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14<h1 align="left">MATH_IFFT <img src="../../image/NTR.gif"align="middle"><img src="../../image/TWL.gif" align="middle"></H1>
15<H2>Syntax</H2>
16
17<dl>
18  <dd>
19  <PRE><CODE>#include &lt;nitro/math/fft.h&gt;
20
21void MATH_IFFT( fx32* data, u32 nShift, const fx16* sinTable );
22</CODE></PRE>
23  </dd>
24</dl><h2>Arguments</h2>
25
26<table border="1" width="100%">
27    <TR>
28      <TD width="176"><em><strong><font face="Courier New">data</font></strong></em></TD>
29      <TD width="670">Pointer to the data to transform. Data after the transform is overwritten.</TD>
30    </TR>
31    <TR>
32      <TD width="176"><em><strong><font face="Courier New">nShift</font></strong></em></TD>
33      <TD width="670">The value obtained by taking the base-2 logarithm of the number of the input complex numbers.</TD>
34    </TR>
35    <TR>
36      <TD width="176"><em><strong><font face="Courier New">sinTable</font></strong></em></TD>
37      <TD width="670">Pointer to the table of sine values.</TD>
38    </TR>
39  </table>
40<h2>Return Values</h2>
41<p>None.</p>
42<H2>Description</H2>
43<P>
44Uses a fast Fourier transform algorithm to perform the inverse transform of a discrete Fourier transform. Takes a sequence of complex number as input, and outputs a sequence of complex numbers. This is the reverse operation of the <A href="MATH_FFT.html">MATH_FFT</A> function.
45</P>
46<P>
47In the explanation below, the value 2<sup>nShift</sup> (2 to the nShift power) is represented as N. <I>data</I> is a type fx32 array of length 2*N. N number of complex numbers is passed to data in a format that stores real numbers and imaginary numbers alternately. Thus, if <i>i</i> is the unit for imaginary numbers, then the input data is the complex number sequence of N length <CODE>{data[0]+<i>i</i>*data[1], data[2]+<i>i</i>*data[3], ..., data[N*2-2]+<i>i</i>*data[N*2-1]}</CODE>. <I>sinTable</I> is the pointer to the array of N*3/4 length that has fx16 type sine values assigned that satisfy <CODE>sinTable[k] = <i>sin</i>( (2&#x3C0;/N) * k )  (k = 0, 1,..., N*3/4-1)</CODE>. This can be created using the <CODE><A href="MATH_MakeFFTSinTable.html">MATH_MakeFFTSinTable</A></CODE> function. The result of the inverse transform of a discrete Fourier transform also becomes a sequence of complex numbers, and overwritten in data as the same format as the input and returned.
48</P>
49<P>
50The calculations are performed using fixed-decimal numbers, so if a large value is given as the input, there is a risk of overflow. When the input value is viewed as type s32, the absolute value should not be greater than or equal to <CODE>0x80000000/N</CODE>. Also note that the maximum error when performing both the forward transform and inverse transform is around several times <CODE>FX32_ONE</CODE>.
51</P>
52<h2>See Also</h2>
53<P><CODE><A href="MATH_MakeFFTSinTable.html">MATH_MakeFFTSinTable</A>, <A href="MATH_FFT.html">MATH_FFT</A>, <A href="MATH_FFTReal.html">MATH_FFTReal</A>, <A href="MATH_IFFTReal.html">MATH_IFFTReal</A></CODE></P>
54<H2>Revision History</H2>
55<P>
562005/07/21 Corrected the explanation for <CODE>sinTable</CODE>.<BR>2005/07/11 Corrected the explanation.<BR> 2005/05/13 Initial version.
57</P>
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