예제: nfact 및 ofact 수정자 사용

기호 > 키워드 및 수정자 > 예제: nfact 및 ofact 수정자 사용

정규화 승수(nfact) 및 진동 계수(ofact)는 다음과 같이 표현됩니다.

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            <id xml:space="preserve">fourier</id>
            <apply>
              <equal />
              <id xml:space="preserve">nfact
</id>
              <id xml:space="preserve">a</id>
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          <apply>
            <equal />
            <id xml:space="preserve">ofact</id>
            <id xml:space="preserve">b</id>
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            <lambda>
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              <apply>
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                <apply>
                  <id xml:space="preserve" labels="VARIABLE">f</id>
                  <id xml:space="preserve" labels="VARIABLE">t</id>
                </apply>
                <apply>
                  <pow />
                  <id xml:space="preserve" labels="CONSTANT">e</id>
                  <apply>
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                    <apply>
                      <mult />
                      <apply>
                        <mult />
                        <id xml:space="preserve" labels="VARIABLE">ω</id>
                        <id xml:space="preserve" labels="VARIABLE">b</id>
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                      <id xml:space="preserve" labels="VARIABLE">t</id>
                    </apply>
                    <imag symbol="i">1</imag>
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                </apply>
              </apply>
            </lambda>
            <lowerBound>
              <apply>
                <neg />
                <id xml:space="preserve" labels="CONSTANT">∞</id>
              </apply>
            </lowerBound>
            <upperBound>
              <id xml:space="preserve" labels="CONSTANT">∞</id>
            </upperBound>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
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            <id xml:space="preserve">invfourier</id>
            <apply>
              <equal />
              <id xml:space="preserve">nfact
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              <id xml:space="preserve">a</id>
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          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">ofact</id>
            <id xml:space="preserve">b</id>
          </apply>
        </sequence>
      </command>
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        <apply>
          <mult />
          <id xml:space="preserve" labels="VARIABLE">a</id>
          <apply>
            <integral />
            <lambda>
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                <id xml:space="preserve" labels="VARIABLE">ω</id>
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              <apply>
                <mult />
                <apply>
                  <id xml:space="preserve" labels="VARIABLE">f</id>
                  <id xml:space="preserve" labels="VARIABLE">ω</id>
                </apply>
                <apply>
                  <pow />
                  <id xml:space="preserve" labels="CONSTANT">e</id>
                  <apply>
                    <mult />
                    <apply>
                      <mult />
                      <apply>
                        <mult />
                        <id xml:space="preserve" labels="VARIABLE">ω</id>
                        <id xml:space="preserve" labels="VARIABLE">b</id>
                      </apply>
                      <id xml:space="preserve" labels="VARIABLE">t</id>
                    </apply>
                    <imag symbol="i">1</imag>
                  </apply>
                </apply>
              </apply>
            </lambda>
            <lowerBound>
              <apply>
                <neg />
                <id xml:space="preserve" labels="CONSTANT">∞</id>
              </apply>
            </lowerBound>
            <upperBound>
              <id xml:space="preserve" labels="CONSTANT">∞</id>
            </upperBound>
          </apply>
        </apply>
      </symResult>
    </symEval>
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Fourier 및 역 Fourier 변환은 정규화 및 진동 계수와만 다릅니다. 일반적으로 이 계수는 이후 정 및 역 변환 수행 시 원래 함수가 나오게 하기 위해 선택됩니다. 예를 들면 다음과 같습니다.

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        <command>
          <id xml:space="preserve">fourier</id>
        </command>
        <symResult>
          <apply>
            <plus />
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              <apply>
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                <id xml:space="preserve" labels="VARIABLE">ω</id>
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            </apply>
            <apply>
              <div />
              <imag symbol="i">1</imag>
              <id xml:space="preserve" labels="VARIABLE">ω</id>
            </apply>
          </apply>
        </symResult>
      </symEval>
      <command>
        <sequence>
          <id xml:space="preserve">invfourier</id>
          <id xml:space="preserve">simplify</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <id xml:space="preserve" labels="FUNCTION">Φ</id>
          <id xml:space="preserve" labels="VARIABLE">t</id>
        </apply>
      </symResult>
    </symEval>
  </math>
</region>

