{"id":108656,"date":"2026-09-22T09:57:11","date_gmt":"2026-09-22T01:57:11","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/108656.html"},"modified":"2026-09-22T09:57:11","modified_gmt":"2026-09-22T01:57:11","slug":"dpcm-%e7%bc%96%e8%a7%a3%e7%a0%81%e4%bf%a1%e6%81%af%e4%b8%8d%e5%af%b9%e7%ad%89%e4%b8%8e%e8%af%af%e5%b7%ae%e5%88%86%e6%9e%90","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/108656.html","title":{"rendered":"DPCM \u7f16\u89e3\u7801\u4fe1\u606f\u4e0d\u5bf9\u7b49\u4e0e\u8bef\u5dee\u5206\u6790"},"content":{"rendered":"

\"\"<\/p>\n

DPCM \u7f16\u89e3\u7801\u4fe1\u606f\u4e0d\u5bf9\u7b49\u4e0e\u8bef\u5dee\u6839\u6cbb\u539f\u7406<\/h2>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u91cf\u5316\u8bef\u5dee\u4f1a\u4e0d\u65ad\u7d2f\u79ef\u3002\u7406\u8bba\u4e0a，\u5982\u679c\u91cf\u5316\u8bef\u5dee\u662f\u96f6\u5747\u503c\u968f\u673a\u8fc7\u7a0b，\u957f\u671f\u6765\u770b\u8bef\u5dee\u4f1a\u76f8\u4e92\u62b5\u6d88\u3002\u4f46\u5de5\u7a0b\u5b9e\u9645\u4e2d，\u8fdc\u672a\u7b49\u5230\u8bef\u5dee\u62b5\u6d88，\u6709\u9650\u5b57\u957f\u7684\u8fd0\u7b97\u5c31\u4f1a\u9020\u6210\u91cd\u5efa\u503c\u6ea2\u51fa\u3002 \u6ce8\u610f\u5230\u7f16\u7801\u5668\u548c\u89e3\u7801\u5668\u4f7f\u7528\u7684\u4fe1\u606f\u5e76\u4e0d\u5bf9\u7b49：\u7f16\u7801\u5668\u57fa\u4e8e\u539f\u59cb\u91c7\u6837\u503c\u8ba1\u7b97\u5dee\u503c，\u800c\u89e3\u7801\u5668\u662f\u5728\u5df2\u7ecf\u5931\u771f\u7684\u91cd\u5efa\u4fe1\u53f7\u57fa\u7840\u4e0a\u53e0\u52a0\u91cf\u5316\u5dee\u503c\u3002 \u89e3\u51b3\u8be5\u95ee\u9898\u7684\u601d\u8def：\u5f3a\u5236\u7f16\u7801\u5668\u3001\u89e3\u7801\u5668\u5728\u6c42\u5dee\u548c\u91cd\u5efa\u8fd0\u7b97\u4e2d\u4f7f\u7528\u5b8c\u5168\u76f8\u540c\u7684\u4fe1\u606f\u3002\u63a5\u6536\u7aef\u4ec5\u80fd\u83b7\u53d6\u91cd\u5efa\u5e8f\u5217 \"(\\\\hat，\u7f16\u7801\u5668\u4fa7\u4e5f\u53ef\u4ee5\u5f97\u5230\u8be5\u91cd\u5efa\u5e8f\u5217\u3002\u56e0\u6b64\u4fee\u6539\u6c42\u5dee\u89c4\u5219：\u4e0d\u518d\u4f7f\u7528\u539f\u59cb\u524d\u4e00\u91c7\u6837 \"(x_{n-1})\"，\u800c\u662f\u4f7f\u7528\u524d\u4e00\u65f6\u523b\u7684\u91cd\u5efa\u503c\"(\\\\hat\u3002<\/p>\n

\n

\u4e8c\u3001\u7406\u8bba\u65e0\u8bef\u5dee\u5206\u6790<\/h3>\n

1. \u7406\u8bba\u5047\u8bbe<\/h4>\n

\u91cf\u5316\u8bef\u5dee \"(q_n)\"\u662f\u96f6\u5747\u503c\u767d\u566a\u58f0，\u6b63\u8d1f\u968f\u673a\u51fa\u73b0\u3002 \u6570\u5b66\u4e0a，\u65e0\u7a77\u957f\u65f6\u95f4\u7d2f\u52a0：<\/p>\n

