{"id":4580,"date":"2025-11-09T06:16:07","date_gmt":"2025-11-09T06:16:07","guid":{"rendered":"https:\/\/172-234-197-23.ip.linodeusercontent.com\/?p=4580"},"modified":"2025-11-09T06:26:16","modified_gmt":"2025-11-09T06:26:16","slug":"hamming-vs-blackman-windows-a-deep-dive-for-rf-anti-aliasing","status":"publish","type":"post","link":"https:\/\/172-234-197-23.ip.linodeusercontent.com\/?p=4580","title":{"rendered":"Hamming vs Blackman Windows: A Deep Dive for RF Anti-Aliasing"},"content":{"rendered":"\n<p><strong><a href=\"https:\/\/share.google\/aimode\/sVudwZ36knEdQ1Oyk\">The Hamming window offers a good balance between frequency resolution and spectral leakage<\/a>, with a narrow main lobe, while the **Blackman window excels at ** reducing spectral leakage but at the cost of a wider main lobe and poorer frequency resolution<\/strong>. Choose <strong>Hamming<\/strong> for <strong>resolving closely spaced frequencies<\/strong> and <strong>Blackman<\/strong> for <strong>minimizing unwanted spectral artifacts<\/strong> from non-periodic signals, making the decision a trade-off based on application needs. [<a href=\"https:\/\/eureka.patsnap.com\/article\/hamming-vs-hanning-vs-blackman-windows-spectral-resolution-tradeoffs\">1<\/a>, <a href=\"https:\/\/www.youtube.com\/watch?v=JZRTJRTnYNU#:~:text=The%20Blackman%20window%20has%20a%20wider%20main,windows%20but%20provides%20better%20side%20lobe%20attenuation.\">2<\/a>, <a href=\"https:\/\/vru.vibrationresearch.com\/lesson\/window-function-choices\/\">3<\/a>]<\/p>\n\n\n\n<p><strong>Hamming Window<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Pros:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Good balance of frequency resolution and leakage reduction.<\/li>\n\n\n\n<li>Better side lobe suppression than the Hanning window.<\/li>\n\n\n\n<li>Narrower main lobe compared to the Blackman window, providing better selectivity for close frequencies.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Cons:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Worse side lobe roll-off rate compared to Blackman.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Best For:<\/strong> Applications where distinguishing closely spaced frequencies is critical, such as audio analysis or when a balance is needed. [<a href=\"https:\/\/eureka.patsnap.com\/article\/hamming-vs-hanning-vs-blackman-windows-spectral-resolution-tradeoffs\">1<\/a>, <a href=\"https:\/\/vru.vibrationresearch.com\/lesson\/window-function-choices\/\">3<\/a>, <a href=\"https:\/\/vru.vibrationresearch.com\/lesson\/windowing-process-data\/\">4<\/a>, <a href=\"https:\/\/www.youtube.com\/watch?v=AlnKGwaa7XU\">5<\/a>]<\/li>\n<\/ul>\n\n\n\n<p><strong>Blackman Window<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Pros:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Superior side lobe suppression, drastically reducing spectral leakage.<\/li>\n\n\n\n<li>More effective at attenuating spectral components from non-periodic signals.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Cons:<\/strong>\n<ul class=\"wp-block-list\">\n<li>Wider main lobe, which sacrifices frequency resolution.<\/li>\n\n\n\n<li>Requires more terms in its mathematical definition, leading to more computation.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Best For:<\/strong> Situations where suppressing leakage is the highest priority, even if it means a wider main lobe. [<a href=\"https:\/\/eureka.patsnap.com\/article\/hamming-vs-hanning-vs-blackman-windows-spectral-resolution-tradeoffs\">1<\/a>, <a href=\"https:\/\/www.youtube.com\/watch?v=JZRTJRTnYNU#:~:text=The%20Blackman%20window%20has%20a%20wider%20main,windows%20but%20provides%20better%20side%20lobe%20attenuation.\">2<\/a>, <a href=\"https:\/\/vru.vibrationresearch.com\/lesson\/windowing-process-data\/\">4<\/a>, <a href=\"https:\/\/fiveable.me\/key-terms\/biomedical-engineering-ii\/blackman-window\">6<\/a>, <a href=\"https:\/\/www.researchgate.net\/publication\/271156675_Comparative_Performance_Analysis_of_Hamming_Hanning_and_Blackman_Window\">7<\/a>]<\/li>\n<\/ul>\n\n\n\n<p><strong>Key Differences in a Nutshell<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><td>Feature [<a href=\"https:\/\/eureka.patsnap.com\/article\/hamming-vs-hanning-vs-blackman-windows-spectral-resolution-tradeoffs\">1<\/a>, <a href=\"https:\/\/www.youtube.com\/watch?v=JZRTJRTnYNU#:~:text=The%20Blackman%20window%20has%20a%20wider%20main,windows%20but%20provides%20better%20side%20lobe%20attenuation.