Скачать или смотреть Understanding the FFT Output: How to Accurately Recover Amplitude and Phase in Python's numpy

A step-by-step guide for Python users on accurately interpreting the output of FFT for amplitude and phase recovery from sine waves. Learn how to avoid common pitfalls and achieve correct results.
---
This video is based on the question https://stackoverflow.com/q/70759395/ asked by the user 'Antoni Parellada' ( https://stackoverflow.com/u/4089351/ ) and on the answer https://stackoverflow.com/a/70760108/ provided by the user 'Hersh Joshi' ( https://stackoverflow.com/u/8456383/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

Visit these links for original content and any more details, such as alternate solutions, latest updates/developments on topic, comments, revision history etc. For example, the original title of the Question was: Output of fft.fft() for magnitude and phase (angle) not corresponding the the values set up

Also, Content (except music) licensed under CC BY-SA https://meta.stackexchange.com/help/l...
The original Question post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/... ) license, and the original Answer post is licensed under the 'CC BY-SA 4.0' ( https://creativecommons.org/licenses/... ) license.

If anything seems off to you, please feel free to write me at vlogize [AT] gmail [DOT] com.
---
Understanding the FFT Output: How to Accurately Recover Amplitude and Phase in Python's numpy

When working with signal processing in Python, you might encounter discrepancies when trying to recover the amplitude and phase of a generated sine wave using the Fast Fourier Transform (FFT). If you've set up a sine wave with specific parameters and noticed that the outputs for magnitude and phase don't correlate with your original values, you're not alone! This guide aims to clarify the common mistakes and provide a clear path toward accurate results.

The Problem

You set up a sine wave with defined amplitude, frequency, and phase, and you expected the FFT to retrieve those original parameters accurately. For instance, if you set:

Frequency (f0): 25 Hz

Amplitude (A): 50

Phase (phi): π/6 (approximately 0.524)

After computing the FFT, you found the magnitude to be around 21785 and the phase to be approximately -1.2 instead of the expected values. What went wrong? This post will unpack the necessary steps to correct these results.

The Solution

To rectify the issues with FFT output, follow these organized guidelines:

1. Normalize the FFT Output

The first solution is to properly normalize the FFT result. It’s essential to scale your FFT output to reflect real-world values correctly.

Instead of:

[[See Video to Reveal this Text or Code Snippet]]

Use:

[[See Video to Reveal this Text or Code Snippet]]

Also, when calculating the magnitude, modify it as follows:

[[See Video to Reveal this Text or Code Snippet]]

2. Find the Peak Frequency Correctly

Another common mistake is using an incorrect method to find the frequency closest to f0. Instead of relying on:

[[See Video to Reveal this Text or Code Snippet]]

Utilize np.argmax which yields the peak magnitude:

[[See Video to Reveal this Text or Code Snippet]]

This will identify the frequency peak close to your desired frequency.

3. Calculate Phase Accurately

Phase calculations may lead to errors due to potential offsets with np.angle. Instead, manually calculate the phase as follows:

[[See Video to Reveal this Text or Code Snippet]]

This approach will ensure your phase measurements are accurate.

4. Increase Your Sample Count

To enhance the accuracy of your FFT results, consider increasing the number of sample points. For example, using:

[[See Video to Reveal this Text or Code Snippet]]

This change improves the frequency resolution and the fidelity of your waveform analysis.

5. Adjust Magnitude for Two-Sided DFT

FFT results reflect both positive and negative frequencies in a Discrete Fourier Transform (DFT). The peak on the positive side is only half the actual amplitude, so adjust as follows:

[[See Video to Reveal this Text or Code Snippet]]

This multiplication corrects the discrepancy in magnitude calculations, ensuring that you account for both sides of the spectrum.

Example Implementation

Here’s a compiled example reflecting all the adjustments discussed above:

[[See Video to Reveal this Text or Code Snippet]]

Conclusion

By following these straightforward modifications, you can achieve accurate amplitude and phase recovery from your FFT analysis in Python. Remember that normalization, peak detection, manual phase calculation, increasing sample count, and correcting magnitude all play pivotal roles in refining your results. Happy coding, and may you always find the precise frequencies you seek!