Why do I get different answer between circular shifting and modulation for FFT?

I was trying to get a 64 point DFT of a sequence that does not start from the origin: ( x[-2], x[-1], x[0], x[1], x[2], x[3], x[4], x[5]), x[n] all equal to 5 for n= -2 to 5. and I tried to do it in two ways: first is do the circular shift and then use fft lke:

xcircst = horzcat( horzcat( [5 5 5 5 5 5], zeros( 1, 56)),[5 5]);

XK = fft (xcircst);

But it end up with a different answer from :

k = (0 :1: 63);

modulate = exp(-j*2*pi*k*2/64); 

X = fft([5 5 5 5 5 5 5 5]) .*modulate;

Can some one tell me the reason why this happened? I through the circular shift would lead to the same result as modulation in frequency domain after DFT, but the results seems to disagree with that.

[Jiayu He]

there is a typo at the last line, it should be .*modulat

[Jiayu He]

X is the sequence after modulation, XK is the sequence after circular shift

[Adam]

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Answer 1

[Honglei Chen]

You are shifting the signal by 62 samples, not 2 samples, so you should define your modulate as

modulate = exp(-j*2*pi*k*62/64);

HTH

[Jiayu He]

Thanks, seems I messed up with the sign.