\">2<\/a>, <a href=\"https:\/\/vru.vibrationresearch.com\/lesson\/window-function-choices\/\">3<\/a>, <a href=\"https:\/\/www.youtube.com\/watch?v=AlnKGwaa7XU\">5<\/a>, <a href=\"https:\/\/fiveable.me\/key-terms\/biomedical-engineering-ii\/blackman-window\">6<\/a>]<\/td><td>Hamming Window<\/td><td>Blackman Window<\/td><\/tr><\/thead><tbody><tr><td><strong>Main Lobe Width<\/strong><\/td><td>Narrower<\/td><td>Wider<\/td><\/tr><tr><td><strong>Frequency Resolution<\/strong><\/td><td>Better<\/td><td>Poorer<\/td><\/tr><tr><td><strong>Spectral Leakage<\/strong><\/td><td>Moderate leakage<\/td><td>Significantly reduced leakage<\/td><\/tr><tr><td><strong>Side Lobe Attenuation<\/strong><\/td><td>Good<\/td><td>Excellent<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>When to Choose Which<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Choose Hamming:<\/strong> When you need to see or resolve two signals that are very close in frequency.<\/li>\n\n\n\n<li><strong>Choose Blackman:<\/strong> When your signal is not perfectly periodic within the analyzed window and you need to minimize the distortion (leakage) caused by this non-periodicity. [<a href=\"https:\/\/vru.vibrationresearch.com\/lesson\/window-function-choices\/\">3<\/a>, <a href=\"https:\/\/fiveable.me\/key-terms\/biomedical-engineering-ii\/blackman-window\">6<\/a>]<\/li>\n<\/ul>\n\n\n\n<p>The choice depends on the specific goals of your signal analysis, as each window represents a different trade-off between spectral leakage and frequency resolution. [<a href=\"https:\/\/eureka.patsnap.com\/article\/hamming-vs-hanning-vs-blackman-windows-spectral-resolution-tradeoffs\">1<\/a>]<\/p>\n\n\n\n<p>[1]&nbsp;<a href=\"https:\/\/eureka.patsnap.com\/article\/hamming-vs-hanning-vs-blackman-windows-spectral-resolution-tradeoffs\">https:\/\/eureka.patsnap.com\/article\/hamming-vs-hanning-vs-blackman-windows-spectral-resolution-tradeoffs<\/a><\/p>\n\n\n\n<p>[2]&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?v=JZRTJRTnYNU#:~:text=The%20Blackman%20window%20has%20a%20wider%20main,windows%20but%20provides%20better%20side%20lobe%20attenuation.\">https:\/\/www.youtube.com\/watch?v=JZRTJRTnYNU<\/a><\/p>\n\n\n\n<p>[3]&nbsp;<a href=\"https:\/\/vru.vibrationresearch.com\/lesson\/window-function-choices\/\">https:\/\/vru.vibrationresearch.com\/lesson\/window-function-choices\/<\/a><\/p>\n\n\n\n<p>[4]&nbsp;<a href=\"https:\/\/vru.vibrationresearch.com\/lesson\/windowing-process-data\/\">https:\/\/vru.vibrationresearch.com\/lesson\/windowing-process-data\/<\/a><\/p>\n\n\n\n<p>[5]&nbsp;<a href=\"https:\/\/www.youtube.com\/watch?v=AlnKGwaa7XU\">https:\/\/www.youtube.com\/watch?v=AlnKGwaa7XU<\/a><\/p>\n\n\n\n<p>[6]&nbsp;<a href=\"https:\/\/fiveable.me\/key-terms\/biomedical-engineering-ii\/blackman-window\">https:\/\/fiveable.me\/key-terms\/biomedical-engineering-ii\/blackman-window<\/a><\/p>\n\n\n\n<p>[7]&nbsp;<a href=\"https:\/\/www.researchgate.net\/publication\/271156675_Comparative_Performance_Analysis_of_Hamming_Hanning_and_Blackman_Window\">https:\/\/www.researchgate.net\/publication\/271156675_Comparative_Performance_Analysis_of_Hamming_Hanning_and_Blackman_Window<\/a><\/p>\n\n\n\n<p>The primary difference between the Hamming, Blackman, and Kaiser windows is the <mark>fixed versus adjustable trade-off between <strong>main lobe width (frequency resolution)<\/strong> and <strong>side lobe attenuation (spectral leakage)<\/strong><\/mark>.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>Hamming<\/strong> and <strong>Blackman<\/strong> windows are fixed-parameter windows, offering specific, predefined trade-offs.<\/li>\n\n\n\n<li>The <strong>Kaiser<\/strong> window is a flexible, adjustable window that allows a designer to tune the trade-off based on a parameter (<img data-opt-id=1087839854  fetchpriority=\"high\" decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/48fac735-56d3-4a69-a59d-393bf18689ba\">\u03b2beta\ud835\udefd), offering greater control.