The transfer function H(f) of the zero - order - hold circuit is the Sinc function

Since the spectrum of the ideally sampled signal is 

The spectrum of the zero- order - hold sampled signal x_ZOH(t) is given by the product

This spectrum is illustrated in Figure shown below :

Figure : Spectrum of a zero - order - hold sampled signal

The term sinc( f / f_s ) attenuates the spectral images X( f - k f_s ) and causes their distortion.