\"(\\\\sum_{n=1}^{\\\\infty}q_n \u4e5f\u5c31\u662f：\u957f\u671f\u6b63\u8d1f\u8bef\u5dee\u62b5\u6d88，\u6574\u4f53\u65e0\u504f\u3002<\/p>\n

2. \u5b9e\u9645\u5de5\u7a0b\u73b0\u5b9e<\/h4>\n
  • \u8bed\u97f3\u3001\u56fe\u50cf\u90fd\u662f\u6709\u9650\u957f\u5e8f\u5217，\u6839\u672c\u7b49\u4e0d\u5230\u8bef\u5dee\u62b5\u6d88；<\/li>\n
  • \u8ba1\u7b97\u673a\u5b58\u50a8\u662f\u6709\u9650\u5b57\u957f\u6d6e\u70b9 \/ \u5b9a\u70b9\u8fd0\u7b97，\u7d2f\u79ef\u8bef\u5dee\u53ea\u4f1a\u5355\u5411\u504f\u79fb；<\/li>\n
  • \u8bef\u5dee\u6301\u7eed\u53e0\u52a0\u4f1a\u5bfc\u81f4\u91cd\u5efa\u6570\u503c\u8d8a\u8dd1\u8d8a\u504f，\u6700\u7ec8\u6570\u503c\u6ea2\u51fa\u3001\u6ce2\u5f62\u5931\u771f\u3001\u753b\u9762\u82b1\u5c4f\u3002<\/li>\n

    👉 \u7ed3\u8bba：\u7406\u8bba\u6536\u655b，\u5de5\u7a0b\u53d1\u6563，\u6734\u7d20\u5dee\u5206\u7f16\u7801\u5b8c\u5168\u65e0\u6cd5\u843d\u5730\u3002<\/p>\n

    \n

    \u4e09\u3001\u7f16\u89e3\u7801\u4fe1\u606f\u4e0d\u5bf9\u7b49\u6839\u6e90<\/h3>\n

    1. \u6734\u7d20\u5dee\u5206\u7f16\u7801\u7684\u65e7\u516c\u5f0f（\u9519\u8bef\u7ed3\u6784）<\/h4>\n

    \"(d_n<\/p>\n

    2. \u4e24\u7aef\u4fe1\u606f\u5b8c\u5168\u5272\u88c2<\/h4>\n
      \n
    • \u7f16\u7801\u5668（\u53d1\u9001\u7aef） \u624b\u63e1\u7eaf\u51c0\u539f\u59cb\u4fe1\u53f7\"(x_n,x_{n-1})\"\u7528\u771f\u5b9e\u5dee\u503c\u505a\u7f16\u7801，\u57fa\u51c6\u7edd\u5bf9\u51c6\u786e\u3002<\/li>\n
    • \u89e3\u7801\u5668（\u63a5\u6536\u7aef） \u6c38\u8fdc\u770b\u4e0d\u5230\u539f\u59cb\u4fe1\u53f7！ \u53ea\u80fd\u5728\u5df2\u7ecf\u5931\u771f\u3001\u5e26\u8bef\u5dee\u7684\u91cd\u5efa\u4fe1\u53f7 \"(\\\\hat \u57fa\u7840\u4e0a\u7d2f\u52a0\u3002<\/li>\n<\/ul>\n

      3. \u4e0d\u5bf9\u79f0\u7684\u672c\u8d28<\/h4>\n
        \n
      • \u7f16\u7801\u5668：\u5728\u771f\u5b9e\u8f68\u9053\u8fd0\u7b97<\/li>\n
      • \u89e3\u7801\u5668：\u5728\u5931\u771f\u8f68\u9053\u8fed\u4ee3<\/li>\n<\/ul>\n

        \u4e24\u6761\u8f68\u9053\u4e0d\u91cd\u5408，\u6bcf\u4e00\u6b21\u91cf\u5316\u8bef\u5dee\u90fd\u4f1a\u88ab\u7ee7\u627f，\u6c38\u8fdc\u7d2f\u79ef\u3002<\/p>\n