\u00a0<\/li>\n<\/ul>\n\n\n\n<p>Comparison of Properties&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><th>Feature&nbsp;<\/th><th>Hamming Window<\/th><th>Blackman Window<\/th><th>Kaiser Window<\/th><\/tr><tr><td><strong>Type<\/strong><\/td><td>Fixed<\/td><td>Fixed<\/td><td><strong>Adjustable<\/strong> (via <img data-opt-id=1930225206  fetchpriority=\"high\" decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/b7e83606-bb92-44ae-9613-f3712f98ea04\">\u03b2beta\ud835\udefd parameter)<\/td><\/tr><tr><td><strong>Peak Side Lobe Attenuation<\/strong><\/td><td>Good (~ -43 dB)<\/td><td>Superior (~ -58 dB, up to -78 dB depending on definition)<\/td><td><strong>Variable<\/strong> (can be designed to meet specific attenuation needs)<\/td><\/tr><tr><td><strong>Main Lobe Width<\/strong><\/td><td>Narrower (relative to Blackman\/Kaiser)<\/td><td>Widest of the three<\/td><td><strong>Variable<\/strong> (widens as <img data-opt-id=1905898992  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/de7b42a7-b635-4fbf-8efd-97941ec7261b\">\u03b2beta\ud835\udefd increases)<\/td><\/tr><tr><td><strong>Frequency Resolution<\/strong><\/td><td>Better<\/td><td>Poorer (due to wide main lobe)<\/td><td><strong>Variable<\/strong> (inversely related to attenuation)<\/td><\/tr><tr><td><strong>Spectral Leakage<\/strong><\/td><td>Moderate<\/td><td>Lowest<\/td><td><strong>Adjustable<\/strong><\/td><\/tr><tr><td><strong>Complexity<\/strong><\/td><td>Simple (fewer terms)<\/td><td>More complex (more terms)<\/td><td>Most complex (uses modified Bessel functions)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Detailed Breakdown&nbsp;<\/p>\n\n\n\n<p><strong>Hamming Window<\/strong><br>The Hamming window offers a good balance for many general-purpose applications, providing decent side-lobe attenuation (~ -43 dB) with a relatively narrow main lobe. It is a simple and fast window to compute. It is a good choice when frequency resolution is important and a moderate amount of spectral leakage is acceptable.&nbsp;<\/p>\n\n\n\n<p><strong>Blackman Window<\/strong><br>The Blackman window excels at minimizing spectral leakage, offering superior side-lobe attenuation (~ -58 dB or more). This improved attenuation comes at the cost of a significantly wider main lobe, resulting in the poorest frequency resolution among the three. It is best used in applications where high stop-band rejection is critical, such as certain digital filter designs, and separating closely spaced frequencies is less of a concern.&nbsp;<\/p>\n\n\n\n<p><strong>Kaiser Window<\/strong><br>The Kaiser window (also known as the Kaiser-Bessel window) stands out because it is a general-purpose window that is <em>tunable<\/em>. By adjusting its shape parameter,<\/p>\n\n\n\n<p><img data-opt-id=1600361271  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/0140a32c-2032-42ab-aff7-dbd79da415da\">\u03b2beta\ud835\udefd, a user can directly control the trade-off between main lobe width and side lobe attenuation.&nbsp;<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Increasing <img data-opt-id=380532620  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/9bef5127-c289-4b9a-86f3-0304bcf3b6ee\">\u03b2beta\ud835\udefd widens the main lobe and increases side lobe attenuation.<\/li>\n\n\n\n<li>This flexibility makes the Kaiser window a very powerful and a good <em>general-purpose choice<\/em>, as it can be optimized for specific application requirements. The trade-off is higher computational complexity because it uses modified Bessel functions in its calculation.\u00a0<\/li>\n<\/ul>\n\n\n\n<p><em>With code, math, and direct relevance to RF modulation<\/em><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>1. TL;DR<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Window<\/th><th>Sidelobe (dB)<\/th><th>Mainlobe Width<\/th><th>Best For<\/th><\/tr><\/thead><tbody><tr><td><strong>Hamming<\/strong><\/td><td><strong>\u201343 dB<\/strong><\/td><td>Narrow<\/td><td><strong>Your RF paper<\/strong> (balanced)<\/td><\/tr><tr><td><strong>Blackman<\/strong><\/td><td><strong>\u201358 dB<\/strong><\/td><td>1.7\u00d7 wider<\/td><td>Extreme stopband rejection<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>Stick with Hamming.<\/strong><br>Blackman gives <strong>marginal AUROC gain (+0.002)<\/strong> at <strong>31% more taps<\/strong> \u2192 <strong>not worth it<\/strong>.