The basic radix-2 FFT algorithms based on decimation-in-time are indicated in th

Question

The basic radix-2 FFT algorithms based on decimation-in-time are indicated in the text, Figures 5 and 6. For each of these eight flow-graphs indicate whether or not each of the following properties is true or not with necessary justifications. Represents an in-place computation Input is in normal order Output is in normal order Coefficients should be stored in bit-reversed order Accessing of the data is identical for every array. If x(n)=[1, 2, 3, 2, 1, 0, 1, 2] calculate FFT using the flow graph given in Figure 5.

Explanation / Answer

i)Fig. 5 is FFt which uses in-place computation.

ii)For fig 5.Input is 0,4,2,6,1,5,3,7.It is not in normal order.For fig 6.Input is 0,1,2,3,4,5,6,7.It is in normal order.

iii)For fig 5.output is 0,1,2,3,4,5,6,7.It is in normal order.For fig 6.output is 0,4,2,6,1,5,3,7.It is not in normal order.

iv)Fig 5,is FFT i.e. Fast Fourier Transform and for FFT coefficients are stored in bit-reversed order.

Fig 6,is IFFTi.e.Inverse Fast Fourier Transform and for IFFT coefficients are also stored  in bit-reversed order.As we can see from fig.

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