Merits and demerits of flat-top sampling

Flat-top sampling produces pulses whose amplitude equals the instantaneous sample value $m(nT_s)$ and stays constant (flat) for the pulse duration $T$. It is produced by a sample-and-hold circuit.

Mathematical model

The flat-top signal is

$$s(t) = \sum_{n=-\infty}^{\infty} m(nT_s)\,h(t - nT_s), \qquad h(t) = \begin{cases} 1, & 0 < t < T \\ 0, & \text{otherwise} \end{cases}$$

This equals the ideally sampled signal convolved with $h(t)$:

$$s(t) = \left[m(t)\sum_n \delta(t - nT_s)\right] * h(t) = m_\delta(t) * h(t)$$

Taking the Fourier transform:

$$S(f) = M_\delta(f)\,H(f) = f_s\sum_{k=-\infty}^{\infty} M(f - kf_s)\;H(f)$$

where

$$H(f) = T\,\text{sinc}(fT)\,e^{-j\pi fT}$$

 |H(f)|
  T |\___
    |    \__              sinc envelope
    |       \___          attenuates higher
    +-----------\----->f  message frequencies
    0   W        1/T

Merits

1. Easy to generate with a sample-and-hold circuit; the constant level gives the ADC time to quantize, so it is the usual practical method before PCM encoding.
2. Pulse tops are flat, so amplitude detection is simple and noise riding on the top is easier to handle.
3. Since the amplitude is constant during the pulse, the energy per sample is well defined, giving a better SNR than very narrow pulses.

Demerits

1. Aperture effect: each spectral copy is multiplied by $\text{sinc}(fT)$, so higher message frequencies are attenuated: amplitude distortion. Example: at $f = W$ with $T = T_s$ and $f_s = 2W$, $\text{sinc}(0.5) = 0.637$, i.e. a 3.9 dB loss.
2. Delay distortion: the term $e^{-j\pi fT}$ introduces a delay of $T/2$.
3. An equalizer with response $\frac{1}{H(f)} = \frac{\pi f}{\sin(\pi fT)}e^{j\pi fT}$ (within the message band) is needed after the reconstruction LPF. The distortion is negligible if $T/T_s \le 0.1$.
4. Wide pulses leave less guard time between samples, which increases crosstalk between channels in TDM.

Compared with natural sampling (where each copy of $M(f)$ keeps its shape), flat-top sampling distorts the spectrum, but it is preferred in practice because of the simple hold-circuit implementation.