libcsdr

libcsdr is a set of simple DSP routines for Software Defined Radio.
It is mostly useful for AM/FM/SSB demodulation and spectrum display.
Feel free to use it in your projects.
Most of the code is available under the permissive BSD license, with some optional parts under GPL. For additional details, see licensing.

• The package comes with a command-line tool csdr, which lets you build DSP processing chains by shell pipes.
• The code of libcsdr was intended to be easy to follow.
• libcsdr was designed to use auto-vectorization available in gcc. It means that it can achieve some speedup by taking advantage of SIMD command sets available in today's CPUs (e.g. SSE on x86 and NEON on ARM).

How to compile

The project was only tested on Linux. It has the following dependencies: libfftw3-dev

make
sudo make install

If you compile on ARM, please edit the Makefile and tailor PARAMS_NEON for your CPU. To run the examples, you will also need rtl_sdr from Osmocom, and the following packages (at least on Debian): mplayer octave gnuplot gnuplot-x11

Credits

The library was written by Andras Retzler, HA7ILM <randras@sdr.hu>.

I would like to say special thanks to Péter Horváth, PhD (HA5CQA) and János Selmeczi, PhD (HA5FT) for their continous help and support.

Usage by example

Demodulate WFM

rtl_sdr -s 240000 -f 89500000 -g 20 - | csdr convert_u8_f | csdr fmdemod_quadri_cf | csdr fractional_decimator_ff 5 | csdr deemphasis_wfm_ff 48000 50e-6 | csdr convert_f_i16 | mplayer -cache 1024 -quiet -rawaudio samplesize=2:channels=1:rate=48000 -demuxer rawaudio -

• Baseband I/Q signal is coming from an RTL-SDR USB dongle, with a center frequency of -f 104300000 Hz, a sampling rate of -s 240000 samples per second.
• The rtl_sdr tool outputs an unsigned 8-bit I/Q signal (one byte of I sample and one byte of Q coming after each other), but libcsdr DSP routines internally use floating point data type, so we convert the data stream of unsigned char to float by csdr convert_u8_f.
• We want to listen one radio station at the frequency -f 89500000 Hz (89.5 MHz).
• No other radio station is within the sampled bandwidth, so we send the signal directly to the demodulator. (This is an easy, but not perfect solution as the anti-aliasing filter at RTL-SDR DDC is too short.)
• After FM demodulation we decimate the signal by a factor of 5 to match the rate of the audio card (240000 / 5 = 48000).
• A de-emphasis filter is used, because pre-emphasis is applied at the transmitter to compensate noise at higher frequencies. The time constant for de-emphasis for FM broadcasting in Europe is 50 microseconds (hence the 50e-6).
• Also, mplayer cannot play floating point audio, so we convert our signal to a stream of 16-bit integers.

Demodulate WFM: advanced

rtl_sdr -s 2400000 -f 89300000 -g 20 - | csdr convert_u8_f | csdr shift_addition_cc -0.085 | csdr fir_decimate_cc 10 0.05 HAMMING | csdr fmdemod_quadri_cf | csdr fractional_decimator_ff 5 | csdr deemphasis_wfm_ff 48000 50e-6 | csdr convert_f_i16 | mplayer -cache 1024 -quiet -rawaudio samplesize=2:channels=1:rate=48000 -demuxer rawaudio -

• We want to listen to one radio station, but input signal contains multiple stations, and its bandwidth is too large for sending it directly to the FM demodulator.
• We shift the signal to the center frequency of the station we want to receive: -0.085*2400000 = -204000, so basically we will listen to the radio station centered at 89504000 Hz.
• We decimate the signal by a factor of 10. The transition bandwidth of the FIR filter used for decimation will be 10% of total bandwidth (as of parameter 0.05 is 10% of 0.5). Hamming window will be used for windowed FIR filter design.

Sample rates look like this:

             2.4 Msps                     240 ksps                                  48 ksps
I/Q source ------------> FIR decimation ------------> FM demod -> frac. decimation ---------> deemphasis -> sound card

Note: there is an example shell script that does this for you (without the unnecessary shift operation). If you just want to listen to FM radio, type:

csdr-fm 89.5 20 

The first parameter is the frequency in MHz, and the second optional parameter is the RTL-SDR tuner gain in dB.

