Given that there are some FFT chips sampled at 8 points, how can we use these chips to compute a 24-point DFT?

Options:
A. $$
\begin{aligned} {{f ( n )}} & {{} {{} {{}=x ( 8 n ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 2}}} \\ {{g ( n )}} & {{} {{} {{}=x ( 8 n+1 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 2}}} \\ {{{h ( n )}}} & {{} {{} {{}=x ( 8 n+2 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 2}}} \\ \end{aligned}
$$
$$
X ( k )=F ( ( k ) )_{2}+W_{12}^{k} G ( ( k ) )_{2}+W_{12}^{( 2 k ) \mathrm{mod12}} H ( ( k ) )_{2}, \; \; \; k=0, 1, 2, \cdots, 23
$$
B. $$
\begin{aligned} {{f ( n )}} & {{} {{} {{}=x ( 5 n ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 4}}} \\ {{g ( n )}} & {{} {{} {{}=x ( 5 n+1 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 4}}} \\ {{{h ( n )}}} & {{} {{} {{}=x ( 5 n+2 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 4}}} \\ \end{aligned}
$$
$$
X ( k )=F ( ( k ) )_{5}+W_{16}^{k} G ( ( k ) )_{5}+W_{16}^{( 2 k ) \mathrm{mod16}} H ( ( k ) )_{5}, \; \; \; k=0, 1, 2, \cdots, 23
$$
C. $$
\begin{aligned} {{f ( n )}} & {{} {{} {{}=x ( 10 n ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 1}}} \\ {{g ( n )}} & {{} {{} {{}=x ( 10 n+1 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 1}}} \\ {{{h ( n )}}} & {{} {{} {{}=x ( 10 n+2 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 1}}} \\ \end{aligned}
$$
$$
X ( k )=F ( ( k ) )_{1}+W_{8}^{k} G ( ( k ) )_{1}+W_{8}^{( 2 k ) \mathrm{mod8}} H ( ( k ) )_{1}, \; \; \; k=0, 1, 2, \cdots, 23
$$
```
D. $$
\begin{aligned} {{f ( n )}} & {{} {{} {{}=x ( 9 n ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 2}}} \\ {{g ( n )}} & {{} {{} {{}=x ( 9 n+1 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 2}}} \\ {{{h ( n )}}} & {{} {{} {{}=x ( 9 n+2 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 2}}} \\ \end{aligned}
$$
$$
X ( k )=F ( ( k ) )_{2}+W_{10}^{k} G ( ( k ) )_{2}+W_{10}^{( 2 k ) \mathrm{mod10}} H ( ( k ) )_{2}, \; \; \; k=0, 1, 2, \cdots, 23
$$
E. $$
\begin{aligned} {{f ( n )}} & {{} {{} {{}=x ( 3 n ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 7}}} \\ {{g ( n )}} & {{} {{} {{}=x ( 3 n-1 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 7}}} \\ {{{h ( n )}}} & {{} {{} {{}=x ( 3 n-2 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 7}}} \\ \end{aligned}
$$
$$
X ( k )=F ( ( k ) )_{8}+W_{30}^{k} G ( ( k ) )_{8}+W_{30}^{( 2 k ) \mathrm{mod30}} H ( ( k ) )_{8}, \; \; \; k=0, 1, 2, \cdots, 23
$$
F. $$
\begin{aligned} {{f ( n )}} & {{} {{} {{}=x ( 4 n ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 5}}} \\ {{g ( n )}} & {{} {{} {{}=x ( 4 n+1 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 5}}} \\ {{{h ( n )}}} & {{} {{} {{}=x ( 4 n+2 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 5}}} \\ \end{aligned}
$$
$$
X ( k )=F ( ( k ) )_{6}+W_{20}^{k} G ( ( k ) )_{6}+W_{20}^{( 2 k ) \mathrm{mod20}} H ( ( k ) )_{6}, \; \; \; k=0, 1, 2, \cdots, 23
$$
G. $$
\begin{aligned} {{f ( n )}} & {{} {{} {{}=x ( 2 n ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 2 \,, 4 \,, \cdots\,, 14}}} \\ {{g ( n )}} & {{} {{} {{}=x ( 2 n+1 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 2 \,, 4 \,, \cdots\,, 14}}} \\ {{{h ( n )}}} & {{} {{} {{}=x ( 2 n+2 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 2 \,, 4 \,, \cdots\,, 14}}} \\ \end{aligned}
$$
$$
X ( k )=F ( ( k ) )_{12}+W_{24}^{k} G ( ( k ) )_{12}+W_{24}^{( 2 k ) \mathrm{mod24}} H ( ( k ) )_{12}, \; \; \; k=0, 1, 2, \cdots, 23
$$
H. $$
\begin{aligned} {{f ( n )}} & {{} {{} {{}=x ( 6 n ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 3}}} \\ {{g ( n )}} & {{} {{} {{}=x ( 6 n+1 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 3}}} \\ {{{h ( n )}}} & {{} {{} {{}=x ( 6 n+2 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 3}}} \\ \end{aligned}
$$
$$
X ( k )=F ( ( k ) )_{4}+W_{18}^{k} G ( ( k ) )_{4}+W_{18}^{( 2 k ) \mathrm{mod18}} H ( ( k ) )_{4}, \; \; \; k=0, 1, 2, \cdots, 23
$$
I. $$
\begin{aligned} {{f ( n )}} & {{} {{} {{}=x ( 7 n ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 3}}} \\ {{g ( n )}} & {{} {{} {{}=x ( 7 n+1 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 3}}} \\ {{{h ( n )}}} & {{} {{} {{}=x ( 7 n+2 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 3}}} \\ \end{aligned}
$$
$$
X ( k )=F ( ( k ) )_{3}+W_{14}^{k} G ( ( k ) )_{3}+W_{14}^{( 2 k ) \mathrm{mod14}} H ( ( k ) )_{3}, \; \; \; k=0, 1, 2, \cdots, 23
$$
J. $$
\begin{aligned} {{f ( n )}} & {{} {{} {{}=x ( 3 n ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 7}}} \\ {{g ( n )}} & {{} {{} {{}=x ( 3 n+1 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 7}}} \\ {{{h ( n )}}} & {{} {{} {{}=x ( 3 n+2 ) \,,}}} & {{{}}} & {{{} {{} n=0 \,, 1 \,, 2 \,, \cdots\,, 7}}} \\ \end{aligned}
$$
$$
X ( k )=F ( ( k ) )_{8}+W_{2 4}^{k} G ( ( k ) )_{8}+W_{2 4}^{( 2 k ) \mathrm{mod24}} H ( ( k ) )_{8}, \; \; \; k=0, 1, 2, \cdots, 23
$$
Answer: J