# Sampling rate and aliasing effect

## What is meant by sampling rate?

In general, a measurement chain designed for digital signal conditioning consists of several components, such as sensors, cables, amplifiers, data acquisition hardware and software. To acquire analog measured values, an analog-digital converter is required which is integrated into the data acquisition hardware. The acquisition of the measurement data is realised by a sampling rate, which is a periodic process. The analog signal is sampled at a defined rate – samples per second – and converted into a digital signal.

In order to accurately capture the original analog measurement signal without loss, the Nyquist-Shannon sampling theorem must be observed. To acquire the maximum frequency of interest, the theorem specifies the selection of a sampling rate that is at least twice as high (sampling rate = 2 x Fmax). This ensures that the sampled discrete-time signal contains the expected frequencies. An aliasing error will occur in the signal, if this theorem is not observed.

## What is the aliasing effect?

The aliasing effect is a measurement error in the signal occurring due to an incorrectly set sampling rate. If the sampling rate is too low, the Nyquist-Shannon sampling theorem is not observed and thus the measurement signal is not acquired correctly.

Frequency components that were originally higher than half the sampling rate are interpreted as lower frequencies. This happens due to undersampling of the signal, which results in incorrect amplitudes and low frequencies in the digitized signal.
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9673566818237305, "perplexity": 645.459401267315}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320305141.20/warc/CC-MAIN-20220127042833-20220127072833-00180.warc.gz"}