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        <command>
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            <sequence>
              <id xml:space="preserve">fourier</id>
              <apply>
                <equal />
                <id xml:space="preserve">nfact
</id>
                <real>1</real>
              </apply>
            </sequence>
            <apply>
              <equal />
              <id xml:space="preserve">ofact</id>
              <real>1</real>
            </apply>
          </sequence>
        </command>
        <symResult>
          <apply>
            <plus />
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              <mult />
              <id xml:space="preserve" labels="CONSTANT">π</id>
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                <id xml:space="preserve" labels="FUNCTION">Δ</id>
                <id xml:space="preserve" labels="VARIABLE">ω</id>
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            </apply>
            <apply>
              <div />
              <imag symbol="i">1</imag>
              <id xml:space="preserve" labels="VARIABLE">ω</id>
            </apply>
          </apply>
        </symResult>
      </symEval>
      <command>
        <sequence>
          <sequence>
            <sequence>
              <id xml:space="preserve">invfourier</id>
              <apply>
                <equal />
                <id xml:space="preserve">nfact
</id>
                <apply>
                  <div />
                  <real>1</real>
                  <apply>
                    <mult />
                    <real>2</real>
                    <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">π</id>
                  </apply>
                </apply>
              </apply>
            </sequence>
            <apply>
              <equal />
              <id xml:space="preserve">ofact</id>
              <real>-1</real>
            </apply>
          </sequence>
          <id xml:space="preserve">simplify</id>
        </sequence>
      </command>
      <symResult>
        <apply>
          <id xml:space="preserve" labels="FUNCTION">Φ</id>
          <id xml:space="preserve" labels="VARIABLE">t</id>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
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서로 다른 수학 및 엔지니어링 분야에서는 다른 유형의 신호를 표준화하기 위해 정규화 및 진동 계수를 다르게 선택합니다.

1. 확률 이론(단위가 없는 모델)

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          <apply>
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            <id xml:space="preserve">ofact</id>
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              <id xml:space="preserve">nfact
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          <apply>
            <equal />
            <id xml:space="preserve">ofact</id>
            <real>-1</real>
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          <real>1</real>
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            <real>2</real>
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                    <id xml:space="preserve" labels="VARIABLE">t</id>
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                  <imag symbol="i">1</imag>
                </apply>
              </apply>
            </apply>
          </lambda>
          <lowerBound>
            <apply>
              <neg />
              <id xml:space="preserve" labels="CONSTANT">∞</id>
            </apply>
          </lowerBound>
          <upperBound>
            <id xml:space="preserve" labels="CONSTANT">∞</id>
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                        <imag symbol="i">1</imag>
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            </lambda>
            <lowerBound>
              <apply>
                <neg />
                <id xml:space="preserve" labels="CONSTANT">∞</id>
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            </lowerBound>
            <upperBound>
              <id xml:space="preserve" labels="CONSTANT">∞</id>
            </upperBound>
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          <apply>
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            <real>2</real>
            <id xml:space="preserve" labels="CONSTANT">π</id>
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          <apply>
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                    <id xml:space="preserve" labels="VARIABLE">t</id>
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                  <imag symbol="i">1</imag>
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          <lowerBound>
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              <neg />
              <id xml:space="preserve" labels="CONSTANT">∞</id>
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                        <imag symbol="i">1</imag>
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            <lowerBound>
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            <upperBound>
              <id xml:space="preserve" labels="CONSTANT">∞</id>
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          <apply>
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            <id xml:space="preserve" labels="CONSTANT">π</id>
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2. 전기 공학(헤르츠 단위의 주파수, 볼프람 세트 중 하나)

