Unexpected behavior of `fft` function with large array sizes in MATLAB R2023a
I'm writing unit tests and I'm wondering if anyone has experience with I tried several approaches but none seem to work... I tried several approaches but none seem to work. Hey everyone, I'm running into an issue that's driving me crazy. I'm encountering unexpected results when using the `fft` function on large arrays in MATLAB R2023a. Specifically, when I try to perform a Fast Fourier Transform on an array with one million elements, the output seems to be different from what I expected based on a smaller test case. For example, I have the following code: ```matlab N = 1e6; % Number of points x = rand(1, N); % Generate random signal Y = fft(x); % Perform FFT ``` When I examine the magnitude of the FFT output, I find the values to be significantly smaller than expected. Here's what I'm doing to analyze the results: ```matlab magnitude = abs(Y); % Compute magnitude plot(magnitude); % Plotting the magnitude ``` In smaller cases (e.g., with 1000 elements), the outputs were consistent with my manual calculations. I also tried normalizing the FFT output by dividing the result by `N` (the number of points) as follows: ```matlab Y_normalized = Y / N; ``` However, the result still doesn't match the expected theoretical values for the magnitude spectrum. Additionally, I double-checked that I am using single precision for my random data, and the workspace is clear of any previous variables. Is there something specific about using the `fft` function with such large arrays that I might be missing? Are there any best practices or configuration settings I should be aware of that could influence the output? For context: I'm using Matlab on macOS. This is part of a larger service I'm building. Thanks in advance! My development environment is Ubuntu. How would you solve this? Thanks in advance! Am I approaching this the right way?