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Sampling Continuous Time Signal01:11

Sampling Continuous Time Signal

324
In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...
324
Basic Discrete Time Signals01:16

Basic Discrete Time Signals

273
The unit step sequence is defined as 1 for zero and positive values of the integer n. This sequence can be graphically displayed using a set of eight sample points, showing a step function starting from n=0 and remaining constant thereafter.
The unit impulse or sample sequence is mathematically expressed as zero for all n values except at n=0, where it is one. The unit impulse sequence, denoted by δ(n), is the first difference of the unit step sequence, while the unit step sequence u(n) is...
273
Sampling Theorem01:15

Sampling Theorem

695
In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.
695
Bandpass Sampling01:17

Bandpass Sampling

241
In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2....
241
Upsampling01:22

Upsampling

286
Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
286
Downsampling01:20

Downsampling

224
When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
224

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Related Experiment Video

Updated: Aug 19, 2025

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
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Research on a step delay method in sequential equivalent time sampling (ETS).

Haitao Li1, Binkang Li1, Zongjing Lv1

  • 1State Key Laboratory of Intense Pulsed Radiation Simulation and Effect (Northwest Institute of Nuclear Technology), Xi'an, Shaanxi 710024, China.

The Review of Scientific Instruments
|December 3, 2022
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Summary
This summary is machine-generated.

A new frequency-based step delay method enhances sequential equivalent time sampling (ETS), significantly increasing sampling rates for repetitive signals. This technique achieves higher equivalent sampling rates, capturing more waveform details.

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Area of Science:

  • Electrical Engineering
  • Signal Processing
  • Instrumentation

Background:

  • Sequential equivalent time sampling (ETS) is a crucial technique in data acquisition instruments like oscilloscopes.
  • Existing step delay methods in ETS have limitations in achieving higher sampling rates.
  • The need for enhanced sampling rates is critical for accurately characterizing high-frequency repetitive signals.

Purpose of the Study:

  • To propose a novel step delay method for sequential equivalent time sampling (ETS) based on frequency difference.
  • To demonstrate the capability of this new method to achieve significantly higher equivalent sampling rates.
  • To validate the proposed method's effectiveness through experimental verification.

Main Methods:

  • A novel step delay method is introduced, leveraging the frequency difference between signals in the frequency domain to generate fine time-domain delays.
  • The core principle involves selecting an appropriate frequency difference to achieve the desired equivalent sampling rate.
  • Experimental validation was conducted using a digital storage oscilloscope and a custom data acquisition system.

Main Results:

  • Achieved an equivalent sampling rate of 5 PS/s for signals at or above 4.999 GHz.
  • A data acquisition system demonstrated a theoretical equivalent sampling rate of 585 GS/s.
  • Comparison with real-time sampling showed the proposed method captures more waveform information for a 1 GHz signal.

Conclusions:

  • The proposed frequency-difference-based step delay method effectively increases the sampling rate in sequential ETS for repetitive signals.
  • The method is capable of achieving very high equivalent sampling rates, surpassing conventional techniques.
  • Further enhancements like oversampling can improve vertical resolution, and integration with sample-and-hold amplifiers can boost analog bandwidth.