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      <apply>
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        <id xml:space="preserve">t</id>
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      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">fourier</id>
            <apply>
              <equal />
              <id xml:space="preserve">nfact
</id>
              <real>1</real>
            </apply>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">ofact</id>
            <apply>
              <mult />
              <real>-2</real>
              <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">π</id>
            </apply>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <integral />
          <lambda>
            <boundVars>
              <id xml:space="preserve" labels="VARIABLE">t</id>
            </boundVars>
            <apply>
              <mult />
              <apply>
                <id xml:space="preserve" labels="VARIABLE">f</id>
                <id xml:space="preserve" labels="VARIABLE">t</id>
              </apply>
              <apply>
                <pow />
                <id xml:space="preserve" labels="CONSTANT">e</id>
                <apply>
                  <neg />
                  <parens>
                    <apply>
                      <mult />
                      <apply>
                        <mult />
                        <apply>
                          <mult />
                          <apply>
                            <mult />
                            <real>2</real>
                            <id xml:space="preserve" labels="VARIABLE">ω</id>
                          </apply>
                          <id xml:space="preserve" labels="VARIABLE">t</id>
                        </apply>
                        <id xml:space="preserve" labels="CONSTANT">π</id>
                      </apply>
                      <imag symbol="i">1</imag>
                    </apply>
                  </parens>
                </apply>
              </apply>
            </apply>
          </lambda>
          <lowerBound>
            <apply>
              <neg />
              <id xml:space="preserve" labels="CONSTANT">∞</id>
            </apply>
          </lowerBound>
          <upperBound>
            <id xml:space="preserve" labels="CONSTANT">∞</id>
          </upperBound>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
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      <apply>
        <id xml:space="preserve">f</id>
        <id xml:space="preserve">ω</id>
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      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">invfourier</id>
            <apply>
              <equal />
              <id xml:space="preserve">nfact
</id>
              <real>1</real>
            </apply>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">ofact</id>
            <apply>
              <mult />
              <real>2</real>
              <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">π</id>
            </apply>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <integral />
          <lambda>
            <boundVars>
              <id xml:space="preserve" labels="VARIABLE">ω</id>
            </boundVars>
            <apply>
              <mult />
              <apply>
                <id xml:space="preserve" labels="VARIABLE">f</id>
                <id xml:space="preserve" labels="VARIABLE">ω</id>
              </apply>
              <apply>
                <pow />
                <id xml:space="preserve" labels="CONSTANT">e</id>
                <apply>
                  <mult />
                  <apply>
                    <mult />
                    <apply>
                      <mult />
                      <apply>
                        <mult />
                        <real>2</real>
                        <id xml:space="preserve" labels="VARIABLE">ω</id>
                      </apply>
                      <id xml:space="preserve" labels="VARIABLE">t</id>
                    </apply>
                    <id xml:space="preserve" labels="CONSTANT">π</id>
                  </apply>
                  <imag symbol="i">1</imag>
                </apply>
              </apply>
            </apply>
          </lambda>
          <lowerBound>
            <apply>
              <neg />
              <id xml:space="preserve" labels="CONSTANT">∞</id>
            </apply>
          </lowerBound>
          <upperBound>
            <id xml:space="preserve" labels="CONSTANT">∞</id>
          </upperBound>
        </apply>
      </symResult>
    </symEval>
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3. 전기 공학(각주파수 사용)

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          <sequence>
            <id xml:space="preserve">fourier</id>
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              <equal />
              <id xml:space="preserve">nfact
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              <real>1</real>
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          <apply>
            <equal />
            <id xml:space="preserve">ofact</id>
            <real>-1</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <real>1</real>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
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        <id xml:space="preserve">ω</id>
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          <sequence>
            <id xml:space="preserve">invfourier</id>
            <apply>
              <equal />
              <id xml:space="preserve">nfact
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              <apply>
                <div />
                <real>1</real>
                <apply>
                  <mult />
                  <real>2</real>
                  <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">π</id>
                </apply>
              </apply>
            </apply>
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          <apply>
            <equal />
            <id xml:space="preserve">ofact</id>
            <real>1</real>
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      <symResult>
        <apply>
          <div />
          <real>1</real>
          <apply>
            <mult />
            <real>2</real>
            <id xml:space="preserve" labels="CONSTANT">π</id>
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              <real>1</real>
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          <apply>
            <equal />
            <id xml:space="preserve">ofact</id>
            <real>-1</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <integral />
          <lambda>
            <boundVars>
              <id xml:space="preserve" labels="VARIABLE">t</id>
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                <id xml:space="preserve" labels="VARIABLE">f</id>
                <id xml:space="preserve" labels="VARIABLE">t</id>
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              <apply>
                <pow />
                <id xml:space="preserve" labels="CONSTANT">e</id>
                <apply>
                  <neg />
                  <parens>
                    <apply>
                      <mult />
                      <apply>
                        <mult />
                        <id xml:space="preserve" labels="VARIABLE">ω</id>
                        <id xml:space="preserve" labels="VARIABLE">t</id>
                      </apply>
                      <imag symbol="i">1</imag>
                    </apply>
                  </parens>
                </apply>
              </apply>
            </apply>
          </lambda>
          <lowerBound>
            <apply>
              <neg />
              <id xml:space="preserve" labels="CONSTANT">∞</id>
            </apply>
          </lowerBound>
          <upperBound>
            <id xml:space="preserve" labels="CONSTANT">∞</id>
          </upperBound>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
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      <apply>
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        <id xml:space="preserve">ω</id>
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          <sequence>
            <id xml:space="preserve">invfourier</id>
            <apply>
              <equal />
              <id xml:space="preserve">nfact
</id>
              <apply>
                <div />
                <real>1</real>
                <apply>
                  <mult />
                  <real>2</real>
                  <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">π</id>
                </apply>
              </apply>
            </apply>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">ofact</id>
            <real>1</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <integral />
            <lambda>
              <boundVars>
                <id xml:space="preserve" labels="VARIABLE">ω</id>
              </boundVars>
              <apply>
                <mult />
                <apply>
                  <id xml:space="preserve" labels="VARIABLE">f</id>
                  <id xml:space="preserve" labels="VARIABLE">ω</id>
                </apply>
                <apply>
                  <pow />
                  <id xml:space="preserve" labels="CONSTANT">e</id>
                  <apply>
                    <mult />
                    <apply>
                      <mult />
                      <id xml:space="preserve" labels="VARIABLE">ω</id>
                      <id xml:space="preserve" labels="VARIABLE">t</id>
                    </apply>
                    <imag symbol="i">1</imag>
                  </apply>
                </apply>
              </apply>
            </lambda>
            <lowerBound>
              <apply>
                <neg />
                <id xml:space="preserve" labels="CONSTANT">∞</id>
              </apply>
            </lowerBound>
            <upperBound>
              <id xml:space="preserve" labels="CONSTANT">∞</id>
            </upperBound>
          </apply>
          <apply>
            <mult />
            <real>2</real>
            <id xml:space="preserve" labels="CONSTANT">π</id>
          </apply>
        </apply>
      </symResult>
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4. 정 및 역 대칭의 경우 변환이 중요합니다. (변환의 변수가 다른) 동일한 입력은 적절한 nfact 및 ofact 값 세트를 사용하면 동일한 출력 결과를 반환합니다.

