Discrete Signal and the Stem Plot

I will start using this blog to start researching and documenting the start of the book, "Digital Signal Processing using gnuRadio." After the introduction, the first chapter is on discrete signals. Therefore, let us see what we can do in gnuRadio and python to represent and visualize discrete signals. The gnuRadio data types are as follows:

• Byte: 8 bits per data element
• Short: 2 byte integer
• Int: 4 byte integer
• Float: 4 byte floating point
• Complex: two floats, 8 bytes

A discrete signal is represented by a set of numbers denoted as a sequence

x(n) = {..., x(-1), x(0), x(1), ...}

This is easily done in gnuRadio using a vector block. Since gnuRadio is really about streams of data, it can be a little akward to work outside this framework to demsonstrate some basic DSP principles. First, we will just plot a sequence using gnuRadio and pylab. The discrete nature of the signal can be emphazied through a stem plot. A picture of the discrete signal, x(n) = {-4, -2, 0, 2, 4} for the samples, n = {-2, -1, 0, 1, 2} is given below using pylab, without really using gnuRadio. The code for this example is stem_pylab.py.

Next, we use gnuRadio to add the constant value 2.0 to the above signal. This is accomplished using the add_const_ff(2.0) signal processing block along with the Vector Sink and Source blocks. Note how we set up the gnuRadio graph, Vector Source Block -> Add Constant Block -> Vector Sink Block. We then access the data through dst.data() and plot it using pylab. The code for this example is stem_gnuradio.py.