input stage. In the 12 In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform. Consequently, the periodic summation of a function is completely defined by discrete samples of the original function's Fourier transform. Conversely, the periodic summation of a function's Fourier transform is completely defined by discrete samples of the original function. - f, S /2 f S /2 - fs - BW /2 fs + BW / 2 - -BW / 2 BW /2 fs - BW /2 fs+ BW / 2 BW < fs Aliasing moves the frequency content toward DC Input signal frequency content leaking into second Nyquist zone Zone 1 Zone 2 Zone 3 Nyquist zones BW > fs Zone 1 Zone 2 Aliasing Aliasing First and second Nyquist zones Figure 5.20 Illustration of the Nyquist zone concept [15]. New Radio Access RF and Transceiver Design Considerations 711 digital signal processing domain, sample-and-hold processing is equivalent to convolution of the frequency spectrum of the impulse train (due to the sampling clock) with the fre- quency spectrum of the analog input. This convolution results in periodicity of the fre- quency spectrum that is observed over various Nyquist zones, as previously explained. When the input signal contains frequency components above the Nyquist frequency (fs/2), the adjacent Nyquist zones start overlapping and result in aliasing. Aliasing in DACs is a consequence of the zero-order-hold processing (used to avoid code-dependent output glitches) of the discrete-time samples at the output stage. The zero-order-hold processing in the DSP domain is equivalent to convolution of the sin(x)/x type of frequency spectrum (of the rectangular function appearing due to holding discrete-time samples) with the DAC core's output-impulse train frequency spectrum (of varying amplitude, in general). As in the case of ADCs, the periodicity of the output spectrum over different Nyquist zones can be attributed to this convolution (see Fig. 5.21). Da