had prepared my data, or rather hadn't prepared my data, that was causing the difference. Don't expect diamonds if you plant weeds as the saying goes. In this video, we'll look at three different things the libraries might be doing to your signal before it enters the FFT, and show you how you can do these things yourself and maintain control over your data. Stay tuned to discover how you too can master the Fourier Transform. Hi, I'm Mark Newman, and I'm here to help you understand the fascinating world of signals and systems. So here's the big news. In order for the FFT to work, your signal must contain a number of samples that is a power of two. It's this property of your signal that makes the fast Fourier Transform fast. A signal containing 1,024 samples? No problem. 4,096 samples? A cinch. 4,000 samples? Could you make your signal 96 samples longer, please? Not of your signal doesn't contain a number of samples that is a power of two. This will likely be the case for most signals, so loads of brilliant ideas have been floated over the years to try and mitigate this problem, ranging from displaying an error message and refusing to run, to some pretty ingenious ways of modifying your signal so that it does contain a number of samples that is a power of two. Each of these ideas affects your signal in different ways, producing slightly different frequency spectra. The problem is, you as the user have no idea what your chosen library is doing to your signal once it enters the library's black box. So if your FFT algorithm is refusing to process your signal, or if you want greater control over what happens to your signal before it enters the FFT, here are three possible solutions that you can implement yourself. Number one, zero padding. This is perhaps the simplest way to ensure that your signal contains the correct number of samples. Zeros are simply added to the end of the signal until its length becomes a power of two. It's easy to implement and computationally very efficient, but it reduces the frequency resolution of the output as the zero samples smear the frequency peaks like blurring of picture. Number two, re-sampling. Re-sampling involves changing the sample rate of the signal to achieve the desired length. This can be done using methods like kube-expline interpolation to try and guess their missing sample values. It can be an extremely accurate way of reproducing your signal with the correct power of two number of samples, meaning that the FFT will be able to give you an extremely faithful frequency representation of your signal. Also, interpolation is very flexible, being able to handle unevenly spaced data points, which can be useful for signals with irregular sampling intervals. However, in cases with sparse data or noisy signals, kube-explines might overfit the data introducing artificial oscillations and potentially leading to inaccuracies in the FFT spectrum. They're also quite complex to calculate. If you're stuck for processing power, though, you could go for a linear interpolation, which, while being slightly less accurate, can still give you excellent results, especially if the jump to the nearest power of two samples isn't too large. Number three, overlap and add. The overlap and add method breaks down the signal into smaller frames. Each frame contains a number of samples that is a power of two, but here's the clever part. The frames are overlapped, meaning that some samples from the end of one frame are processed again at the beginning of the next. This means that we can arrange our frame size and overlap factor such that the whole signal is covered with power of two sample-long frames, just as the FFT likes. Now, we may have to pad a few zeros onto the last frame to bring it up to size, but if we choose our FFT size and overlap factor carefully, the number of zeros needed will be much smaller, reducing the adverse effect of zero padding on the output of the FFT. We then run the FFT on each frame separately and combine the results of each FFT by adding them together. The frequencies corresponding to the overlapping sections are averaged to smooth out the transition between frames. The overlap and add method has a number of advantages. It allows us to process signals of any length, not just the power of two. It reduces spectral leakage, especially if you apply a windowing function to each frame, and it can also be very fast, especially if you have more than one processor available as different frames can be sent off simultaneously to FFTs on different processors which can run in parallel. However, there are some disadvantages too. It's computationally complex, requires more memory, and if you don't choose your parameters like frame size, overlap factor, and windowing function carefully, can in some cases distort your signal and mask features you are looking for in the frequency spectrum. For example, the larger the frame size, the better your frequency resolution will be. And if you are windowing each frame, make sure to choose a windowing function that strikes the right balance for your application between reducing spectral leakage and broadening the frequency peaks. If high accuracy is crucial for your application, it's important to be aware of your FFT library's framing approach and its potential impact on your analysis. Be sure to consult the library's documentation to see if they use this approach, and if so, they may offer you ways of controlling it by changing such parameters as windowing functions or overlap factor. So now your signal is ready for the FFT, but the real magic happens inside the black box. Ever wondered what's going on in there? Understanding the Fourier transform isn't just about using it, it's about unlocking its true potential. Imagine being able to interpret its 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 byte-size lessons, no more feeling lost in equations. On the course, you'll learn to unravel the mystery of sine waves and build a solid foundation for understanding the building blocks of the Fourier transform. We'll demystify the world of complex numbers and learn how they make your calculations a lot easier to do, and you'll discover the power of convolution to reveal the secrets your data has been hiding. 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, automatic updates as new lectures are completed, revealing how all these concepts combine to form the Fourier series and the Fourier transform, and a chance to shape the development of the course with your valuable feedback. Don't wait to unlock the awesome power of the Fourier transform. Click the link in the description and secure your spot as one of the lucky 50 today.