A limited number of bar patterns may be regarded as a continuous square wave pattern chopped by a rectangular pulse. In effect the square wave spectra is multiplied by the sine function in frequency space, this being equivalent to convolving the square wave with the rectangular pulse in real space.

In general, any MTF cutting off within the harmonic range must affect the profile of the image seen in the space domain, because the harmonics determine the profile. For a 3 cycle target, the single-valued fundamental frequency of the square wave is replaced by a relatively broad band, centered near the fundamental frequency, but slightly below it, and moves nearer to it as the number of bars increases. Also, the fundamental band gets narrower as the number of target bars increases and the pattern approaches closed to an infinite square wave.

If the MTF cuts out the third harmonic, only the fundamental is left, and the image will be a pure sinewave at reduced modulation. This account is only true if the square wave extends indefinitely. As soon as it is truncated to some finite number of cycles, the spectrum losses its purity and the lines are replaced by bands.

The essential characteristic of all these spectra is the replacement of the single-valued fundamental frequency of the square wave by a broad band, centered near a frequency which is the nominal frequency of the bar target i.e. the reciprocal of the target period. The peak of the fundamental band in not exactly at the fundamental frequency, but slightly below it, and moves nearer to it as the number of bands increases. Also, the fundamental band gets narrower as the number of target bands increases and the pattern approaches closer to the infinite square wave. Negative values significantly revered phase. It is noticed that the fundamental band of frequencies is in positive phase for targets with odd number of bars, but negative phase for those with even number of bars.

In general accurate prediction requires a full Fourier analysis, especially for square waves which have more complex spectra. The exact derivation of CTF requires a two-dimensional Fourier analysis, to take into account the finite lengths of the bars. Except near the limits of resolution, the effects of spread function is relatively small for bar targets where the length exceeds the width by at least a factor of three, and a useful approximation can be made with one-dimensional Fourier analysis.