Windowing (DSP)

[max.smith@emailgo.de]

Hey @ all,

when windowing in DSP (digital signal processing) in time domain one multiplies all recorded time samples with a weighting factor (hanning, hamming, etc.), followed by a fourier transform (FFT) to reduce sidelobes in the spectral domain.

But now when thinking about starting up in frequency domain where I have multiplied my frequency data with a rectangular window, i.e. I have only non-zero frequencies from fstart to fend ( ... 0 0 0 0 0 0 0 fstart f1 f2 f3 f4 f5 fend 0 0 0 0 ... ). (or alternatively I only have frequency datas recorded at finite points.) What happens to my time domain data after performing the inverse FFT due to the rectangular window?


But in general: How do one has to perform windowing in frequency domain? Really by multiplying the "origianal" (i.e. time domain) window-coefficients with the spectral components? Or performing convolution (with the origignal window, or the fourier transformed coefficients?) since this is the fourier-pair to multiplication?

Thanks for any ideas.

[Blayne_K]

Hello Max,

Many non-standard signals require a near infinite number of frequency components to be properly categorized in the frequency domain. This scenario creates a difficulty for digital systems to transfer and manipulate such signals. Windowing in the frequency domain is a procedure used to restrict the possible set of frequency components to some finite number of frequencies based on the size and shape of a given window. Depending on the window being used, suppose in this case a rectangular window, the resulting spectral domain data contains fewer extraneous frequency components and an inverse FFT will result in a time domain signal that will lack frequency components outside the frequency range of the window. Also, due to a property known as duality, a multiplication of a signal in the frequency domain is the equivalent of convolution of a signal in the time domain.

Best,

Blayne Kettlewell

ELP Engineer