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          <sequence>
            <id xml:space="preserve">fourier</id>
            <apply>
              <equal />
              <id xml:space="preserve">nfact
</id>
              <apply>
                <div />
                <real>1</real>
                <apply>
                  <nthRoot />
                  <placeholder />
                  <apply>
                    <mult />
                    <real>2</real>
                    <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">π</id>
                  </apply>
                </apply>
              </apply>
            </apply>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">ofact</id>
            <real>-1</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <nthRoot />
            <placeholder />
            <real>2</real>
          </apply>
          <apply>
            <mult />
            <real>2</real>
            <apply>
              <nthRoot />
              <placeholder />
              <id xml:space="preserve" labels="CONSTANT">π</id>
            </apply>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
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      <apply>
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          <sequence>
            <id xml:space="preserve">invfourier</id>
            <apply>
              <equal />
              <id xml:space="preserve">nfact
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              <apply>
                <div />
                <real>1</real>
                <apply>
                  <nthRoot />
                  <placeholder />
                  <apply>
                    <mult />
                    <real>2</real>
                    <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">π</id>
                  </apply>
                </apply>
              </apply>
            </apply>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">ofact</id>
            <real>1</real>
          </apply>
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      </command>
      <symResult>
        <apply>
          <div />
          <apply>
            <nthRoot />
            <placeholder />
            <real>2</real>
          </apply>
          <apply>
            <mult />
            <real>2</real>
            <apply>
              <nthRoot />
              <placeholder />
              <id xml:space="preserve" labels="CONSTANT">π</id>
            </apply>
          </apply>
        </apply>
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    </symEval>
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      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
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  </math>
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              <id xml:space="preserve">nfact
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                <real>1</real>
                <apply>
                  <nthRoot />
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                    <real>2</real>
                    <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">π</id>
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            </apply>
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          <apply>
            <equal />
            <id xml:space="preserve">ofact</id>
            <real>-1</real>
          </apply>
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        <apply>
          <div />
          <apply>
            <mult />
            <apply>
              <nthRoot />
              <placeholder />
              <real>2</real>
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            <apply>
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                  <id xml:space="preserve" labels="VARIABLE">t</id>
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                    <id xml:space="preserve" labels="VARIABLE">t</id>
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                    <id xml:space="preserve" labels="CONSTANT">e</id>
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                            <mult />
                            <id xml:space="preserve" labels="VARIABLE">ω</id>
                            <id xml:space="preserve" labels="VARIABLE">t</id>
                          </apply>
                          <imag symbol="i">1</imag>
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                    </apply>
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              <lowerBound>
                <apply>
                  <neg />
                  <id xml:space="preserve" labels="CONSTANT">∞</id>
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              <upperBound>
                <id xml:space="preserve" labels="CONSTANT">∞</id>
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          </apply>
          <apply>
            <mult />
            <real>2</real>
            <apply>
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              <id xml:space="preserve" labels="CONSTANT">π</id>
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              <id xml:space="preserve">nfact
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                <real>1</real>
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                    <mult />
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          <apply>
            <equal />
            <id xml:space="preserve">ofact</id>
            <real>1</real>
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          <div />
          <apply>
            <mult />
            <apply>
              <nthRoot />
              <placeholder />
              <real>2</real>
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              <lambda>
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                  <id xml:space="preserve" labels="VARIABLE">ω</id>
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                <apply>
                  <mult />
                  <apply>
                    <id xml:space="preserve" labels="VARIABLE">f</id>
                    <id xml:space="preserve" labels="VARIABLE">ω</id>
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                  <apply>
                    <pow />
                    <id xml:space="preserve" labels="CONSTANT">e</id>
                    <apply>
                      <mult />
                      <apply>
                        <mult />
                        <id xml:space="preserve" labels="VARIABLE">ω</id>
                        <id xml:space="preserve" labels="VARIABLE">t</id>
                      </apply>
                      <imag symbol="i">1</imag>
                    </apply>
                  </apply>
                </apply>
              </lambda>
              <lowerBound>
                <apply>
                  <neg />
                  <id xml:space="preserve" labels="CONSTANT">∞</id>
                </apply>
              </lowerBound>
              <upperBound>
                <id xml:space="preserve" labels="CONSTANT">∞</id>
              </upperBound>
            </apply>
          </apply>
          <apply>
            <mult />
            <real>2</real>
            <apply>
              <nthRoot />
              <placeholder />
              <id xml:space="preserve" labels="CONSTANT">π</id>
            </apply>
          </apply>
        </apply>
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Fourier와 역 Fourier 간 가역성