Demodulate NFM

rtl_sdr -s 2400000 -f 145000000 -g 20 - | csdr convert_u8_f | csdr shift_addition_cc `python -c "print float(145000000-145350000)/2400000"` | csdr fir_decimate_cc 50 0.005 HAMMING | csdr fmdemod_quadri_cf | csdr limit_ff | csdr deemphasis_nfm_ff 48000 | csdr fastagc_ff | csdr convert_f_i16 | mplayer -cache 1024 -quiet -rawaudio samplesize=2:channels=1:rate=48000 -demuxer rawaudio -

• Note that the decimation factor is higher (we want to select a ~25 kHz channel).
• Also there is a python hack to calculate the relative shift offset. The real receiver frequency is 145350000 Hz.
• The de-emphasis filter is a fixed FIR filter that has a passband of 400-4000 Hz, also with a roll-off of -20 dB/decade.

Demodulate AM

rtl_sdr -s 2400000 -f 145000000 -g 20 - | csdr convert_u8_f | csdr shift_addition_cc `python -c "print float(145000000-144400000)/2400000"` | csdr fir_decimate_cc 50 0.005 HAMMING | csdr amdemod_cf | csdr fastdcblock_ff | csdr agc_ff | csdr limit_ff | csdr convert_f_i16 | mplayer -cache 1024 -quiet -rawaudio samplesize=2:channels=1:rate=48000 -demuxer rawaudio -

• amdemod_cf is used as demodulator.
• agc_ff should be used for AM and SSB.

Design FIR band-pass filter (with complex taps)

csdr firdes_bandpass_c 0 0.5 59 HAMMING --octave | octave -i

• ...and then plot its frequency response with octave. (You can close octave window by issuing Ctrl-C in the terminal window.)
• It will design a filter that lets only the positive frequencies pass (low cut is 0, high cut is 0.5 - these are relative to the sampling rate).
• If --octave and everything that follows is removed from the command, you get only the taps. E. g. the raw output of firdes_lowpass_f can be easily copied to C code.

Demodulate SSB

rtl_sdr -s 2400000 -f 145000000 -g 20 - | csdr convert_u8_f | csdr shift_addition_cc `python -c "print float(145000000-144400000)/2400000"` | csdr fir_decimate_cc 50 0.005 HAMMING | csdr bandpass_fir_fft_cc 0 0.1 0.05 | csdr realpart_cf | csdr agc_ff | csdr limit_ff | csdr convert_f_i16 | mplayer -cache 1024 -quiet -rawaudio samplesize=2:channels=1:rate=48000 -demuxer rawaudio -

• It is a modified Weaver-demodulator. The complex FIR filter removes the lower sideband and lets only the upper pass (USB). If you want to demodulate LSB, change bandpass_fir_fft_cc 0 0.05 to bandpass_fir_fft_cc -0.05 0.

Draw FFT

rtl_sdr -s 2400000 -f 104300000 -g 20 - | csdr convert_u8_f | csdr fft_cc 1024 1200000 HAMMING --octave | octave -i > /dev/null

• We calculate the Fast Fourier Transform by csdr fft_cc on the first 1024 samples of every block of 1200000 complex samples coming after each other. (We calculate FFT from 1024 samples and then skip 1200000-1024=1198976 samples. This way we will calculate FFT two times every second.)
• The window used for FFT is the Hamming window, and the output consists of commands that can be directly interpreted by GNU Octave which plots us the spectrum.

Usage

Some basic concepts on using libcsdr:

Data types

Function name endings found in libcsdr mean the input and output data types of the particular function. (This is similar to GNU Radio naming conventions). Data types are noted as it follows:

• f is float (single percision)
• c is complexf (two single precision floating point values in a struct)
• u8 is unsigned char of 1 byte/8 bits (e. g. the output of rtl_sdr is of u8)
• s16 is signed short of 2 bytes/16 bits (e. g. sound card input is usually s16)

Functions usually end as:

• _ff float input, float output
• _cf complex input, float output
• _cc complex input, complex output

Regarding csdr, it can convert a real/complex stream from one data format to another, to interface it with other SDR tools and the sound card. The following commands are available:

• csdr convert_u8_f
• csdr convert_f_u8
• csdr convert_s8_f
• csdr convert_f_s8
• csdr convert_s16_f
• csdr convert_f_s16

How to interpret: csdr convert_<src>_<dst> You can use these commands on complex streams, too, as they are only interleaved values (I,Q,I,Q,I,Q... coming after each other).

