Interpolation Tutorials

Introduction

Interpolation, also known as upsampling in the case of Digital Signal Processing, is a process that provides an approximation of the signal that would have been obtained if it had been sampled at a higher sample rate.

Before continuing with this tutorial for further reading for understanding Interpolation read the following resources:

• ​DSPGuru - Interpolation
• ​Wiki - Upsampling

Materials Required

• ​Orbit Account
• Installation of GNURadio
• Reservation on Orbit Lab
• WAV File

Installing GNURadio

If running on a Ubuntu or Debian distribution of Linux use the following command for installation:

sudo apt-get install gnuradio

For other OS's follow the instructions from this ​guide.

Interpolation of a Sinusoidal Wave with GNURadio

In GNURadio on your computer implement the following flow chart to obtain the following FFT and Scope Plots:

Next add a Interpolation FIR Filter with an Interpolation of 3 as seen below:

Verify that the Scope and FFT plots are:

The waveforms can be seen with 3 zeros inserted from the Interpolation FIR Filter between every sampled point. Next apply a Low Pass Filter as seen below to smooth out the waveform.

Verify that the smoothed out signal plots resemble:

Interpolation of a .WAV File with GNURadio

For the following download the .WAV File and listen to the audio file. Then set up the following flowgraph in GNURadio:

Go back to the original .WAV File and listen to the audio. Then listen to the output file and notice the difference and effects of upsampling an audio sample.

Interpolation of a Sinusoidal Wave with Octave

To start off make a simple sine wave

signal = sin(2*pi*3.*[0:.01:1]);
plot(signal);

Then continue by entering

signal_zeropadded = [signal;zeros(3,length(signal))];
signal_zeropadded = signal_zeropadded(:);
pkg load signal
b = fir1(10,.12);
signal_interpolated=filter(b,1,signal_zeropadded);
plot(signal_interpolated)

Interpolation of a .WAV File with Octave

[signal, fs] = auload("island(1).wav");
signal_zeropadded = [signal;zeros(3,length(fs))];
signal_zeropadded = signal_zeropadded(:);
pkg load signal
b = fir1(10,.12);
signal_interpolated = filter(b,1,signal_zeropadded);
plot(signal_interpolated)

The plot should look like

Then to save the interpolated signal as a .WAV file with the following command

wavwrite(signal_interpolated, 'islands.wav');

Troubleshooting

Audio Package

If your receive an error stating that you don't have the audio package in Octave you will need to install the following package.

sudo octave
pkg install -forge audio

If this tells you to install liboctave-dev, in a different terminal enter

sudo apt-get install liboctave-dev

then retry the above steps for package installation.

To verify that you have the package installed you can enter

pkg list

and should see the following

The audio package uses external software to play and record audio. The following should be sufficient.

sudo apt-get install sox

Signal Package

If you receive the following error

you will need to install the signal package.

To install the signal package you will need to use the following commands

sudo octave
pkg install -forge signal

If you receive the following error:

you will need to install the control package with the command

pkg install -forge control

Then redo the package installation for the signal package.