{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "Following Section 2.3.3.1 of [Müller, FMP, Springer 2015], we discuss in this notebook the effect of signal interference and the phenomenon of beating.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Interference\n", "\n", "In signal processing, **interference** occurs when a wave is superimposed with another wave of similar frequency. When a crest of one wave meets a crest of the other wave at some point, then the individual magnitudes add up for a certain period of time, which is known as **constructive interference**. Vice versa, when a crest of one wave meets a trough of the other wave, then the magnitudes cancel out for a certain period of time, which is known as **destructive interference**." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:59:54.844049Z", "iopub.status.busy": "2024-02-15T08:59:54.843778Z", "iopub.status.idle": "2024-02-15T08:59:57.823307Z", "shell.execute_reply": "2024-02-15T08:59:57.822646Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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