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?

you want to center the sinc function and the Kaiser window together. that's now how you are displaying it now. — robert bristow-johnson, Oct 04 '22 at 15:31

score 2 · Accepted Answer · answered Oct 04 '22 at 08:36

2

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.

answered Oct 04 '22 at 08:36

a concerned citizen

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I understand the issue now. Could you also explain how the kaiser window can be converted to change with t-n ? The in-built numpy package only allows for a kaiser window to be generated based on a fixed t. – Hari Oct 05 '22 at 07:56
If it doesn't allow shifting then you may need to implement the function, yourself. This might help. – a concerned citizen Oct 05 '22 at 16:12
okay thank you, I will try implementing the function myself – Hari Oct 06 '22 at 03:36

Applying Kaiser Window to sinc interpolation

1 Answers1