Nontraditional Windows in Spectral Analysis

This thesis studies a new data weighting function, which consists of a complex valued window known as the linear complex valued FM chirp window. This type of window, when used with the Fourier transform, produces a magnitude spectrum which permits identification of single sinusoids and multiple sinusoids which can be separated in frequency by less than one DFT bin. This allows determination of whether or not one or multiple signals are present. The chirp window seems to have better resolution properties than classical windows. When the chirp window is used with a signal that contains a frequency step i.e., FSK, the resultant spectrum is markedly different for the upward shift and downward shift cases. The work of this thesis consists of replicating the results of J. Griffiths in his paper A Novel Window For High Resolution Fourier Transform to establish the signal to noise ratio dependency of this type of window, and to study its behavior when damped sinusoids are present. Additionally, a review of classical windows and sidelobe behavior is presented. All simulations where performed using MATLAB. Spectral analysis, Fourier transform, Autocorrelation, Bias and Variance, Fast fourier transform, Periodogram, Classical windows, Nontraditional windows, Damped sinusoids, Frequency resolution, Record length.