[[TOC(DSP/Interpolation*, depth=3)]]

= 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.[[BR]]

Before continuing with this tutorial for further reading for understanding Interpolation read the following resources:
* [http://dspguru.com/dsp/faqs/multirate/interpolation DSPGuru - Interpolation]
* [http://en.wikipedia.org/wiki/Upsampling Wiki - Upsampling] 

== Materials Required ==
* [http://www.orbit-lab.org/userManagement/register 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 [http://gnuradio.org/redmine/projects/gnuradio/wiki/InstallingGR 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:

[[Image(img1.png,650px)]]

[[Image(img2.png, 500px)]][[Image(img3.png, 500px)]]

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

[[Image(img4.png,650px)]] [[BR]]

Verify that the Scope and FFT plots are:

[[Image(img5.png, 500px)]][[Image(img6.png, 500px)]]

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.

[[Image(img7.png, 650px)]]

Verify that the smoothed out signal plots resemble:

[[Image(img8.png, 500px)]][[Image(img9.png, 500px)]] 
== 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:

[[Image(img10.png, 650px)]]

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 ==