{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\"FMP\"\n", "\"AudioLabs\"\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\"C2\"\n", "

Interference and Beating

\n", "
\n", "\n", "
\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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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "import sys\n", "sys.path.append('..')\n", "import libfmp.c1\n", "%matplotlib inline\n", "\n", "def plot_interference(x1, x2, t, figsize=(8, 2), xlim=None, ylim=None, title=''):\n", " \"\"\"Helper function for plotting two signals and its superposition\n", "\n", " Notebook: C2/C2S3_InterferenceBeating.ipynb\n", "\n", " Args:\n", " x1: Signal 1\n", " x2: Signal 2\n", " t: Time\n", " figsize: figure size (Default value = (8, 2))\n", " xlim: x limits (Default value = None)\n", " ylim: y limits (Default value = None)\n", " title: figure title (Default value = '')\n", " \"\"\"\n", " plt.figure(figsize=figsize)\n", " plt.plot(t, x1, color='gray', linewidth=1.0, linestyle='-', label='x1')\n", " plt.plot(t, x2, color='cyan', linewidth=1.0, linestyle='-', label='x2')\n", " plt.plot(t, x1+x2, color='red', linewidth=2.0, linestyle='-', label='x1+x2')\n", " if xlim is None:\n", " plt.xlim([0, t[-1]])\n", " else:\n", " plt.xlim(xlim)\n", " if ylim is not None:\n", " plt.ylim(ylim)\n", " plt.xlabel('Time (seconds)')\n", " plt.ylabel('Amplitude')\n", " plt.title(title)\n", " plt.legend(loc='upper right')\n", " plt.tight_layout()\n", " plt.show()\n", "\n", "dur = 5\n", "x1, t = libfmp.c1.generate_sinusoid(dur=dur, Fs=1000, amp=1, freq=1.05, phase=0.0)\n", "x2, t = libfmp.c1.generate_sinusoid(dur=dur, Fs=1000, amp=1, freq=0.95, phase=0.8)\n", "plot_interference(x1, x2, t, xlim=[0, dur], ylim=[-2.2,2.2], title='Constructive Interference');\n", "\n", "dur = 5\n", "x1, t = libfmp.c1.generate_sinusoid(dur=dur, Fs=1000, amp=1, freq=1.05, phase=0.0)\n", "x2, t = libfmp.c1.generate_sinusoid(dur=dur, Fs=1000, amp=1, freq=1.00, phase=0.4)\n", "plot_interference(x1, x2, t, xlim=[0, dur], ylim=[-2.2,2.2], title='Destructive Interference');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Beating\n", "\n", "The previous figure shows that two sinusoids of similar frequency may add up (constructive interference) or cancel out (destructive interference). Let $f_1(t)=\\sin(2\\pi \\omega_1 t)$ and $f_2(t)=\\sin(2\\pi \\omega_2 t)$ be two such sinusoids\n", "with distinct but nearby frequencies $\\omega_1\\approx\\omega_2$. We now show that the superposition $f_1+f_2$ of these two sinusoids results in a function that looks like a single sine wave with a slowly varying amplitude, a phenomenon also known as **beating**. Mathematically, this phenomenon results from a **trigonometric identity** yielding \n", "\n", "$$\n", "\\sin(2\\pi \\omega_1 t)+\\sin(2\\pi \\omega_2 t)=\n", "2\\cos\\left(2\\pi\\frac{\\omega_1-\\omega_2}{2}t\\right)\\sin\\left(2\\pi\\frac{\\omega_1+\\omega_2}{2}t\\right).\n", "$$\n", "\n", "If the difference $\\omega_1-\\omega_2$ is small, the cosine term has a low frequency compared to the sine term. As a result the signal $f_1+f_2$ can be seen as a sine wave of frequency $(\\omega_1+\\omega_2)/2$ with a slowly varying amplitude envelope of frequency $|\\omega_1-\\omega_2|$. Note that this rate is twice the frequency $(\\omega_1-\\omega_2)/2$ of the cosine term. The following code example illustrates the beating effect." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:59:57.826399Z", "iopub.status.busy": "2024-02-15T08:59:57.826098Z", "iopub.status.idle": "2024-02-15T08:59:58.302375Z", "shell.execute_reply": "2024-02-15T08:59:58.301846Z" } }, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import IPython.display as ipd\n", "%matplotlib inline\n", "\n", "Fs = 4000\n", "dur = 5\n", "x1, t = libfmp.c1.generate_sinusoid(dur=dur, Fs=Fs, amp=0.5, freq=200)\n", "x2, t = libfmp.c1.generate_sinusoid(dur=dur, Fs=Fs, amp=0.5, freq=203)\n", "plot_interference(x1, x2, t, ylim=[-1.1,1.1], xlim=[0, dur],\n", " title=r'Beating with beating frequency $|\\omega_1-\\omega_2|=3$ ($\\omega_1=200, \\omega_2=203$)');\n", "plot_interference(x1, x2, t, ylim=[-1.1,1.1], xlim=[1.115, 