In the L5 Lab you recorded a few seconds of the FM band to fm_capture.cfile. The figure is a file of the same kind: 2.4 million complex samples per second around 100.0 MHz, holding a station at 100.3 MHz and a weaker one at 99.5 MHz. It came from a GNU Radio flowgraph rather than an antenna, so the figure carries a “Simulated” label. The station at 100.3 MHz carries a two-tone message, the L6 message of 1 kHz and 2.5 kHz, and its name, “ECE 448”, in RDS data.

By the end of the lesson we will turn that file into audio, read the station’s name out of it, and then point the same flowgraph at the live band. We will also build an AM receiver for the aircraft band and compare AM and FM in the same noise.

Frequency modulation (FM) leaves the carrier’s amplitude alone and moves its frequency instead. The instantaneous frequency is

where the message \(x(t)\) stays between \(-1\) and 1, and the peak deviation \(\Delta f\) is the farthest the carrier ever moves. Broadcast FM sets \(\Delta f\) = 75 kHz and carries audio up to \(W\) = 15 kHz, which makes it wideband FM (WBFM). Two-way radios use narrowband FM, with \(\Delta f\) near 2.5 or 5 kHz. The ratio of the deviation to the message frequency \(f_m\) is the modulation index, \(\beta = \Delta f / f_m\); for broadcast FM at its top audio frequency it is 75/15 = 5.

An FM signal is a little wider than \(2\Delta f\), because the frequency swings at audio rates. A rule of thumb, Carson’s rule, puts the width at about \(2(\Delta f + W)\), which is the number we need to set the receiver’s channel filter. For broadcast audio that is \(2(75 + 15)\) = 180 kHz, which fits the 200 kHz spacing of US FM channels, 88.1 to 107.9 MHz. An AM signal carrying the same audio would be 30 kHz wide.

L07-wbfm-rx.grc is the whole receiver in six processing blocks. The File Source plays a recording, and the PlutoSDR Source receives live at the same 2.4 MS/s, with manual gain from the RF gain slider; GRC grays it out because we disabled it. Both feed the same channel filter, so switching from a file to the air means disabling one source and enabling the other. Neither path needs a Throttle: the Audio Sink takes exactly 48,000 samples per second, as in Lesson 6, and that paces the File Source too.

The two variables at the top tie the receiver to the radio. fc_mhz is the frequency we tune the SDR to, or the center frequency we recorded the file at, and station_mhz is the station we want. The next four frames describe the chain one block at a time.

The station sits 300 kHz above the center of the capture, and everything else in the 2.4 MHz is something we do not want. The Frequency Xlating FIR Filter does three jobs in one block. It multiplies by a complex tone at \(-300\) kHz, which moves the station to 0 Hz, the same frequency shift as Lesson 6’s coherent receiver. It applies a low-pass filter, here a 105 kHz cutoff with a 30 kHz transition, which passes ±90 kHz and is 28 dB down by ±120 kHz, far enough to remove the station at 99.5 MHz. Then it keeps every tenth sample.

Decimating by 10 leaves 240,000 samples per second. That rate holds everything the filter passes, and it holds the whole demodulated signal of the next frames, which reaches 59.4 kHz. Its center frequency is the expression (station_mhz - fc_mhz) * 1e6, so typing 99.5 into Station tunes the other station.

After the channel filter the station is a complex signal whose phase turns faster or slower as the frequency moves. The Quadrature Demod block measures how far the phase turns from one sample to the next, which is the frequency at that instant.

The gain scales that frequency into a convenient number. With the gain above, a carrier 75 kHz above center produces an output of exactly 1, so the output is the transmitted message at its original scale. The block ignores amplitude entirely, which is why an FM receiver needs no AGC, and why a weakening FM station keeps its volume until the noise gets strong enough to break it up, as a later frame shows.

The demodulator does not output audio; it outputs whatever the station put on its carrier, which is several signals side by side. The mono audio, the sum of the left and right channels, fills 0 to 15 kHz, so a mono receiver works by keeping only that band. A stereo station adds the difference of the two channels as DSB-SC on 38 kHz, the signal of Lesson 6 that needs carrier recovery, and sends a 19 kHz pilot so receivers can rebuild the 38 kHz carrier by doubling it. Above that, at 57 kHz, three times the pilot, sits RDS.