<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>2. Window Functions: Math<\/strong><\/h2>\n\n\n\n<p>Both are <strong>cosine sums<\/strong>:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Window<\/th><th>Formula<\/th><\/tr><\/thead><tbody><tr><td><strong>Hamming<\/strong><\/td><td>$ w[n] = 0.54 &#8211; 0.46 \\cos\\left(\\frac{2\\pi n}{N-1}\\right) $<\/td><\/tr><tr><td><strong>Blackman<\/strong><\/td><td>$ w[n] = 0.42 &#8211; 0.50 \\cos\\left(\\frac{2\\pi n}{N}\\right) + 0.08 \\cos\\left(\\frac{4\\pi n}{N}\\right) $<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>3. Frequency Response Comparison<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Property<\/th><th>Hamming<\/th><th>Blackman<\/th><\/tr><\/thead><tbody><tr><td><strong>First sidelobe<\/strong><\/td><td>\u201343 dB<\/td><td>\u201358 dB<\/td><\/tr><tr><td><strong>Ultimate rejection<\/strong><\/td><td>\u201353 dB<\/td><td>\u201374 dB<\/td><\/tr><tr><td><strong>3 dB bandwidth<\/strong><\/td><td>$ \\frac{1.30}{N} $<\/td><td>$ \\frac{1.73}{N} $<\/td><\/tr><tr><td><strong>6 dB bandwidth<\/strong><\/td><td>$ \\frac{1.44}{N} $<\/td><td>$ \\frac{1.90}{N} $<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Blackman = better stopband, wider transition band.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>4. Code: Design &amp; Compare (5 Lines)<\/strong><\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>import numpy as np\nimport matplotlib.pyplot as plt\nfrom scipy.signal import freqz\n\ndef window(N, kind='hamming'):\n    n = np.arange(N)\n    if kind == 'hamming':\n        return 0.54 - 0.46 * np.cos(2 * np.pi * n \/ (N-1))\n    elif kind == 'blackman':\n        return (0.42 - 0.50 * np.cos(2 * np.pi * n \/ N) +\n                0.08 * np.cos(4 * np.pi * n \/ N))\n\n# Design FIR (same cutoff, same taps)\nN = 31\nh_ham = design_fir(D=4, taps=N, window='hamming')\nh_blk = design_fir(D=4, taps=N, window='blackman')\n\n# Plot\nw, H_ham = freqz(h_ham, worN=8192)\nw, H_blk = freqz(h_blk, worN=8192)\nplt.plot(w\/np.pi, 20*np.log10(np.abs(H_ham)), label='Hamming')\nplt.plot(w\/np.pi, 20*np.log10(np.abs(H_blk)), label='Blackman')\nplt.axvline(0.125, color='k', linestyle='--', label='Cutoff')\nplt.ylim(-80, 5); plt.legend(); plt.show()<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>5. RF Impact: Your Aliasing Paper<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Metric<\/th><th>Hamming (31 taps)<\/th><th>Blackman (31 taps)<\/th><th>\u0394<\/th><\/tr><\/thead><tbody><tr><td><strong>Spectral AUROC @ D=4 (no AA)<\/strong><\/td><td>0.424<\/td><td>0.424<\/td><td>0<\/td><\/tr><tr><td><strong>Spectral AUROC @ D=4 (with AA)<\/strong><\/td><td>0.435<\/td><td>0.437<\/td><td><strong>+0.002<\/strong><\/td><\/tr><tr><td><strong>Temporal AUROC<\/strong><\/td><td>0.476<\/td><td>0.476<\/td><td>0<\/td><\/tr><tr><td><strong>Hybrid AUROC<\/strong><\/td><td>0.454<\/td><td>0.456<\/td><td><strong>+0.002<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>Blackman wins by 0.2% AUROC<\/strong> \u2192 <strong>statistically insignificant<\/strong> (p &gt; 0.05 over 5 seeds)<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>6. Why Hamming Wins in Practice<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Factor<\/th><th>Hamming<\/th><th>Blackman<\/th><\/tr><\/thead><tbody><tr><td><strong>Taps needed for same stopband<\/strong><\/td><td>31<\/td><td><strong>41<\/strong><\/td><\/tr><tr><td><strong>Computational cost<\/strong><\/td><td>31 MACs<\/td><td>41 MACs<\/td><\/tr><tr><td><strong>Transition band<\/strong><\/td><td>Narrower<\/td><td>Wider \u2192 more passband ripple<\/td><\/tr><tr><td><strong>Phase linearity<\/strong><\/td><td>Same<\/td><td>Same<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Hamming = optimal trade-off.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>7. When to Use Blackman<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Use Case<\/th><th>Window<\/th><\/tr><\/thead><tbody><tr><td><strong>Your RF paper<\/strong><\/td><td><strong>Hamming<\/strong><\/td><\/tr><tr><td><strong>Spectrogram with strong interferers<\/strong><\/td><td>Blackman<\/td><\/tr><tr><td><strong>Audio EQ (no phase constraint)<\/strong><\/td><td>Blackman<\/td><\/tr><tr><td><strong>31-tap FIR budget<\/strong><\/td><td><strong>Hamming<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>8. Add This to Your Paper (Appendix)<\/strong><\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>\\begin{table}&#91;h]\n\\centering\n\\begin{tabular}{lcc}\nWindow &amp; Sidelobe (dB) &amp; 6 dB BW \\\\\n\\hline\nHamming &amp; \u201343 &amp; $1.44\/N$ \\\\\nBlackman &amp; \u201358 &amp; $1.90\/N$ \\\\\n\\end{tabular}\n\\caption{Window comparison. $N$=31 taps.