Applying Kaiser Window to sinc interpolation

Question

I am trying to apply the kaiser window during sinc interpolation.

The following is my sinc interpolation code:

def sincTrain(sig, interpolationFactor):
    tn = np.arange(0,len(sig),1)
    t  = np.arange(0,len(sig),1/interpolationFactor)
    
    sincTrain = np.zeros((len(t),len(sig)))
    
    w = np.kaiser(len(t),2.5)
    nind = 0
    for n in tn:
        sincTrain[:, nind] = sig[nind]*np.sinc((t - n)) * w
        nind+=1

    return np.sum(sincTrain,1)

I realised that the kaiser window does not follow my sinc function. I have added the plots below to better illustrate the problem I am having.

How can I modify the code such that the kaiser window moves along with the sinc function?

Answer 1

You are using t-n as the argument for sinc(), in order for it to be calculated at different points in time, but you are generating the window based on a fixed t. Try applying t-n there, as well. Also, don't forget that the widow looks to be shifted, while your sinc starts at 0.