        \u8fd9\u5c31\u662f\u6559\u6750\u6240\u8bf4\u7684：\u4fe1\u606f\u4e0d\u5bf9\u7b49\u3002<\/p>\n

        \n

        \u56db\u3001\u6839\u6cbb\u65b9\u6848\u8be6\u7ec6\u5c55\u5f00：\u540c\u6b65\u7f16\u89e3\u7801\u72b6\u6001（DPCM \u6838\u5fc3\u9769\u65b0）<\/h3>\n

        1. \u89e3\u9898\u6838\u5fc3\u601d\u60f3<\/h4>\n

        \u60f3\u8981\u6d88\u9664\u8bef\u5dee\u7d2f\u79ef，\u5fc5\u987b\u8ba9\u7f16\u7801\u5668\u548c\u89e3\u7801\u5668\u7684\u300c\u5386\u53f2\u8fd0\u884c\u72b6\u6001\u5b8c\u5168\u4e00\u6a21\u4e00\u6837\u300d\u3002<\/p>\n

        \u89e3\u7801\u5668\u552f\u4e00\u80fd\u4f7f\u7528\u7684\u5386\u53f2\u6570\u636e：\u91cd\u5efa\u503c \"(\\\\hat \u56e0\u6b64\u7f16\u7801\u5668\u5fc5\u987b\u4e3b\u52a8\u81ea\u964d\u7cbe\u5ea6\u3001\u81ea\u6211\u6a21\u62df\u5931\u771f，\u629b\u5f03\u771f\u5b9e\u6837\u672c\u3002<\/p>\n

        2. \u65b0\u65e7\u516c\u5f0f\u5bf9\u6bd4<\/h4>\n
          \n
        • \u65e7（\u9519\u8bef\u3001\u65e0\u635f\u7ed3\u6784）：\"(d_n（\u771f\u503c \u2212 \u771f\u503c）<\/li>\n
        • \u65b0（\u6b63\u786e\u3001DPCM \u7ed3\u6784）：\"(d_n（\u771f\u503c \u2212 \u91cd\u5efa\u5931\u771f\u503c）<\/li>\n<\/ul>\n

          3. \u4e3a\u4ec0\u4e48\u6539\u5b8c\u5c31\u6ca1\u6709\u7d2f\u79ef？<\/h4>\n
            \n
          • \u7f16\u7801\u5668\u73b0\u5728\u7528\u7684\u662f \u548c\u89e3\u7801\u5668\u4e00\u6a21\u4e00\u6837\u7684\u5386\u53f2\u6570\u636e<\/li>\n
          • \u4e24\u7aef\u8f68\u9053\u5f7b\u5e95\u5bf9\u9f50\u3001\u72b6\u6001\u5b8c\u5168\u540c\u6b65<\/li>\n
          • \u6bcf\u4e00\u6b65\u8bef\u5dee\u53ea\u505c\u7559\u5728\u5f53\u524d\u5e27，\u4e0d\u7ee7\u627f\u5386\u53f2\u8bef\u5dee<\/li>\n<\/ul>\n

            \u6700\u7ec8\u8fed\u4ee3\u7ed3\u679c：<\/p>\n

            \"(\\\\hat\u65e0\u6c42\u548c\u3001\u65e0\u7d2f\u52a0\u3001\u65e0\u6f02\u79fb\u3001\u65e0\u6ea2\u51fa<\/p>\n<\/p>\n

            \u4e94\u3001\u6734\u7d20\u5dee\u5206\u7f16\u7801（\u65e7\u65b9\u6848） vs DPCM（\u4fee\u6b63\u65b9\u6848）\u539f\u7406 + \u6570\u503c\u5b9e\u4f8b\u5bf9\u6bd4<\/h3>\n

            \u8bbe\u5b9a\u6761\u4ef6：<\/p>\n

            \u539f\u59cb\u4fe1\u53f7\u5e8f\u5217：\"(x_0=10,\\\\;x_1=12,\\\\;x_2=11,\\\\;x_3=13)\"<\/p>\n

            \u91cf\u5316\u89c4\u5219：\u5dee\u503c\u91cf\u5316\u540e\u5f15\u5165\u91cf\u5316\u8bef\u5dee \"(q_1=+0.2,\\\\;q_2=-0.3,\\\\;q_3=+0.4)\"<\/p>\n

