The first stage DIT-FFT of a sequence x(n) is given by:

A) \[X\left( k \right) = \left\{ \begin{array}{l} G\left( k \right) + W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\ G\left( {k + \frac{N}{2}} \right) - W_N^kH\left( {k + \frac{N}{2}} \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right) \end{array} \right.\] B) \[X\left( k \right) = \left\{ \begin{array}{l} G\left( k \right) - W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\ G\left( {k + \frac{N}{2}} \right) - W_N^kH\left( {k + \frac{N}{2}} \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right) \end{array} \right.\] C) \[X\left( k \right) = \left\{ \begin{array}{l} G\left( k \right) - W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\ G\left( k \right) + W_N^kH\left( k \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right) \end{array} \right.\] D) \[X\left( k \right) = \left\{ \begin{array}{l} G\left( {k + N} \right) - W_N^kH\left( k \right)\,\,\,\,\,0 \le k \le \left( {\frac{N}{2} - 1} \right)\\ G\left( k \right) + W_N^kH\left( k \right)\,\,\,\,\,\frac{N}{2} \le k \le \left( {N - 1} \right) \end{array} \right.\]

Answer & Solution

Correct Answer: Option C

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The first stage DIT-FFT of a sequence x(n) is given by...

The first stage DIT-FFT of a sequence x(n) is given by:

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