A Decimating FIR Filter keeps the mono band, 0 to 15 kHz with a 3 kHz transition, and decimates by 5 to the sound card’s 48 kHz. Every other part of the multiplex is above 15 kHz, so this one filter removes the pilot, the stereo signal, and RDS.

The transmitter boosts the treble of its audio before modulating, a step called pre-emphasis. The FM Deemphasis block applies the opposite filter, set by a 75 μs time constant with its corner at 2.1 kHz, which restores the original audio balance. Because the noise rises with frequency, cutting the treble at the receiver removes noise where the noise is strongest. Europe uses 50 μs, so a European station received with the US setting sounds slightly dull but is otherwise correct.

The figure is the receiver running on the test file. The bottom right sink is the audio after de-emphasis, with the 1 kHz and 2.5 kHz tones of the message and nothing else above the floor, which is the check that the receiver works: the demodulated audio matches what the test transmitter sent. Type 99.5 into Station and the audio changes to the second station’s single, different test tone.

To use your own L5 capture, set the File Source’s file to fm_capture.cfile, type the center frequency you recorded at into SDR center, and set Station to the station you centered. To receive live, disable the File Source, enable the PlutoSDR Source, and run it again. A real station’s audio sink will show music or speech rather than two lines.

The Radio Data System (RDS, called RBDS in North America) adds a slow digital channel to an FM station. It runs at 1187.5 bits per second, which is 57 kHz divided by 48, on a 57 kHz subcarrier. The bits ride the subcarrier as BPSK, which is a DSB-SC signal like Lesson 6’s, so the receiver has to recover the carrier. The bits are also differentially coded, so the receiver needs only the changes between bits, and a 180° error in the recovered carrier does no harm.

The data arrives in short groups, a fraction of a second each. The PI code is the station’s identifier, the PS name is the eight characters a car radio displays, sent two per group, and the radiotext is up to 64 characters of free text.

L07-rds-rx.grc is the WBFM receiver with an RDS branch added to the demodulator’s output, following the receiver that ships with gr-rds. A second Frequency Xlating FIR Filter moves 57 kHz to 0 Hz and decimates to 24 kHz, and a Rational Resampler converts to 19 kHz, which is exactly 16 samples per bit. A filter matched to the RDS symbol shape, an AGC, and a Symbol Sync find the bit timing, and the Constellation Receiver recovers the subcarrier’s phase, which is the carrier recovery Lesson 6 said DSB-SC needs. The two tight clusters on the constellation show it working. A Differential Decoder undoes the differential coding, and the three gr-rds blocks find the groups, check them, and display what they carry.

The panel shows “ECE 448” and the test transmitter’s radiotext. It also shows the station’s PI code, 1093 in hexadecimal, under “Program Type” and the program type under “PI”: the panel swaps those two labels, so read them the other way around on a live station too. The RDS blocks come from gr-rds, which radioconda installs as gnuradio-rds.

Aircraft and control towers talk in AM between 118 and 137 MHz, and most airports with a control tower broadcast an ATIS, a recorded loop of the current weather and runway in use, continuously on one of those frequencies. That makes ATIS a steady signal to receive, as Lesson 6 suggested. L07-am-rx.grc has the same front end as the FM receiver: a File Source or the PlutoSDR, and a Frequency Xlating FIR Filter. This one cuts off around 5 kHz, just above the 3 kHz voice band, and it decimates by 50, from 2.4 MS/s straight to the sound card’s 48 kS/s.

After the filter, the AM station is a complex signal with its carrier at 0 Hz, and its envelope is the magnitude of each sample. Complex to Mag replaces the Abs block of Lesson 6, and the rest is the L6 receiver: the same 3 kHz low-pass taps and a DC Blocker that removes the carrier’s constant. An AGC block then holds the audio level steady, because a station’s strength depends on the aircraft’s distance and an AM receiver’s output depends on it directly. The figure shows the receiver on L07-am-test.sigmf-data, which carries the L6 two-tone message at \(m\) = 0.5; the audio repeats every 2 ms, as it did in Lesson 6.

L07-am-vs-fm.grc sends one 1 kHz tone two ways with the same transmitted power: as AM at \(m\) = 1, the best case from Lesson 6, and as FM. The figure runs FM at 15 kHz deviation with the Input SNR at 25 dB. Both go through the same noise. Each receiver filters to its own channel, 10 kHz for AM and a wider one for FM, and then the same 5 kHz audio filter. The Input SNR slider sets how strong the signal is against the noise in a 10 kHz channel, and two meters show each receiver’s output SNR, the tone against everything else in its audio. The Listen to buttons switch the speaker between the two.