            \u521d\u59cb\u540c\u6b65：\"(\\\\hat，\u4e24\u7aef\u8d77\u70b9\u4e00\u81f4<\/p>\n

            \u65b9\u6848 A：\u6734\u7d20\u5dee\u5206\u7f16\u7801（\u6cbf\u7528\u65e0\u635f\u5dee\u5206\u516c\u5f0f，\u6709\u635f\u573a\u666f，\u4f1a\u4ea7\u751f\u8bef\u5dee\u7d2f\u79ef）<\/h4>\n

            \u5dee\u5206\u5b9a\u4e49：<\/p>\n

            \"(d_n\u7f16\u7801\u5668\u7528\u539f\u59cb\u771f\u503c\u8ba1\u7b97\u5dee\u503c；\u89e3\u7801\u5668\u4f7f\u7528\u91cd\u5efa\u503c\u7d2f\u52a0\u91cf\u5316\u540e\u7684\u5dee\u503c \"(\\\\hat，\u91cd\u5efa\u5f0f：<\/p>\n

            \"(\\\\hat<\/p>\n

            \u9010\u70b9\u6f14\u7b97<\/h4>\n

            \"\"<\/p>\n

            \u7ed3\u8bba（\u6734\u7d20\u5dee\u5206）<\/h4>\n

            \u91cd\u5efa\u8bef\u5dee：\"(e_n=\\\\hat<\/p>\n

            \u2705 \u8bef\u5dee = \u5168\u90e8\u5386\u53f2\u91cf\u5316\u8bef\u5dee\u7d2f\u52a0；\u8bef\u5dee\u4e0d\u65ad\u7ee7\u627f\u4f20\u9012\u3002\u7f16\u7801\u5668\u5728\u771f\u5b9e\u4fe1\u53f7\u8f68\u9053\u7b97\u5dee\u5206，\u89e3\u7801\u5668\u5728\u5931\u771f\u8f68\u9053\u91cd\u5efa，\u7f16\u89e3\u7801\u5386\u53f2\u72b6\u6001\u4e0d\u4e00\u81f4（\u4fe1\u606f\u4e0d\u5bf9\u7b49），\u8bef\u5dee\u6301\u7eed\u7d2f\u79ef\u3002<\/p>\n

            \n

            \u65b9\u6848 B：DPCM（\u4fee\u6b63\u65b9\u6848，\u7f16\u7801\u5668\u5185\u7f6e\u672c\u5730\u91cd\u5efa，\u6d88\u9664\u7d2f\u79ef）<\/h4>\n

            \u5dee\u5206\u5b9a\u4e49\u6539\u4e3a：<\/p>\n

            \"(d_n<\/p>\n

            \u7f16\u7801\u5668\u4e0d\u518d\u4f7f\u7528\u539f\u59cb\u524d\u4e00\u91c7\u6837\"(x_{n-1})\"，\u6539\u7528\u672c\u5730\u91cd\u5efa\u5f97\u5230\u7684\"(\\\\hat（\u548c\u89e3\u7801\u5668\u4f7f\u7528\u7684\u5386\u53f2\u503c\u5b8c\u5168\u4e00\u6837） \u91cf\u5316\u540e\"(\\\\hat，\u89e3\u7801\u5668\u91cd\u5efa\u516c\u5f0f\u4e0d\u53d8：<\/p>\n

            \"(\\\\hat<\/p>\n

            \u9010\u70b9\u6f14\u7b97（\u540c\u4e00\u539f\u59cb\u5e8f\u5217\u3001\u540c\u4e00\u7ec4\u91cf\u5316\u8bef\u5dee）<\/h4>\n

