Exercise 5

Topic: Sampling and interpolation

The task is to study and compare different interpolation techniques to reconstruct the original signal. You shall use this on a band-pass signal, and study frequency downfolding when decimating a time-discrete signal, pre-envelope and complex envelope.

View the example oppgave5.m.  Identify the downfolded frequency components of the decimated signal sz.

Vary the decimation factor. When do we obtain frequency downfolding that is not possible to remove by interpolation (aliasing)?

Use the Matlab command “interp1” to interpolate the decimated signal sd to the original sampling frequency fs. Plot the interpolated signal in time and frequency domain, and also plot the deviation from the original signal. Compare the methods 'nearest', 'linear' and 'spline'. Is it possible to describe all these methods as a transfer-function in the frequency plane? If it is possible, what is the impulse and frequency response?

Also test the Matlab command “interp”. Describe the differences between these two functions. Which method gives the best result?

Find the minimal sampling frequency (max decimation factor) which gives a reconstruction error < 1% (power), that is -20 dB, for the different methods.

What is the result if we decimate/interpolate the complex envelope, and then reconstruct the real band-pass signal? Is it possible to achieve equally good results by using the pre-envelope signal?