1.225], title=r'Zoom-in section');\n", "\n", "\n", "ipd.display(ipd.Audio(x1+x2, rate=Fs))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Chirp Experiment\n", "\n", "To further illustrate the beating effect, we consider a **chirp signal** (also called **sweep signal**), in which the frequency increases with time. Let $\\omega_0,\\omega_1\\in\\mathbb{R}$ be two frequency parameters (given in Hertz) and $T\\in\\mathbb{R}$ a duration parameter (given in seconds). A **linear chirp** of duration $d$ that linearly increases in frequency starting with $\\omega_0$ and ending with $\\omega_1$ is given by:\n", "\n", "$$\n", "f(t)=\\sin\\left(\\pi\\frac{\\omega_1-\\omega_0}{T} t^2 + 2\\pi\\omega_0t\\right) \n", "$$\n", "\n", "for $t\\in[0,T]$. Note that the **instantaneous frequency** of the chirp signal $f$ at time $t$ is given by the derivate of the sinusoid's argument divided by $2\\pi$:\n", "\n", "$$\n", " g(t) = \\frac{\\omega_1-\\omega_0}{T} t + \\omega_0.\n", "$$\n", "\n", "In the following, we consider a linear chirp signal starting with frequency $\\omega_0=220.0~\\mathrm{Hz}$ (pitch $\\mathrm{A3}$) and ending with frequency $\\omega_1=311.1~\\mathrm{Hz}$ (pitch $\\mathrm{E}^\\flat 4$) of duration $T=20~\\mathrm{sec}$. Furthermore, we consider a sinusoid with frequency $261.5~\\mathrm{Hz}$ (pitch $\\mathrm{C4}$) of the same duration. When listening to a superposition of these signal, one first perceives the two separate pitches $\\mathrm{A3}$ and $\\mathrm{C4}$. When the chirp approaches $\\mathrm{C4}$, the two pitches begin fusing into a single sound. At the same time, one can notice a beating effect, which first slows down, then disappears (when the chirp reaches $\\mathrm{C4}$), and then speeds up again. At the end, one again perceives two pitches, now being $\\mathrm{E}^\\flat 4$ and $\\mathrm{C4}$." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2024-02-15T08:59:58.305041Z", "iopub.status.busy": "2024-02-15T08:59:58.304856Z", "iopub.status.idle": "2024-02-15T08:59:58.882708Z", "shell.execute_reply": "2024-02-15T08:59:58.882032Z" } }, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "image/png": { "height": 135, "width": 558 }, "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def generate_chirp_linear(dur, freq_start, freq_end, amp=1.0, Fs=22050):\n", " \"\"\"Generation chirp with linear frequency increase\n", "\n", " Notebook: C2/C2S3_InterferenceBeating.ipynb\n", "\n", " Args:\n", " dur (float): Duration (seconds) of the signal\n", " freq_start (float): Start frequency of the chirp\n", " freq_end (float): End frequency of the chirp\n", " amp (float): Amplitude of chirp (Default value = 1.0)\n", " Fs (scalar): Sampling rate (Default value = 22050)\n", "\n", " Returns:\n", " x (np.ndarray): Generated chirp signal\n", " t (np.ndarray): Time axis (in seconds)\n", " freq (np.ndarray): Instant frequency (in Hz)\n", " \"\"\"\n", " N = int(dur * Fs)\n", " t = np.arange(N) / Fs\n", " a = (freq_end - freq_start) / dur\n", " freq = a * t + freq_start\n", " x = amp * np.sin(np.pi * a * t ** 2 + 2 * np.pi * freq_start * t)\n", " return x, t, freq\n", "\n", "f_pitch = lambda p: 440 * 2 ** ((p - 69) / 12)\n", "\n", "Fs = 4000\n", "dur = 20\n", "freq_start = f_pitch(57) # A3\n", "freq_end = f_pitch(63) # Eflatp4\n", "freq_sin = f_pitch(60) # C4\n", "x1, t, freq = generate_chirp_linear(dur=dur, freq_start=freq_start, freq_end=freq_end, amp=0.5, Fs=Fs)\n", "x2, t = libfmp.c1.generate_sinusoid(dur=dur, Fs=Fs, amp=0.5, freq=freq_sin)\n", "\n", "y = x1 + x2\n", "ipd.display(ipd.Audio(y, rate=Fs))\n", "plot_interference(x1, x2, t, xlim=[0, dur], ylim=[-1.1,1.1], \n", " title=r'Superposition of a linear chirp $x_1$ (A3 to E$^\\flat$4) and sinusoid $x_2$ (C4)');\n", "plot_interference(x1, x2, t, xlim=[7, 11], ylim=[-1.1,1.1], title=r'Zoom-in section');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "Acknowledgment: This notebook was created by Meinard Müller.\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "\n", "
\"C0\"\"C1\"\"C2\"\"C3\"\"C4\"\"C5\"\"C6\"\"C7\"\"C8\"
" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.16" } }, "nbformat": 4, "nbformat_minor": 1 }