Spectrum magnifier: Zooming into local details in the frequency domain

Zooming into a spectrum obtained from the Fast Fourier Transform (FFT) could not be performed directly by linear/cubic interpolations in the frequency domain. A spectrum magnifier is presented in this paper as a two-step procedure: the carrier-wave demodulation and the fractional Fast Fourier Transform¹ (frFFT). Particularly for a narrow-band signal within Nyquist limits, the carrier-wave demodulation shifts the band center to zero; afterward the frFFT efficiently investigates into precision details of the near-zero band without any resolution cost either in the time domain or in the frequency domain. Such a cost is frequently compromised from accuracy and efficiency demands in the methods based on traditional techniques of zero-padding, low- or band-pass filtering, sub-sampling, etc.