Question

Flat-top sampling leads to

• A. Aperture effect
• B. Aliasing
• C. Granular noise
• D. Overload

Hint:

Ideal sampling: Uses impulses. Spectrum is periodic repetition of original signal spectrum.
Flat-top sampling (Practical sampling): Holds sample value for a duration \(\tau\).
Aperture effect: The spectrum of the flat-top sampled signal is distorted (attenuated at higher frequencies) by a sinc function factor due to the finite width of the sampling pulses. This distortion needs to be compensated by an equalizer if significant.

Answer 1

The Correct Option is A

Flat-top sampling is a practical method of sampling where the value of the analog signal is held constant for a finite duration (the "aperture" time \(\tau\)) for each sample, creating a staircase-like approximation of flat-topped pulses. This is in contrast to ideal impulse sampling, where each sample is an impulse with area proportional to the signal value at that instant. The effect of holding the sample value constant for a duration \(\tau\) (flat-top) is equivalent to convolving the ideal impulse train with a rectangular pulse of width \(\tau\). In the frequency domain, this convolution becomes multiplication of the spectrum of the impulse-sampled signal by the Fourier Transform of the rectangular pulse, which is a sinc function: \( \tau \text{sinc}(\omega\tau/2) = \tau \frac{\sin(\omega\tau/2)}{\omega\tau/2} \). This sinc function has a low-pass characteristic. Its magnitude is not flat; it rolls off with frequency. This roll-off causes an attenuation of the higher frequency components of the sampled signal's spectrum. This frequency-dependent attenuation due to the finite width of the sampling pulses is known as the aperture effect. (b) Aliasing: Occurs if the sampling rate is less than the Nyquist rate (\(f_s<2f_{max}\)). Not directly caused by flat-top sampling itself, though flat-top sampling occurs in a system that might also alias if not sampled fast enough. (c) Granular noise: Associated with delta modulation or quantization with large steps for low amplitude signals. (d) Overload (slope overload): Associated with delta modulation when the signal changes too fast. Therefore, flat-top sampling leads to the aperture effect. \[ \boxed{\text{Aperture effect}} \]