입력 포현식에 fourier 키워드를 적용하고 결과에 invfourier 키워드를 적용하면 처음의 표현식으로 돌아갑니다. fourier 또는 invfourier 키워드를 기본값 nfact 및 ofact 수정자와 함께 사용할 경우 가역성이 지원됩니다.

nfact 및 ofact 수정자를 사용할 때는 다음 조건이 적용됩니다.

• 키워드 이름 바로 뒤에 nfact 및 ofact 수정자를 넣어야 합니다. 두 수정자를 따로 사용하거나 한 표현식에 둘 다 포함할 수 있습니다.

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          <apply>
            <equal />
            <id xml:space="preserve">nfact
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            <apply>
              <div />
              <real>1</real>
              <apply>
                <mult />
                <real>2</real>
                <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">π</id>
              </apply>
            </apply>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <neg />
          <parens>
            <apply>
              <mult />
              <imag symbol="i">1</imag>
              <apply>
                <id xml:space="preserve" labels="FUNCTION">Δ</id>
                <sequence>
                  <real>1</real>
                  <id xml:space="preserve" labels="VARIABLE">ω</id>
                </sequence>
              </apply>
            </apply>
          </parens>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

<region id="ID0EA22KB" actualWidth="268.98666666666668" actualHeight="39.2" top="2342.4000000000005" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="85">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <id xml:space="preserve">t</id>
      <command>
        <sequence>
          <id xml:space="preserve">fourier</id>
          <apply>
            <equal />
            <id xml:space="preserve">ofact</id>
            <real>-1</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <mult />
          <apply>
            <mult />
            <apply>
              <mult />
              <real>2</real>
              <id xml:space="preserve" labels="CONSTANT">π</id>
            </apply>
            <imag symbol="i">1</imag>
          </apply>
          <apply>
            <id xml:space="preserve" labels="FUNCTION">Δ</id>
            <sequence>
              <real>1</real>
              <id xml:space="preserve" labels="VARIABLE">ω</id>
            </sequence>
          </apply>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

• 행렬은 계수로 사용할 수 없습니다.

