| 摘要 |
<p>Method of a N-point discrete Fourier transform. The original set, consisting of N input data elements {a(k)} k=0, 1,2, ... N-1 is converted into two sets of data elements {b<Sub>1</Sub>(q)} q=<Sub>1</Sub>,<Sub>2</Sub>, ... M and {b<Sub>2</Sub>(q)} q=1,2, ... M, which each comprise M=(N-1)/2 data elements, each element being a linear combination of two of the original input data elements a (k). These sequences are circularly convolved with the impulse response h<Sub>1</Sub>(v) = a cos (<MathDetails id="matha01"><MathText><![CDATA[ <img id="ia01" file="imga0001.tif" wi="5" he="4" img-content="math" img-format="tif" inline="yes" /> ]]></MathText></MathDetails> g <Sup>v</Sup>) and h<Sub>2</Sub>(v) = jβ sin (<MathDetails id="matha02"><MathText><![CDATA[ <img id="ia02" file="imga0002.tif" wi="5" he="5" img-content="math" img-format="tif" inline="yes" /> ]]></MathText></MathDetails> g<Sup>v</Sup>), respectively, for generating a set of third data elements y,(p) and a set of fourth data elements y<Sub>2</Sub>(p). Herein N is a prime and a, β and g represent constants and it holds that p, v = 1, 2, ... M, whereas j = <MathDetails id="matha03"><MathText><![CDATA[ <img id="ia03" file="imga0003.tif" wi="8" he="5" img-content="math" img-format="tif" inline="yes" /> ]]></MathText></MathDetails></p><p>The desired output data element can be obtained by means of a linear combination of the data elements y1(p), y2(p) and a(0).</p> |