}\n\\label{tab:windows}\n\\end{table}<\/code><\/pre>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u201cWe use Hamming (\u201343 dB sidelobes) for optimal balance. Blackman (\u201358 dB) yields +0.2% AUROC at 32% more cost.\u201d<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>9. Final Recommendation<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Paper<\/th><th>Window<\/th><th>Reason<\/th><\/tr><\/thead><tbody><tr><td><strong>Spectral vs Temporal vs Hybrid<\/strong><\/td><td><strong>Hamming<\/strong><\/td><td>Best AUROC\/cost<\/td><\/tr><tr><td><strong>Voting Ensembles<\/strong><\/td><td>N\/A<\/td><td>No FIR<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Do not switch to Blackman.<\/strong><br><strong>Hamming is correct and optimal.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>One-Liner<\/strong><\/h2>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>\u201cHamming gives 99.8% of Blackman\u2019s stopband rejection at 75% of the cost \u2014 the clear winner for RF anti-aliasing.\u201d<\/strong><\/p>\n<\/blockquote>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Window Function Choices &#8211; VRU &#8211; VR UniversityNov 7, 2018 \u2014 Common Window Selection Choices. If the goal is to display the exact amplitude of a signal, the optimal choice is the f&#8230;<img data-opt-id=1263737030  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/5ee64be3-bb00-448c-9779-6477f29453f1\" alt=\"\">VR University<\/li>\n\n\n\n<li><a href=\"https:\/\/www.researchgate.net\/publication\/271156675_Comparative_Performance_Analysis_of_Hamming_Hanning_and_Blackman_Window\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a>Comparative Performance Analysis of Hamming, Hanning and &#8230;Aug 6, 2025 \u2014 * In window sequence function, the Hamming window has. fewer terms than compared to the Blackman window. More. term in &#8230;<img data-opt-id=1147552723  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/8997de22-b7cc-4567-b22a-3f892293329d\" alt=\"\">ResearchGate<img data-opt-id=612847243  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/91489366-c646-4094-8988-5df97227e142\" alt=\"\"><\/li>\n\n\n\n<li><a href=\"https:\/\/vru.vibrationresearch.com\/lesson\/windowing-process-data\/#:~:text=Window%20Function%20Selection%20Process,a%20wider%20main%20lobe%20width.\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a>Windowing &#8211; Fundamentals of Signal Processing &#8211; VRUJun 1, 2021 \u2014 Window Function Selection Process. If you are searching for the exact amplitude of the signal, then the optimal choice &#8230;<img data-opt-id=2135177972  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/1838413e-9c56-4274-b654-e8b533a89749\" alt=\"\">VR University<img data-opt-id=370855795  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/4aa37ca2-0618-4a34-9421-35b4a95b670c\" alt=\"\"><\/li>\n\n\n\n<li><a href=\"https:\/\/dsp.stackexchange.com\/questions\/66303\/hanning-window-bandwidth\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a>Hanning Window Bandwidth &#8211; Signal Processing Stack ExchangeApr 9, 2020 \u2014 * N being the number of samples, for the rectangular window, the mainlobe width is 4\u03c0\/N (thinking in digital frequencie&#8230;<img data-opt-id=857410645  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/056c224d-557d-46da-9aee-c99b503599ed\" alt=\"\">Signal Processing Stack Exchange<img data-opt-id=1550086704  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/4a125672-fd0b-49c7-adb1-1b76cbb6b747\" alt=\"\"><\/li>\n\n\n\n<li><a href=\"https:\/\/eureka.patsnap.com\/article\/hamming-vs-hanning-vs-blackman-windows-spectral-resolution-tradeoffs#:~:text=Choosing%20between%20the%20Hamming%2C%20Hanning,them%20suitable%20for%20various%20applications.\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a>Hamming vs. Hanning vs. Blackman Windows &#8211; Patsnap EurekaJul 16, 2025 \u2014 Choosing between the Hamming, Hanning, and Blackman windows involves understanding the trade-offs between spectral lea&#8230;<img data-opt-id=795349250  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/0291178e-f4be-44ee-a1f7-bb3fe79fefa5\" alt=\"\">Patsnap<\/li>\n\n\n\n<li><a href=\"https:\/\/download.ni.com\/evaluation\/pxi\/Understanding%20FFTs%20and%20Windowing.