When you calculate the Fast Fourier Transform (FFT) of three AC signals at different frequencies but with the same amplitude, it is expected to obtain slightly different amplitudes in the resulting frequency spectra. There are a few factors that can contribute to this variation:
Leakage: The FFT assumes that the signal being analyzed is periodic, but in practice, most signals have finite duration. This finite duration can lead to spectral leakage, where energy from one frequency component "leaks" into neighboring frequency bins. Spectral leakage can cause the amplitudes of the frequency components to appear lower or higher than their actual values.
Resolution: The FFT produces a discrete frequency spectrum with a finite number of frequency bins. The resolution of each frequency bin depends on the duration of the signal and the number of samples used in the FFT. If the frequency components of your AC signals fall between two frequency bins, the amplitudes may not be accurately represented and can appear slightly different.
Windowing: Before applying the FFT, it is common to apply a window function to the input signal. Windowing helps to reduce spectral leakage but can also affect the amplitude accuracy. Different window functions have different properties, and some can introduce additional amplitude variations.
These factors can collectively contribute to the observed slight differences in the amplitudes of the frequency components in the FFT results. To minimize these effects, you can try the following:
- Increase the number of samples used in the FFT to improve frequency resolution.
- Use a window function that suits your specific requirements. Common window functions include Hamming, Hanning, and Blackman.
- Ensure that the duration of your input signals is sufficiently long to capture multiple periods of each frequency component.
By carefully selecting parameters and considering these factors, you can minimize the amplitude variations and obtain more accurate results in your FFT analysis.