Multiplication with a rectangular window in the time domain corresponds to convolution with a formula_45 function in the frequency domain, resulting in spurious ringing artifacts for short/localized temporal windows. With the continuous-time Fourier Transform, formula_46 and this convolution is with a delta function in Fourier space, resulting in the true Fourier transform of the signal formula_47. The window function may be some other apodizing filter, such as a Gaussian. The choice of windowing function will affect the approximation error relative to the true Fourier transform.