2
$\begingroup$

According to Sampling theorem, in order to reconstruct a signal we need to sample it at the rate => twice the highest frequency component of that signal. (provided signal is band limited).

Let's say, we have a signal with f= 2MHz (highest freq component), so we will be sampling it at 4MHz or more as Sampling theorem say's.. and we will have N Samples in signal.

Now, what if I want to know the exact value of a sample (information) between two samples..??

How can we find the value at every possible instantaneous.. in a signal..when we know we only have N samples after sampling..??

I know we can increasing sampling rate to have more sample. But is there any other way to do it..?

This question was asked to me in an interview at NCRA-TIFR, Pune, India.

|improve this question
$\endgroup$
4
$\begingroup$

Interpolation using a Sinc function kernel. This assumes that the sampled signal was perfectly bandlimited to below half the sampling rate.

Note that perfectly bandlimited signal are infinite in extent. For finite-length "real world" signals, using a windowed Sinc interpolation kernel (thus a finite computation with a noise floor) is a common method to approximate points between samples (for upsampling, for instance).

|improve this answer
$\endgroup$
  • $\begingroup$ Answer with the sinc kernel is correct. It is due to the fact that sinc is the inverse fourier transform of the ideal lowpass filter. $\endgroup$ – VK69UK Feb 21 '16 at 8:12
  • $\begingroup$ Perfectly bandlimited, and not quantized in amplitude! $\endgroup$ – Laurent Duval Feb 21 '16 at 15:22
  • $\begingroup$ Quantization is just one of the potential contributors to the noise floor. Often not the biggest. $\endgroup$ – hotpaw2 Feb 21 '16 at 17:42
3
$\begingroup$

Another way to do it (eg: converting N samples to 2N): take the N point FFT of the signal, then zero pad the frequency domain result to 2N. Then compute the 2N sized inverse.

But note that when zero padding the N point frequency domain result, the zero padding is done in the middle of the spectrum, and the Fs/2 bin is split between the upper and lower halves of the spectrum. For instance, using 8 points as an example, where element A is the zero frequency bin, and element E is your Fs/2 bin:

A B C D E F G H ---- zero pad ----> A B C D E/2 0 0 0 0 0 0 0 E/2 F G H -------> inverse FFT

Such an operation will give you a 2N result where every other value is an interpolated one.

|improve this answer
$\endgroup$
0
$\begingroup$

watch Digital show & Tell from Xiph.org. Same situation only sound frequency. They explain better as i can why there is just one possible solution from every set of samples

|improve this answer
$\endgroup$
0
$\begingroup$

Another practical approach is to delay the signal a fraction of the sample period using a fractional delay filter.

|improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.