# Signal Resampling by a non integer factor with convolution

to start I am a newbie in signal processing, I just started a month ago so please be as detailed as possible.

From what I understood to resample a signal by a non integer factor you can do an upsample followed by a downsample. So, imagining a sample set of size 10 and if you want to upsample it to 15, you can upsample it by 3 and downsample it by 2, correct?

If that is true, does one can create a kernel by merging the two kernels the upsampling and downsampling ones?

To upsample by 3 we can use the kernel [1/3, 2/3, 1, 2/3, 1/3] and to downsample by 2 we can use the kernel [1, 0]. Can I create just a kernel to do both operations?

If instead I use interpolation, can I do it using a kernel as the above?

• You can by multiplying "convolving" the two sequences to create the combined one. Be aware of tail effects due to length of "filters" and possible aliasing. – Moti May 5 '18 at 1:09
• @Moti How can I multiply the convolution then? Can you point me in the right direction please? – Pedro Pereira May 5 '18 at 13:52
• Implement to sequential processes, starting with the upsampling. You may also "calculate" each sample to its location (given the value) but the coefficients will be different from sample to sample. – Moti May 7 '18 at 0:42