            \"\"<\/p>\n

            \u7ed3\u8bba（DPCM \u4fee\u6b63\u65b9\u6848）<\/h4>\n

            \u91cd\u5efa\u8bef\u5dee：\"(e_n=\\\\hat\u2705 \u6bcf\u4e00\u4e2a\u65f6\u523b\u7684\u91cd\u5efa\u8bef\u5dee\u53ea\u7b49\u4e8e\u5f53\u524d\u8fd9\u4e00\u6b65\u7684\u91cf\u5316\u8bef\u5dee，\u4e0d\u7ee7\u627f\u524d\u9762\u7684\u5386\u53f2\u8bef\u5dee\u3002\u7f16\u7801\u5668\u5728\u5185\u90e8\u590d\u523b\u4e86\u89e3\u7801\u5668\u91cd\u5efa\u94fe\u8def，\u7f16\u7801\u5668\u548c\u89e3\u7801\u5668\u5171\u4eab\u540c\u4e00\u5957\u5386\u53f2\u91cd\u5efa\u72b6\u6001，\u4e24\u6761\u8f68\u9053\u5b8c\u5168\u5bf9\u9f50，\u91cf\u5316\u566a\u58f0\u4e0d\u518d\u7d2f\u79ef\u3002<\/p>\n

            \n

            \u5bf9\u6bd4\u6c47\u603b\u8868<\/h3>\n\n\u9879\u76ee\u6734\u7d20\u5dee\u5206\u7f16\u7801（\u65e7\u65b9\u6848）DPCM \u4fee\u6b63\u5dee\u5206\u7f16\u7801（\u65b0\u65b9\u6848）<\/tr>\n\n\n\n\n\n\n\n\n
            \u5dee\u503c\u516c\u5f0f<\/td>\n\"(d_n=x_n-x_{n-1})\"，\u7528\u539f\u59cb\u771f\u503c\u505a\u9884\u6d4b<\/td>\n\"(d_n=x_n-\\\\hat，\u7528\u91cd\u5efa\u5931\u771f\u503c\u505a\u9884\u6d4b<\/td>\n<\/tr>\n
            \u7f16\u7801\u5668\u5386\u53f2\u6570\u636e\u6e90<\/td>\n\u539f\u59cb\u65e0\u5931\u771f\u6837\u672c\"(x_{n-1})\"<\/td>\n\u7f16\u7801\u5668\u672c\u5730\u91cd\u5efa\u51fa\u7684\u5931\u771f\u6837\u672c\"(\\\\hat<\/td>\n<\/tr>\n
            \u89e3\u7801\u5668\u5386\u53f2\u6570\u636e\u6e90<\/td>\n\u91cd\u5efa\u5931\u771f\u6837\u672c\"(\\\\hat<\/td>\n\u91cd\u5efa\u5931\u771f\u6837\u672c\"(\\\\hat<\/td>\n<\/tr>\n
            \u8bef\u5dee\u8868\u8fbe\u5f0f<\/td>\n\"(e_n=\\\\sum_{k=1}^n，\u5386\u53f2\u8bef\u5dee\u7d2f\u52a0<\/td>\n\"(e_n=q_n)\"，\u4ec5\u5f53\u524d\u91cf\u5316\u8bef\u5dee<\/td>\n<\/tr>\n
            \u7f16\u89e3\u7801\u72b6\u6001<\/td>\n\u4e0d\u4e00\u81f4，\u4e24\u6761\u72ec\u7acb\u8f68\u9053<\/td>\n\u5b8c\u5168\u540c\u6b65，\u5171\u7528\u540c\u4e00\u5931\u771f\u8f68\u9053<\/td>\n<\/tr>\n
            \u73b0\u8c61<\/td>\n\u8bef\u5dee\u9010\u70b9\u7d2f\u79ef，\u5e8f\u5217\u957f\u65f6\u53d1\u751f\u6f02\u79fb\u6ea2\u51fa<\/td>\n\u8bef\u5dee\u5355\u70b9\u72ec\u7acb，\u65e0\u7d2f\u79ef\u6f02\u79fb<\/td>\n<\/tr>\n
            \u9002\u7528\u573a\u666f<\/td>\n\u4ec5\u65e0\u635f\u7f16\u7801；\u6709\u635f\u573a\u666f\u4e0d\u53ef\u7528<\/td>\n\u6709\u635f\u9884\u6d4b\u7f16\u7801，\u8bed\u97f3 \/ \u56fe\u50cf\u538b\u7f29\u6807\u51c6\u91c7\u7528<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

            \u6838\u5fc3\u539f\u7406\u4e00\u53e5\u8bdd\u603b\u7ed3<\/h3>\n

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