With this strong signal the FM output is clearly the cleaner one, even though the FM receiver’s wider channel lets in more noise. The spectrum shows it: FM’s noise floor sits well under AM’s. Drag the deviation up and FM’s meter climbs further; drag it down and most of the advantage goes away. FM buys a cleaner output with bandwidth.

Now drag the Input SNR slider down with the speaker on FM. The FM output stays clean longer than AM’s does, and then it starts to crackle with clicks and its meter drops quickly. In the figure, at 8 dB with 15 kHz deviation, the two meters read about the same, and both tones on the time sink are ragged. That sudden collapse is the point where FM breaks into clicks: FM’s advantage lasts only while the signal stays well above the noise in its own, wider channel. AM has no such point; its hiss rises steadily as the slider comes down, and the tone stays recognizable. Repeat the sweep at a narrower and a wider deviation: the wider the deviation, the cleaner FM sounds when the signal is strong, and the sooner it breaks up as the noise rises.

That trade is why broadcast FM and aircraft radios chose differently. A broadcast station is strong and has a 200 kHz channel to fill, so it uses FM. Aircraft use AM because a weak AM signal stays intelligible, and because two aircraft transmitting at once are both heard, where an FM receiver would lock onto the stronger one.

Before decoding anything on the air, find the station and hear it. Run the Lesson 5 flowgraph, L05-fm-spectrum.grc, on the PlutoSDR and drag across 88 to 108 MHz; a strong station is a tall stripe about 200 kHz wide on the waterfall. Stop it, since only one flowgraph can stream from the Pluto at a time. Open L07-wbfm-rx.grc, disable the File Source, enable the PlutoSDR Source, and run it with Station set to that frequency and SDR center a few hundred kilohertz away; the next frame says why. The station plays.

Write down the frequency and the call sign the station gives at the top of the hour, or the one the FCC lists for that frequency in your area. That name is the check that the RDS flowgraph decodes the station correctly.

The same receiver also plays narrowband FM, badly, which shows what its settings are for. Tune a NOAA weather radio channel, 162.400 to 162.550 MHz in 25 kHz steps, which broadcasts continuously; this is receive only, like everything in this lesson. The deviation is about 5 kHz instead of 75, so the voice comes out about a fifteenth as loud as the receiver expects, and the 180 kHz channel filter lets in far more noise than the few tens of kilohertz the signal occupies.

On the air, the receivers need three settings from Lesson 5. Tune the SDR a few hundred kilohertz away from the station, so the center of the band stays out of the channel filter, and type the station’s real frequency into Station. The center is where the PlutoSDR’s DC tracking acts and where any offset it leaves behind sits, so a shift under about 100 kHz puts both inside the channel, where they show up as distortion or hum. Set the RF gain slider to the highest gain in your L5 Lab gain table at which no new signals appeared between stations. For ATIS, look up the airport’s frequency in the FAA Chart Supplement or on a sectional chart, and expect a weaker signal than broadcast FM, because aircraft band stations are lower in power and need line of sight. The Pluto’s own frequency can be off by a few kilohertz there; if the ATIS sounds muffled, nudge Station by 1 to 3 kHz.

RDS needs a stronger signal than the audio does, because its 57 kHz subcarrier sits where the multiplex noise is highest. If the station name never appears, raise the gain or choose a stronger station before changing the flowgraph. As Lesson 2 said, receiving is unrestricted and transmitting is not; every flowgraph here uses only the PlutoSDR’s receive port, and nothing in this lesson transmits.

Today we built a broadcast FM receiver, added an RDS decoder to it, built an AM receiver for the aircraft band, and watched what FM’s extra bandwidth does as the noise goes up. The L7 Lab is the bench version: play your own L5 capture through the receiver, receive a live station and its RDS name, receive an ATIS broadcast, and turn the noise up on AM and FM yourself.

An extension from the 2025 course: build a dual FM receiver, two Frequency Xlating FIR Filters on one capture, that plays two stations at once.

Lesson 8 moves from analog to digital modulation. Its first signal, frequency-shift keying, is FM with a message that takes only two values, so its receiver uses the same quadrature demodulator as today’s.