Proving the form of reconstructed sampled signal (without using Matlab)

[scdoro]

Hi all,

Can someone help me to prove this question without using Matlab.

I have found the sampled signal x to be
x=[0 0.125 0.25 0.125 0 -0.125 -0.25,-0.125] since 8 samples in 1 secs.

Qn1) since the sampled signal is x=[0 0.125 0.25 0.125 0 -0.125 -0.25 -0.125]
we can actually show that the reconstructed signal of 2 sine waves by purely using FFT in Matlab.

But how can i prove it without using Matlab? Cani present it by drawing the graph of the original triangular wave and then sampled it using those points above. After that, i deduce that i can form 2 sine waves from there. i will first connect sample set A[0,0.25,0,-0.25] and the other sample set B[0,0.125,0,125,0,-0.125,-0.125].

Please enlightened.

thanks

regards
scdoro

 

[pixel]

Re: Proving

I would do also as you, but everything depends on how much your teacher likes math.

 

[vadkudr]

Re: Proving

I recommended you in PM to analyze multiplication of signal vector to FFT matrix.

It can be proved in next way.
1. signal has one full period during observed interval.
2. signal is antisymmetrical.

these two observations lead to
1. spectrum is fully imaginary
2. spectrum will have non-zero coefficients only on odd frequency bins.

So they are 1st and 3rd bins
Two sinusoids