--- title: "Aliasing and aperture effects; types of sampling" subject: "Communication Systems" chapter: 4 key: "semester_6/communication_systems:aliasing-aperture-sampling-types" source: https://www.bctengineer.com/q/semester_6/communication_systems/aliasing-aperture-sampling-types site: BCT Engineering --- # Aliasing and aperture effects; types of sampling Communication Systems · Chapter 4: Pulse Modulation - Asked in: 2075 Chaitra (CS II), 4+6 marks - Video: [Sampling Types in digital communication - Ideal, Natural, Flat top Sampling - Aperture effect](https://www.youtube.com/watch?v=sFiCgEVpTWs) — Electronics Subjectified - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_6/communication_systems/aliasing-aperture-sampling-types - Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-4 ## Question Define the Aliasing and Aperture effects in Sampling. Explain the types of sampling techniques with waveforms. ## Short answer Aliasing is spectral overlap from sampling below Nyquist rate. Aperture effect is high-frequency loss in flat-top sampling. Sampling types: ideal (impulse), natural, flat-top. ## Answer #### Aliasing **Aliasing** is the overlap of the shifted spectral copies of a sampled signal that occurs when the sampling rate is less than the Nyquist rate ($f_s < 2W$), or when the signal is not strictly band-limited. A high-frequency component $f$ then appears falsely as a low frequency $|f - nf_s|$ and the original signal cannot be recovered. Remedies: anti-aliasing low-pass filter before the sampler, and sampling a little above $2W$ (guard band). #### Aperture effect In flat-top sampling each sample is held for a width $\tau$; the spectrum is multiplied by $H(f) = \tau\,\text{sinc}(f\tau)$. This attenuates higher message frequencies, a distortion called the **aperture effect**. It is reduced by keeping $\tau \ll T_s$ and corrected by an equalizer with response $1/H(f)$. #### Types of sampling **1. Ideal (impulse) sampling** $$ g_\delta(t) = \sum_n g(nT_s)\delta(t - nT_s), \qquad G_\delta(f) = f_s\sum_n G(f - nf_s) $$ Samples are zero-width impulses. Theoretical only, since impulses cannot be generated. **2. Natural sampling** $$ s(t) = g(t)c(t), \qquad S(f) = \frac{\tau}{T_s}\sum_n \text{sinc}(nf_s\tau)G(f - nf_s) $$ Pulses of width $\tau$ whose tops follow the signal; done by an analog switch (chopper). No aperture distortion. **3. Flat-top sampling** $$ s(t) = \sum_n g(nT_s)h(t - nT_s), \qquad S(f) = f_sH(f)\sum_n G(f - nf_s) $$ Pulses of width $\tau$ with constant height equal to the sample value (sample-and-hold). Practical; has aperture effect. **Waveforms** ```text g(t) .-~~~-. .' '.___ Ideal ^ ^ ^ ^ ^ impulses, height=g(nTs) | | | | | Natural ▄ █ █ ▆ ▂ tops follow curve Flat-top ■ ■ ■ ■ ■ flat tops, held 0 Ts 2Ts 3Ts 4Ts ``` | Type | Pulse | Spectrum copies | Practical? | |---|---|---|---| | Ideal | Impulse | Exact $G(f)$, equal height | No | | Natural | Width $\tau$, curved top | Exact $G(f)$, sinc-scaled height | Yes | | Flat-top | Width $\tau$, flat top | $G(f)H(f)$, distorted | Yes (most used) | ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Aliasing occurs when: A. fs is above the Nyquist rate B. fs is below 2W, so spectral copies overlap C. The pulse width is too large D. The signal is quantized Answer: B. Copies overlap if fs < 2W, and high frequencies appear as false low ones. (Key point: Aliasing) 2. Which is a remedy for aliasing? A. An equalizer 1/H(f) B. An anti-aliasing low-pass filter before the sampler C. Making tau very large D. Using natural sampling Answer: B. An anti-aliasing LPF band-limits the signal; sampling slightly above 2W also helps. (Key point: Aliasing remedy) 3. Why is ideal sampling only theoretical? A. It needs impulses of zero width, which cannot be generated B. It causes aperture effect C. It needs fs < 2W D. It has no spectrum Answer: A. Ideal sampling uses impulses; practical systems use natural or flat-top pulses. (Key point: Ideal sampling) 4. Which sampling type produces copies G(f)H(f), i.e. distorted? A. Ideal B. Natural C. Flat-top D. None of them Answer: C. Flat-top copies are shaped by H(f); ideal copies are exact and natural copies are only scaled. (Key point: Spectrum comparison) ## Related in Communication Systems - [Sampling theorem; aliasing and aperture effect remedies](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Asampling-theorem-aliasing-aperture-remedy) — Communication Systems, chapter 4 - [Prove sampling theorem; aliasing and aperture effect](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Asampling-prove-aliasing-aperture) — Communication Systems, chapter 4 - [Nyquist-Kotelnikov sampling theorem; aliasing and aperture](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Anyquist-kotelnikov-aliasing-aperture) — Communication Systems, chapter 4 - [Aperture and aliasing; sampling 10cos(20πt)cos(200πt) at 250 samples/s](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aaperture-aliasing-10cos20pit-250) — Communication Systems, chapter 4 - [Sub-sampling theory and aperture effect](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Asubsampling-aperture-effect) — Communication Systems, chapter 4 - [Aperture effect correction; bandpass sampling 80–115 kHz](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aaperture-correction-bandpass-80-115) — Communication Systems, chapter 4 ## Related in other subjects - [Impulse train sampling, aliasing, reconstruction](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aimpulse-train-aliasing-reconstruction) — Signals and Systems, chapter 4 - [Aliasing via impulse-train sampling](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aaliasing-impulse-train-frequency) — Signals and Systems, chapter 4 - [Sampling theorem; aliasing cause; Nyquist](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Asampling-aliasing-cause-nyquist) — Signals and Systems, chapter 4 - [Prove sampling theorem; aliasing effect](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aprove-sampling-theorem-aliasing) — Signals and Systems, chapter 4