# Listening to FM Radio in Software, Step by Step

My article “GNU Radio: Tools for Exploring the Radio Frequency
Spectrum” [*LJ*, June 2004] provides an
overview of how the GNU Radio system
works and discusses a couple hardware options for
getting the RF signals digitized and into the computer. This article
takes a look at how to use GNU Radio to listen to FM radio.

The hardware setup used in this article is shown in Figure 1. It's the brute-force, no-frills approach and is good for explaining how everything works. Later in the article, we discuss the Universal Software Radio Peripheral (USRP) and what it can do for you.

Our setup consists of a conventional FM dipole antenna, a cable modem tuner module mounted on an evaluation board and a 20M sample/second PCI analog-to-digital converter (ADC) card. The antenna plugs in to the input of the tuner module. The tuner module IF output is connected with a piece of coaxial cable to the ADC input on the back of the computer. The tuner module eval board is connected to the PC's parallel port so that we have a way of controlling the module.

The specific hardware we're using is a Microtune 4937 DI5 3X7702 cable modem tuner module and a Measurement Computing PCI-DAS 4020/12 ADC board. This particular tuner module is hard to get, but others, such as those from Sharp Microelectronics, ought to work fine (see the on-line Resources section).

The cable modem tuner functions as our RF front end and is responsible for translating the radio frequency signals that we're interested in down to a range that our ADC can deal with. In this case, the module translates a selectable 6MHz chunk of the spectrum in the range of 50MHz–800MHz down to a 6MHz chunk centered at 5.75MHz. For more background on these concepts, see the June article mentioned previously.

First off, let's take a look at what happens when we tune our front end to the middle of the FM band, say 100.1MHz. Figure 2 shows the received samples vs. time. This view, the time domain, is what you'd see on an oscilloscope. It's not particularly enlightening, but it does show that our samples are in the range of –170 to –70, which is fine. In an ideal world, they would be symmetric about zero. For our purposes, the offset won't matter.

The frequency domain provides additional information. In this case, we grab 1,024 samples at a time and compute the discrete Fourier transform using the fast Fourier transform (FFT) algorithm. This gives us a representation of the frequencies that are contained in the input signal. Figure 3 shows the resulting spectrum. The x-axis is frequency, and the y-axis is power in decibels (10 * log10 power). The low end is at zero Hz, and the top end is at 10MHz, half our sampling rate.

Each of the spikes in Figure 3 is a radio station. Our software sees them all at once! To listen to a station, we need a way to separate it from all of the others, translate it to baseband (DC, 0Hz) and reverse the effect of the frequency modulation. We work through this step by step, but first let's talk about FM.

To understand how an FM receiver works, it's helpful to know a bit about how FM signals are generated. With FM, the instantaneous frequency of the transmitted waveform is varied as a function of the input signal. Figure 4 shows m(t), the input signal (the message, music and so forth), and s(t), the resulting modulated output. To be rigorous, the instantaneous frequency at any time is given by the following formula:

f(t) = k*m(t) + fc

m(t) is the input signal, k is a constant that controls the frequency sensitivity and fc is the frequency of the carrier (for example, 100.1MHz). Remember that frequency has units of radians per second. As a result, frequency can be thought of as the rate at which something is rotating. If we integrate frequency, we get phase, or angle. Conversely, differentiating phase with respect to time gives frequency. These are the key insights we use to build the receiver.

## Comments

## @dinesh

and that is why lots of americans don't have jobs, right?

## fm demodulation

sir, i need the total detail of fm demodulation which have sdr applications using vhdl domain and also matlab programs and vhdl coding for all about fm demodu.........

fm demodu rceiver circuit diagram also plz send it to my mailid as soon as possible sir

## details

I would like to start a New Fm station. can u give the details for what r the software we want to bye

## Off-Line station break-out

If the break-down of the signal(s) into multiple stations is too much for your CPU, how about recording a more raw version of the input and then breaking it down into multiple stations at a more leisurely rate, possibly even on more than one computer.

If this seems reasonable, could you give some ideas on where to make these changes?

Thanks