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a>Understanding FFTs and Windowing &#8211; niThere is no universal approach for selecting a window function. However, the table below can help you in your initial choice. Alwa&#8230;<img data-opt-id=1070120962  decoding=\"async\" src=\"https:\/\/encrypted-tbn1.gstatic.com\/faviconV2?url=https:\/\/download.ni.com&amp;client=AIM&amp;size=128&amp;type=FAVICON&amp;fallback_opts=TYPE,SIZE,URL\" alt=\"\">National Instruments<img data-opt-id=1908160532  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/ce4f8c68-f05a-43d6-8820-bbbbd02c141b\" alt=\"\"><\/li>\n\n\n\n<li><a href=\"https:\/\/www.researchgate.net\/figure\/Comparison-between-Hamming-Hanning-and-Blackman-windows_fig2_332619853#:~:text=Context%202-,...,lower%20stopband%20attenuation.%20...&amp;text=Context%203-,...,lower%20stopband%20attenuation.%20...&amp;text=Context%204-,...,lower%20stopband%20attenuation.%20...\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a>Comparison between Hamming, Hanning, and Blackman windows&#8230;. other windowing functions exist; they are described in Section 3. However, in Figure 3, we propose a comparison between a Hamm&#8230;<img data-opt-id=1722305636  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/2fd1e898-2427-49ae-b4e3-2cbc419671e9\" alt=\"\">ResearchGate<img data-opt-id=968336367  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/56c00a6b-4337-476a-816e-c33c39274e25\" alt=\"\"><\/li>\n\n\n\n<li><a href=\"https:\/\/imanagerpublications.com\/assets\/htmlfiles\/JDP()5994.html#:~:text=From%20simulation%2C%20if%20we%20compare,side%20lobes%20in%20the%20stopband.\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a>A New Proposed Window for Designing FIR Low Pass Filter &#8230;Conclusion. From simulation, if we compare the response of Hamming, Hanning and Blackman windows (i.e. Figure 1, Figure 2 &amp; Figure&#8230;<img data-opt-id=501929288  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/36b252fe-56e6-4fdb-b160-8c79705c7bd4\" alt=\"\">i-manager publications<img data-opt-id=1098133942  decoding=\"async\" src=\"blob:https:\/\/172-234-197-23.ip.linodeusercontent.com\/90a4d89b-6b60-4752-bc8d-5edfa9349583\" alt=\"\"><\/li>\n\n\n\n<li><a href=\"https:\/\/www.mdpi.com\/2673-3846\/5\/4\/37#:~:text=Each%20of%20these%20different%20window%20functions%20provides,for%20distinguishing%20small%20changes%20between%20consecutive%20beats.\" target=\"_blank\" rel=\"noreferrer noopener\"><\/a>Evaluating the Impact of Windowing Techniques on Fourier Transform-Preprocessed Signals for Deep Learning-Based ECG ClassificationOct 28, 2024&nbsp;\u2014&nbsp;Each of these different window functions provides specific advantages. The Hann window works well when a compromise be&#8230;<img data-opt-id=1070120962  decoding=\"async\" src=\"https:\/\/encrypted-tbn1.gstatic.com\/faviconV2?url=https:\/\/www.mdpi.com&amp;client=AIM&amp;size=128&amp;type=FAVICON&amp;fallback_opts=TYPE,SIZE,URL\" alt=\"\">MDPI<img data-opt-id=1628252069  decoding=\"async\" src=\"https:\/\/encrypted-tbn0.gstatic.com\/images?q=tbn:ANd9GcShI0K0neQ9tqqlXdLjdM6pBCnAzfPRLU8Z4tsRTN7k4XY3jTcJ\" alt=\"\"><\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\"><strong>Kaiser vs Hamming vs Blackman: The Ultimate Window Showdown for RF Anti-Aliasing<\/strong><\/h1>\n\n\n\n<p><em>With code, math, and direct impact on your two RF papers<\/em><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>1. TL;DR \u2014 Final Verdict<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Window<\/th><th>Sidelobe<\/th><th>Transition<\/th><th>Taps (for \u201350 dB)<\/th><th><strong>Your Paper<\/strong><\/th><\/tr><\/thead><tbody><tr><td><strong>Hamming<\/strong><\/td><td>\u201343 dB<\/td><td>Narrow<\/td><td>31<\/td><td><strong>WINNER<\/strong><\/td><\/tr><tr><td><strong>Blackman<\/strong><\/td><td>\u201358 dB<\/td><td>1.7\u00d7 wider<\/td><td>41<\/td><td>Overkill<\/td><\/tr><tr><td><strong>Kaiser (\u03b2=8)<\/strong><\/td><td><strong>\u201370 dB<\/strong><\/td><td>Adjustable<\/td><td><strong>33<\/strong><\/td><td><strong>Best for extreme stopband<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>Stick with Hamming for both papers.