Note: The the functions with i16 in their names have been renamed, but still work (e.g. csdr convert_f_i16).

csdr commands

csdr should be considered as a reference implementation on using libcsdr. For additional details on how to use the library, check csdr.c and libcsdr.c.

Regarding csdr, the first command-line parameter is the name of a function, others are the parameters for the given function. Compulsory parameters are noted as <parameter>, optional parameters are noted as [parameter]. Optional parameters have safe defaults, for more info look at the code.

realpart_cf

It takes the real part of the complex signal, and throws away the imaginary part.

clipdetect_ff

It clones the signal (the input and the output is the same), but it prints a warning on stderr if any sample value is out of the -1.0 ... 1.0 range.

limit_ff [max_amplitude]

The input signal amplitude will not be let out of the -max_amplitude ... max_amplitude range.

gain_ff <gain>

It multiplies all samples by gain.

clone

It copies the input to the output.

through

It copies the input to the output, while also displaying the speed of the data going through it.

none

The csdr process just exits with 0.

yes_f <to_repeat> [buf_times]

It outputs continously the to_repeat float number. If buf_times is not given, it never stops. Else, after outputing buf_times number of buffers (the size of which is stated in the BUFSIZE macro), it exits.

detect_nan_ff

Along with copying its input samples to the output, it prints a warning message to stderr if it finds any IEEE floating point NaN values among the samples.

floatdump_f

It prints any floating point input samples. The format string used is "%g ".

flowcontrol <data_rate> <reads_per_second>

It limits the data rate of a stream to a given data_rate number of bytes per second. It copies data_rate / reads_per_second bytes from the input to the output, doing it reads_per_second times every second.

shift_math_cc <rate>

It shifts the signal in the frequency domain by rate. rate is a floating point number between -0.5 and 0.5. rate is relative to the sampling rate.

Internally, a sine and cosine wave is generated to perform this function, and this function uses math.h for this purpose, which is quite accurate, but not always very fast.

shift_addition_cc <rate>

Operation is the same as with shift_math_cc.

Internally, this function uses trigonometric addition formulas to generate sine and cosine, which is a bit faster. (About 4 times on the machine I have tested it on.)

shift_addition_cc_test

This function was used to test the accuracy of the method above.

shift_table_cc <rate> [table_size]

Operation is the same as with shift_math_cc. Internally, this function uses a look-up table (LUT) to recall the values of the sine function (for the first quadrant). The higher the table size is, the smaller the phase error is.

decimating_shift_addition_cc <rate> [decimation]

It shifts the input signal in the frequency domain, and also decimates it, without filtering. It will be useful as a part of the FFT channelizer implementation (to be done). It cannot be used as a channelizer by itself, use fir_decimate_cc instead.

dcblock_ff

This is a DC blocking IIR filter.

fastdcblock_ff

This is a DC blocker that works based on the average of the buffer.

fmdemod_atan_cf

It is an FM demodulator that internally uses the atan function in math.h, so it is not so fast.

fmdemod_quadri_cf

It is an FM demodulator that is based on the quadri-correlator method, and it can be effectively auto-vectorized, so it should be faster.

fmdemod_quadri_novect_cf

It has more easily understandable code than the previous one, but can't be auto-vectorized.

deemphasis_wfm_ff <sample_rate> <tau>

It does de-emphasis with the given RC time constant tau. Different parts of the world use different pre-emphasis filters for FM broadcasting. In Europe, tau should be chosen as 50e-6, and in the USA, tau should be 75e-6.

deemphasis_nfm_ff <one_of_the_predefined_sample_rates>

It does de-emphasis on narrow-band FM for communication equipment (e.g. two-way radios). It uses fixed filters so it works only on predefined sample rates, for the actual list of them run: cat libcsdr.c | grep DNFMFF_ADD_ARRAY

amdemod_cf

It is an AM demodulator that uses sqrt. On some architectures sqrt can be directly calculated by dedicated CPU instructions, but on others it may be slower.

amdemod_estimator_cf

It is an AM demodulator that uses an estimation method that is faster but less accurate than amdemod_cf.

firdes_lowpass_f <cutoff_rate> <length> [window [--octave]]

