The effect of the signal initial phase on the amplitudes of a DFT spectrum

Knowing the amplitudes in a spectrum calculated using the Discrete Fourier Transform (DFT) algorithm is essential for precisely estimating the frequencies of a real-valued signal. Since the amplitudes are affected by the signal's initial phase, it is crucial to consider this aspect when estimating the signal frequencies. This paper presents the initial signal phase's effect on the values calculated for the real and imaginary parts and the magnitudes in the DFT of a real-valued signal. Analyzing the evolution of the amplitudes with the initial phase for a complete cycle for the initial phase, we found that the values in the magnitude DFT are subject to minor alteration, while the values of the real and imaginary parts of the DFT are strongly affected by the initial phase.