upsample impulse response

Question

I have a system and I know its impulse response $h$, this impulse response was recorded at $f_s = 48000 \texttt{Hz}$, now I can use Matlab to get the system output to an arbitrary signal ($x$) by convolving it with $h$, right?

So now I want to use an input signal that its at a higher frequency [$3.072 \texttt{MHz}$ (factor $64$)] but want to use the same IR, I was hopping to just upsample the IR, either by zero padding or by interpolating the $63$ spaces between coefficients, but the output was not matching, using Matlab I got the frequency response of the Impulse response, in blue the original sampled at $48 \texttt{KHz}$, the red one is the upsampled one, yellow the interpolated.

They kind of match, but there are several gaps in the plot, is this even doable? This is my Matlab code (top_ir is the impulse response of the system):

[h, w] = freqz(top_ir,1,[],48000);
plot(w,20*log10(abs(h)));
top_ir_3m = upsample(top_ir, 64);
[h, w] = freqz(top_ir_3m,1,[],48000*64);
plot(w,20*log10(abs(h)));
top_ir_3m = interp(top_ir, 64);
[h, w] = freqz(top_ir_3m,1,[],48000*64);
plot(w,20*log10(abs(h)));

EDIT (adding info): I understand that the original IR only contains information up to 24kHz, that is fine, we are actually going to lowpass filter everything up to 24kHz.

Answer 1

NOTE: Your terminology and information provided is somewhat confusing. An impulse response is a time signal. What you plotted seems to be some kind of spectrum. I'm not familiar with matlab, but a quick look in the documentation of freqz leaves me wondering, what your code actually does. The plot does as well.

Anyway, if you recorded your impulse response with a 48kHz sampling frequency, it does not contain any information regarding the system's behaviour above 24kHz. There is no way to garner this information by interpolating/upsampling. While algorithms for bandwidth expansion do exist, a factor of 64 seems to be a very long shot in any case.

Answer 2

After some testing I found out that Matlab caps the frequency response result, changing the taps for the freqz to the length of the coefficients give the actual result, upsampling does generate a usable impulse response, to use an interpolated impulse response, you just need to divide the coefficients by the oversample rate