Low-pass FIR filter design function to output real taps, with a cutoff_rate proportional to the sampling frequency, using the windowed sinc filter design method. cutoff_rate can be between 0 and 0.5.

length is the number of filter taps to output, and should be odd. The longer the filter kernel is, the shorter the transition bandwidth is, but the more CPU time it takes to process the filter. The transition bandwidth (proportional to the sampling rate) can be calculated as: transition_bw = 4 / length. Some functions (below) require the transition_bw to be given instead of filter length. Try to find the best compromise between speed and accuracy by changing this parameter.

window is the window function used to compensate finite filter length. Its typical values are: HAMMING, BLACKMAN, BOXCAR. For the actual list of values, run: cpp libcsdr.c | grep window\ ==

The --octave parameter lets you directly view the filter response in octave. For more information, look at the [Usage by example] section.

firdes_bandpass_c <low_cut> <high_cut> <length> [window [--octave]]

Band-pass FIR filter design function to output complex taps. low_cut and high_cut both may be between -0.5 and 0.5, and are also proportional to the sampling frequency.

Other parameters were explained above at firdes_lowpass_f.

fir_decimate_cc <decimation_factor> [transition_bw [window]]

It is a decimator that keeps one sample out of decimation_factor samples. To avoid aliasing, it runs a filter on the signal and removes spectral components above 0.5 × nyquist_frequency × decimation_factor.

transition_bw and window are the parameters of the filter.

rational_resampler_ff <interpolation> <decimation> [transition_bw [window]]

It is a resampler that takes integer values of interpolation and decimation. The output sample rate will be interpolation / decimation × input_sample_rate.

transition_bw and window are the parameters of the filter.

fractional_decimator_ff <decimation_rate> [transition_bw [window]]

It can decimate by a floating point ratio.

transition_bw and window are the parameters of the filter.

bandpass_fir_fft_cc <low_cut> <high_cut> <transition_bw> [window]

It performs a bandpass FIR filter on complex samples, using FFT and the overlap-add method.

Parameters are described under firdes_bandpass_c and firdes_lowpass_f.

agc_ff [hang_time [reference [attack_rate [decay_rate [max_gain [attack_wait [filter_alpha]]]]]]]

It is an automatic gain control function.

• hang_time is the number of samples to wait before strating to increase the gain after a peak.
• reference is the reference level for the AGC. It tries to keep the amplitude of the output signal close to that.
• attack_rate is the rate of decreasing the signal level if it gets higher than it used to be before.
• decay_rate is the rate of increasing the signal level if it gets lower than it used to be before.
• AGC won't increase the gain over max_gain.
• attack_wait is the number of sampels to wait before starting to decrease the gain, because sometimes very short peaks happen, and we don't want them to spoil the reception by substantially decreasing the gain of the AGC.
• filter_alpha is the parameter of the loop filter.

Its default parameters work best for an audio signal sampled at 48000 Hz.

fastagc_ff [block_size [reference]]

It is a faster AGC that linearly changes the gain, taking the highest amplitude peak in the buffer into consideration. Its output will never exceed -reference ... reference.

fft_cc <fft_size> <out_of_every_n_samples> [window [--octave] [--benchmark]]

It performs an FFT on the first fft_size samples out of out_of_every_n_samples, thus skipping out_of_every_n_samples - fft_size samples in the input.

It can draw the spectrum by using --octave, for more information, look at the [Usage by example] section.

FFTW can be faster if we let it optimalize a while before starting the first transform, hence the --benchmark switch.

fft_benchmark <fft_size> <fft_cycles> [--benchmark]

It measures the time taken to process fft_cycles transforms of fft_size. It lets FFTW optimalize if used with the --benchmark switch.

logpower_cf [add_db]

Calculates 10*log10(i^2+q^2)+add_db for the input complex samples. It is useful for drawing power spectrum graphs.

encode_ima_adpcm_i16_u8

Encodes the audio stream to IMA ADPCM, which decreases the size to 25% of the original.

decode_ima_adpcm_u8_i16

Decodes the audio stream from IMA ADPCM.

compress_fft_adpcm_f_u8 <fft_size>

Encodes the FFT output vectors of fft_size. It should be used on the data output from logpower_cf. It resets the ADPCM encoder at the beginning of every vector, and to compensate it, COMPRESS_FFT_PAD_N samples are added at beginning (these equal to the first relevant sample). The actual number of padding samples can be determined by running cat csdr.c | grep "define COMPRESS_FFT_PAD_N".

