John Mathey
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When we measure a finite length of data then we will always have a data window, by default the rectangular window. In fact we call it a window as the section of the signal we measure is like looking at the world through a window; we do not know what is happening outside the part we have measured (observed). What we measure is represented mathematically as the product of the actual signal multiplied by a rectangular window that is zero before and after our measurement and unity during the measurement time.

When the measured time signal is converted to the frequency domain by a Fourier transform then we have not actually gained or lost any information as the Fourier transform is totally reversible. What we have done is represent the signal in a form that helps us understand it better. The purpose of adding what is actually an extra window to the time domain is to suppress those features of the time domain rectangular window which makes interpretation in the frequency domain more difficult.

When we evaluate the Fourier Transform of what is actually the real signal multiplied by the data window, then the original time domain window, that is the data window, becomes a spectral window (because in the frequency domain we talk about the spectrum of frequencies, or more usually the frequency spectrum). So we are already looking at the frequency spectrum through a spectral window. Mathematically the multiplication in the time domain becomes a convolution in the frequency domain between the actual spectrum and the spectral window. In physical terms the spectral window is the frequency domain filter through which we see the underlying spectrum of the signal. The shape and characteristics of the data window define the nature of the spectral window, or filter, through which we see the frequency spectrum of the original signal.

So the short answer to the question is “yes”, but regretfully we cannot choose the characteristics of the data window and the spectral window independently. There are dozens of different data windows with their corresponding spectral windows, the Hanning window is a good compromise. All useful data windows give spectral windows that tend to be like ideal narrow band filters. This leads to the concept of the Equivalent Noise Band Width (ENBW) measure as one criterion of a good window. Other measures are leakage and bias but that is a tale for another day! Incidentally the best data window measured solely by ENBW is the unavoidable rectangular window, it is the other factors which make it less useful.