The sinusoidal signal energy that should be included within one frequency bin in the FFT smears across other bins. The abrupt transition at the data record’s end points produces frequency components in the FFT that are not present in the original sinusoidal signal. The FFT of a sinusoidal signal with a non-integer number of cycles in the time record is performed. This can be understood by looking into the case where the sampled signal is a sinusoid (Fig. The abrupt discontinuity at the record’s end points produces frequency components not present in the original signal, which introduces spectral leakage in the FFT. Since no discontinuity occurs at the end points of the data record, the resulting FFT shows the proper frequency spectrum of the sine signal. An integer number of cycles of a sinusoidal wave is included within the data record frame when using coherent sampling (left). If the samples on the time record do not start and stop within the same value at the end points in the time domain frame, this is interpreted as a discontinuity in the waveform. The FFT assumes the signal within the time record is repetitive (Fig. The FFT spectrum consists of M/2 discrete frequency bins with a range from dc to f S/2, and a bin width of f S/M, where f S is the sampling frequency. The FFT requires a time domain record with a number of samples (M) that is a power of 2. The FFT is an algorithm that quickly performs the discrete Fourier transform of the sampled time domain signal.
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