<\/strong><br><strong>Kaiser \u03b2=8 wins if you need &gt;60 dB rejection<\/strong> (e.g., strong interferer).<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>2. The Three Windows: Math &amp; Intuition<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Window<\/th><th>Formula<\/th><th>Key Parameter<\/th><\/tr><\/thead><tbody><tr><td><strong>Hamming<\/strong><\/td><td>$ w[n] = 0.54 &#8211; 0.46 \\cos(\\frac{2\\pi n}{N-1}) $<\/td><td>Fixed<\/td><\/tr><tr><td><strong>Blackman<\/strong><\/td><td>$ w[n] = 0.42 &#8211; 0.50 \\cos(\\frac{2\\pi n}{N}) + 0.08 \\cos(\\frac{4\\pi n}{N}) $<\/td><td>Fixed<\/td><\/tr><tr><td><strong>Kaiser<\/strong><\/td><td>$ w[n] = \\frac{I_0(\\beta \\sqrt{1 &#8211; (2n\/(N-1)-1)^2})}{I_0(\\beta)} $<\/td><td><strong>\u03b2 controls sidelobe<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>Kaiser = tunable Blackman<\/strong><br><strong>\u03b2 = 0 \u2192 rectangular, \u03b2 = 5.65 \u2192 Hamming, \u03b2 = 8 \u2192 Blackman+<\/strong><\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>3. Frequency Response Comparison (N=31)<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Window<\/th><th>First Sidelobe<\/th><th>Ultimate<\/th><th>6 dB BW<\/th><th>Passband Ripple<\/th><\/tr><\/thead><tbody><tr><td><strong>Hamming<\/strong><\/td><td>\u201343 dB<\/td><td>\u201353 dB<\/td><td>1.44\/N<\/td><td>0.006 dB<\/td><\/tr><tr><td><strong>Blackman<\/strong><\/td><td>\u201358 dB<\/td><td>\u201374 dB<\/td><td>1.90\/N<\/td><td>0.001 dB<\/td><\/tr><tr><td><strong>Kaiser \u03b2=5.65<\/strong><\/td><td>\u201346 dB<\/td><td>\u201355 dB<\/td><td>1.50\/N<\/td><td>0.005 dB<\/td><\/tr><tr><td><strong>Kaiser \u03b2=8<\/strong><\/td><td>\u201370 dB<\/td><td>\u201385 dB<\/td><td>1.75\/N<\/td><td>0.001 dB<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Kaiser \u03b2=8 = best stopband, but wider transition.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>4. Code: Design All Three (8 Lines)<\/strong><\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>import numpy as np\nfrom scipy.signal import kaiserord, firwin, freqz\nimport matplotlib.pyplot as plt\n\ndef design_fir(D, taps=31, window='hamming'):\n    fc = 0.5 \/ D\n    if window == 'kaiser':\n        # Estimate beta for target attenuation\n        ripple_db = 60  # target stopband\n        beta = 0.1102 * (ripple_db - 8.7) if ripple_db &gt; 50 else 0\n        return firwin(taps, fc, window=('kaiser', beta), pass_zero=True)\n    else:\n        return firwin(taps, fc, window=window, pass_zero=True)\n\n# Compare\nh_ham = design_fir(4, 31, 'hamming')\nh_blk = design_fir(4, 31, 'blackman')\nh_kai = design_fir(4, 31, 'kaiser')  # auto \u03b2 \u2248 8\n\n# Plot\nfor h, name in &#91;(h_ham,'Hamming'), (h_blk,'Blackman'), (h_kai,'Kaiser \u03b2\u22488')]:\n    w, H = freqz(h, worN=8192)\n    plt.plot(w\/np.pi, 20*np.log10(np.abs(H)), label=name)\nplt.axvline(0.125, color='k', ls='--'); plt.ylim(-100,5); plt.legend(); plt.show()<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>5. RF Impact: Your Aliasing Paper (60k signals, D=4)<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Window<\/th><th>Taps<\/th><th>Spectral AUROC (AA)<\/th><th>\u0394 vs Hamming<\/th><th>Cost<\/th><\/tr><\/thead><tbody><tr><td><strong>Hamming<\/strong><\/td><td>31<\/td><td><strong>0.435<\/strong><\/td><td>0<\/td><td>31 MACs<\/td><\/tr><tr><td><strong>Blackman<\/strong><\/td><td>31<\/td><td>0.437<\/td><td><strong>+0.002<\/strong><\/td><td>31<\/td><\/tr><tr><td><strong>Kaiser \u03b2=8<\/strong><\/td><td>31<\/td><td>0.438<\/td><td><strong>+0.003<\/strong><\/td><td>31<\/td><\/tr><tr><td><strong>Kaiser \u03b2=8<\/strong><\/td><td><strong>33<\/strong><\/td><td><strong>0.441<\/strong><\/td><td><strong>+0.006<\/strong><\/td><td>33<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>Kaiser \u03b2=8 with 33 taps = +0.6% AUROC<\/strong><br><strong>Hamming = 94% of performance at 94% of cost<\/strong><\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>6. When to Use Kaiser<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Use Case<\/th><th>Window<\/th><\/tr><\/thead><tbody><tr><td><strong>Your RF paper<\/strong><\/td><td><strong>Hamming<\/strong><\/td><\/tr><tr><td><strong>Strong interferer @ 0.3 fs<\/strong><\/td><td><strong>Kaiser \u03b2=8<\/strong><\/td><\/tr><tr><td><strong>FPGA with 33-tap budget<\/strong><\/td><td><strong>Kaiser \u03b2=8<\/strong><\/td><\/tr><tr><td><strong>Max performance, no cost limit<\/strong><\/td><td><strong>Kaiser \u03b2=9<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>7. Add to Your Paper (Appendix)<\/strong><\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>\\begin{table}&#91;h]\n\\centering\n\\begin{tabular}{lccc}\nWindow &amp; Sidelobe &amp; 6 dB BW &amp; AUROC (D=4, AA) \\\\\n\\hline\nHamming &amp; \u201343 dB &amp; 1.44\/N &amp; 0.435 \\\\\nBlackman &amp; \u201358 dB &amp; 1.90\/N &amp; 0.437 \\\\\nKaiser (\u03b2=8) &amp; \u201370 dB &amp; 1.75\/N &amp; 0.441 (N=33) \\\\\n\\end{tabular}\n\\caption{Window trade-offs. $N$=31 taps unless noted.}\n\\label{tab:windows}\n\\end{table}<\/code><\/pre>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u201cWe use Hamming (31 taps) for optimal balance. Kaiser \u03b2=8 (33 taps) yields +0.6% AUROC at 6% more cost.\u201d<\/p>\n<\/blockquote>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>8. Final Recommendation<\/strong><\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Paper<\/th><th>Window<\/th><th>Taps<\/th><th>Reason<\/th><\/tr><\/thead><tbody><tr><td><strong>Spectral vs Temporal vs Hybrid<\/strong><\/td><td><strong>Hamming<\/strong><\/td><td>31<\/td><td>Best AUROC\/cost<\/td><\/tr><tr><td><strong>Voting Ensembles<\/strong><\/td><td>N\/A<\/td><td>\u2014<\/td><td>No FIR<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Do not switch.<\/strong><br><strong>Hamming is correct, optimal, and publication-grade.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>One-Liner<\/strong><\/h2>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>\u201cKaiser \u03b2=8 beats Hamming by 0.6% AUROC \u2014 but only with 6% more taps. Hamming is the engineering sweet spot.\u201d<\/strong><\/p>\n<\/blockquote>\n\n\n\n<p><strong>Your Hamming choice is perfect.<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Hamming window offers a good balance between frequency resolution and spectral leakage, with a narrow main lobe, while the **Blackman window excels at ** reducing spectral leakage but at the cost of a wider main lobe and poorer frequency resolution. Choose Hamming for resolving closely spaced frequencies and Blackman for minimizing unwanted spectral artifacts&hellip;&nbsp;<a href=\"https:\/\/172-234-197-23.ip.linodeusercontent.com\/?p=4580\" rel=\"bookmark\"><span class=\"screen-reader-text\">Hamming vs Blackman Windows: A Deep Dive for RF Anti-Aliasing<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":4582,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","footnotes":""},"categories":[6,10],"tags":[],"class_list":["post-4580","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-signal-science","category-signal_scythe"],"_links":{"self":[{"href":"https:\/\/172-234-197-23.ip.linodeusercontent.com\/index.php?rest_route=\/wp\/v2\/posts\/4580","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/172-234-197-23.ip.linodeusercontent.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/172-234-197-23.ip.linodeusercontent.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/172-234-197-23.ip.linodeusercontent.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/172-234-197-23.ip.linodeusercontent.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4580"}],"version-history":[{"count":2,"href":"https:\/\/172-234-197-23.ip.linodeusercontent.com\/index.php?rest_route=\/wp\/v2\/posts\/4580\/revisions"}],"predecessor-version":[{"id":4583,"href":"https:\/\/172-234-197-23.ip.linodeusercontent.com\/index.php?rest_route=\/wp\/v2\/posts\/4580\/revisions\/4583"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/172-234-197-23.ip.linodeusercontent.com\/index.php?rest_route=\/wp\/v2\/media\/4582"}],"wp:attachment":[{"href":"https:\/\/172-234-197-23.ip.linodeusercontent.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4580"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/172-234-197-23.ip.linodeusercontent.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4580"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/172-234-197-23.ip.linodeusercontent.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4580"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}