 Are you staring in anguish at the gibberish the FFT spits out after analysing your data? Are you feeling lost? I totally get it. When I first ran an FFT, I took one look at the results and began to despair. Those dreaded complex numbers hold the key to the hidden frequency information, but deciphering them feels like cracking a code. In this video, we will unlock that code together, interpreting the FFT output to again clear insights that reveal the true story within your signal. 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. The whole idea behind the Fourier Transform is that it tells you the frequency spectrum of your signal, but where is the frequency information in this list? Well, it's not here explicitly, but the position of each item in the list hints at what its frequency is. However, there's some missing information that we need to know first. Specifically, what was the sampling rate you sampled your signal at, and how many samples were fed into your FFT? Once you know these two parameters, you can work out the frequency of each item in the list from its position using the following equation. The position of the item in the list, lowercase n, divided by the total number of samples you fed into the FFT, uppercase n, also known as the FFT size, multiplied by the sample rate r. So now we can fill in the frequency information for each item in the list. The relationship between the sampling rate and the FFT size determines your frequency resolution. For a given sampling rate, the bigger the FFT size, or the longer you sampled your signal for, the smaller the jump between adjacent frequencies in the FFT's output, meaning that your frequency resolution will be higher. The output the FFT gives you is a list of complex numbers. Each complex number tells you the amplitudes of the cosine and sine components making up each sinusoid. But to combine these numbers to tell us what the magnitude of the sinusoid is, we have to use Pythagoras theorem. We take the amplitude of the cosine component and square it, then the amplitude of the sine component and square it, then we add the two numbers and take the square root of the result. Magnitude and amplitude mean similar things, but they're not the same. Amplitude can be positive or negative, while magnitude is always positive. But the magnitude of the sinusoid is only half the story. To complete the picture, we need to know the phase of the sinusoid. We can calculate this using the inverse tangent function, however I recommend using the extended inverse tangent function, known in most programming languages as the Atan2 function. The inverse tangent function only tells us the phase of the sinusoid in the range of minus 90 degrees to plus 90 degrees, whereas the Atan2 function preserves the sines of both the cosine and sine amplitudes, giving us a phase in the range of minus 180 degrees to plus 180 degrees. Using these methods, you can find the magnitudes and phases for the entire list and plot the full spectrum for your signal. So now you understand how to interpret that baffling list of complex numbers the FFT gives you, 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 bite-size lessons, no more feeling lost in equations. In 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.