<region id="ID0EQ32KB" actualWidth="224.26666666666668" actualHeight="60.800000000000004" top="2457.6000000000004" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="86">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <id xml:space="preserve">t</id>
      <command>
        <sequence>
          <sequence>
            <sequence>
              <id xml:space="preserve">fourier</id>
              <apply>
                <equal />
                <id xml:space="preserve">nfact
</id>
                <matrix rows="1" cols="1">
                  <apply>
                    <div />
                    <real>1</real>
                    <apply>
                      <mult />
                      <real>2</real>
                      <id xml:space="preserve">π</id>
                    </apply>
                  </apply>
                </matrix>
              </apply>
            </sequence>
            <id xml:space="preserve">t</id>
          </sequence>
          <id xml:space="preserve">s</id>
        </sequence>
      </command>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

<region id="ID0E532KB" actualWidth="246.79666666666668" actualHeight="60.800000000000004" top="2534.4000000000005" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="87">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <id xml:space="preserve">t</id>
      <command>
        <sequence>
          <sequence>
            <sequence>
              <id xml:space="preserve">invfourier</id>
              <apply>
                <equal />
                <id xml:space="preserve">nfact
</id>
                <matrix rows="1" cols="1">
                  <apply>
                    <div />
                    <real>1</real>
                    <apply>
                      <mult />
                      <real>2</real>
                      <id xml:space="preserve">π</id>
                    </apply>
                  </apply>
                </matrix>
              </apply>
            </sequence>
            <id xml:space="preserve">t</id>
          </sequence>
          <id xml:space="preserve">s</id>
        </sequence>
      </command>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

• 수정자의 순서는 역전할 수 있습니다.

<region id="ID0EO52KB" actualWidth="382.86333333333334" actualHeight="60.800000000000004" top="2649.6000000000004" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="88">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <id xml:space="preserve">t</id>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">fourier</id>
            <apply>
              <equal />
              <id xml:space="preserve">ofact</id>
              <apply>
                <div />
                <real>1</real>
                <apply>
                  <mult />
                  <real>2</real>
                  <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">π</id>
                </apply>
              </apply>
            </apply>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">nfact
</id>
            <real>1</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <neg />
          <parens>
            <apply>
              <mult />
              <apply>
                <mult />
                <apply>
                  <mult />
                  <real>8</real>
                  <apply>
                    <pow />
                    <id xml:space="preserve" labels="CONSTANT">π</id>
                    <real>3</real>
                  </apply>
                </apply>
                <imag symbol="i">1</imag>
              </apply>
              <apply>
                <id xml:space="preserve" labels="FUNCTION">Δ</id>
                <sequence>
                  <real>1</real>
                  <id xml:space="preserve" labels="VARIABLE">ω</id>
                </sequence>
              </apply>
            </apply>
          </parens>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

<region id="ID0E352KB" actualWidth="405.39333333333337" actualHeight="60.800000000000004" top="2726.4000000000005" left="19.200000000000003" xmlns="http://schemas.mathsoft.com/worksheet50">
  <math resultRef="89">
    <symEval xmlns="http://schemas.mathsoft.com/math50">
      <id xml:space="preserve">ω</id>
      <command>
        <sequence>
          <sequence>
            <id xml:space="preserve">invfourier</id>
            <apply>
              <equal />
              <id xml:space="preserve">ofact</id>
              <apply>
                <div />
                <real>1</real>
                <apply>
                  <mult />
                  <real>2</real>
                  <id xml:space="preserve" labels="CONSTANT" label-is-contextual="true">π</id>
                </apply>
              </apply>
            </apply>
          </sequence>
          <apply>
            <equal />
            <id xml:space="preserve">nfact
</id>
            <real>1</real>
          </apply>
        </sequence>
      </command>
      <symResult>
        <apply>
          <neg />
          <parens>
            <apply>
              <mult />
              <apply>
                <mult />
                <apply>
                  <mult />
                  <real>8</real>
                  <apply>
                    <pow />
                    <id xml:space="preserve" labels="CONSTANT">π</id>
                    <real>3</real>
                  </apply>
                </apply>
                <imag symbol="i">1</imag>
              </apply>
              <apply>
                <id xml:space="preserve" labels="FUNCTION">Δ</id>
                <sequence>
                  <real>1</real>
                  <id xml:space="preserve" labels="VARIABLE">t</id>
                </sequence>
              </apply>
            </apply>
          </parens>
        </apply>
      </symResult>
    </symEval>
    <resultFormat>
      <matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" />
    </resultFormat>
  </math>
</region>

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