ADCs have two primary characteristics, sampling rate and dynamic range. Sampling rate is the number of times per second that the ADC measures the analog signal. Dynamic range refers to the difference between the smallest and largest signal that can be distinguished; it's a function of the number of bits in the ADC's digital output and the design of the converter. For example, an 8-bit converter at most can represent 256 (28) signal levels, while a 16-bit converter represents up to 65,536 levels. Generally speaking, device physics and cost impose trade-offs between the sample rate and dynamic range.
Before we dive into the software, we need to talk about a bit of theory. In 1927, a Swedish-born physicist and electrical engineer named Harry Nyquist determined that to avoid aliasing when converting from analog to digital, the ADC sampling frequency must be at least twice the bandwidth of the signal of interest. Aliasing is what makes the wagon wheels look like they're going backward in the old westerns: the sampling rate of the movie camera is not fast enough to represent the position of the spokes unambiguously.
Assuming we're dealing with low pass signals - signals where the bandwidth of interest goes from 0 to fMAX, the Nyquist criterion states that our sampling frequency needs to be at least 2 * fMAX. But if our ADC runs at 20 MHz, how can we listen to broadcast FM radio at 92.1 MHz? The answer is the RF front end. The receive RF front end translates a range of frequencies appearing at its input to a lower range at its output. For example, we could imagine an RF front end that translated the signals occurring in the 90 - 100 MHz range down to the 0 - 10 MHz range.
Mostly, we can treat the RF front end as a black box with a single control, the center of the input range that's to be translated. As a concrete example, a cable modem tuner module that we've employed successfully has the following characteristics. It translates a 6 MHz chunk of the spectrum centered between about 50 MHz and 800 MHz down to an output range centered at 5.75 MHz. The center frequency of the output range is called the intermediate frequency, or IF.
In the simplest-thing-that-possibly-could-work category, the RF front end may be eliminated altogether. One GNU Radio experimenter has listened to AM and shortwave broadcasts by connecting a 100-foot piece of wire directly to his 20M sample/sec ADC.
On to the Software
GNU Radio provides a library of signal processing blocks and the glue to tie it all together. The programmer builds a radio by creating a graph (as in graph theory) where the vertices are signal processing blocks and the edges represent the data flow between them. The signal processing blocks are implemented in C++. Conceptually, blocks process infinite streams of data flowing from their input ports to their output ports. Blocks' attributes include the number of input and output ports they have as well as the type of data that flows through each. The most frequently used types are short, float and complex.
Some blocks have only output ports or input ports. These serve as data sources and sinks in the graph. There are sources that read from a file or ADC, and sinks that write to a file, digital-to-analog converter (DAC) or graphical display. About 100 blocks come with GNU Radio. Writing new blocks is not difficult.
Graphs are constructed and run in Python. Example 1 is the "Hello World" of GNU Radio. It generates two sine waves and outputs them to the sound card, one on the left channel, one on the right.
Example 1. Dial Tone Output#!/usr/bin/env python
from gnuradio import gr
from gnuradio import audio
def build_graph ():
sampling_freq = 48000
ampl = 0.1
fg = gr.flow_graph ()
src0 = gr.sig_source_f (sampling_freq, gr.GR_SIN_WAVE, 350, ampl)
src1 = gr.sig_source_f (sampling_freq, gr.GR_SIN_WAVE, 440, ampl)
dst = audio.sink (sampling_freq)
fg.connect ((src0, 0), (dst, 0))
fg.connect ((src1, 0), (dst, 1))
return fg
if __name__ == '__main__':
fg = build_graph ()
fg.start ()
raw_input ('Press Enter to quit: ')
fg.stop ()
We start by creating a flow graph to hold the blocks and connections between them. The two sine waves are generated by the gr.sig_source_f calls. The f suffix indicates that the source produces floats. One sine wave is at 350 Hz, and the other is at 440 Hz. Together, they sound like the US dial tone.
audio.sink is a sink that writes its input to the sound card. It takes one or more streams of floats in the range -1 to +1 as its input. We connect the three blocks together using the connect method of the flow graph.
connect takes two parameters, the source endpoint and the destination endpoint, and creates a connection from the source to the destination. An endpoint has two components: a signal processing block and a port number. The port number specifies which input or output port of the specified block is to be connected. In the most general form, an endpoint is represented as a python tuple like this: (block, port_number). When port_number is zero, the block may be used alone.
These two expressions are equivalent:fg.connect ((src1, 0), (dst, 1))
fg.connect (src1, (dst, 1))
Once the graph is built, we start it. Calling start forks one or more threads to run the computation described by the graph and returns control immediately to the caller. In this case, we simply wait for any keystroke.
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