Can you present the convolution of sinusoidal with itself?
For your data points I get:


  -2.467162e-16 -9.045085e-01 -1.118034e+00  7.725425e-01  2.500000e+00  7.725425e-01 -1.118034e+00 -9.045085e-01 -1.480297e-16


from

#27154    
data &lt;- c(0.951056516295, 0.587785252292, -0.587785252292, -0.951056516295, 0.) 
output &lt;- convolve(data,data, type ="open")