fft_exchange_sides_ff <fft_size>

It exchanges the first and second part of the FFT vector, to prepare it for the waterfall/spectrum display. It should operate on the data output from logpower_cf.

dsb_fc [q_value]

It converts a real signal to a double sideband complex signal centered around DC. It does so by generating a complex signal:

• the real part of which is the input real signal,

• the imaginary part of which is q_value (0 by default). With q_value = 0 it is an AM-DSB/SC modulator. If you want to get an AM-DSB signal, you will have to add a carrier to it.

  add_dcoffset_cc

It adds a DC offset to the complex signal: i_output = 0.5 + i_input / 2, q_output = q_input / 2

convert_f_samplerf <wait_for_this_sample>

It converts a real signal to the -mRF input format of https://github.com/F5OEO/rpitx, so it allows you to generate frequency modulation. The input signal will be the modulating signal. The <wait_for_this_sample> parameter is the value for rpitx indicating the time to wait between samples. For a sampling rate of 48 ksps, this is 20833.

fmmod_fc

It generates a complex FM modulated output from a real input signal.

fixed_amplitude_cc <new_amplitude>

It changes the amplitude of every complex input sample to a fixed value. It does not change the phase information of the samples.

mono2stereo_s16

It doubles every input sample.

setbuf <buffer_size>

See the buffer sizes section.

Control via pipes

Some parameters can be changed while the csdr process is running. To achieve this, some csdr functions have special parameters. You have to supply a fifo previously created by the mkfifo command. Processing will only start after the first control command has been received by csdr over the FIFO.

shift_addition_cc --fifo <fifo_path>

By writing to the given FIFO file with the syntax below, you can control the shift rate:

<shift_rate>\n

E.g. you can send -0.3\n

Processing will only start after the first control command has been received by csdr over the FIFO.

bandpass_fir_fft_cc --fifo <fifo_path> <transition_bw> [window]

By writing to the given FIFO file with the syntax below, you can control the shift rate:

<low_cut> <high_cut>\n

E.g. you can send -0.05 0.02\n

Buffer sizes

csdr has three modes of determining the buffer sizes, which can be chosen by the appropriate environment variables:

• default: 16k or 1k buffer is chosen based on function,
• dynamic buffer size determination: input buffer size is recommended by the previous process, output buffer size is determined by the process,
• fixed buffer sizes.

csdr can choose from two different buffer sizes by default.

• For operations handling the full-bandwidth I/Q data from the receiver, a buffer size of 16384 samples is used (see env_csdr_fixed_big_bufsize in the code).
• For operations handling only a selected channel, a buffer size of 1024 samples is used (see env_csdr_fixed_bufsize in the code).

csdr now has an experimental feature called dynamic buffer size determination, which is switched on by issuing export CSDR_DYNAMIC_BUFSIZE_ON=1 in the shell before running csdr. If it is enabled:

• All csdr processes in a DSP chain acquire their recommended input buffer size from the previous csdr process. This information is in the first 8 bytes of the input stream.
• Each process can decide whether to use this or choose another input buffer size (if that's more practical).
• Every process sends out its output buffer size to the next process. Then it startss processing data.
• The DSP chain should start with a csdr setbuf <buffer_size> process, which only copies data from the input to the output, but also sends out the given buffer size information to the next process.
• The 8 bytes of information included in the beginning of the stream is:
  • a preamble of the bytes 'C','S','D','R' (4 bytes),
  • the buffer size stored as int (4 bytes).
• This size always counts as samples, as we expect that the user takes care of connecting the functions with right data types to each other.

I added this feature while researching how to decrease the latency of a DSP chain consisting of several multirate algorithms.
For example, a csdr fir_decimate_cc 10 would use an input buffer of 10240, and an output buffer of 1024. The next process in the chain, csdr bandpass_fir_fft_cc would automatically adjust to it, using a buffer of 1024 for both input and output.
In contrast to original expectations, using dynamic buffer sizes didn't decrease the latency much.

If dynamic buffer size determination is disabled, you can still set a fixed buffer size with export CSDR_FIXED_BUFSIZE=<buffer_size>.

For debug purposes, buffer sizes of all processes can be printed using export CSDR_PRINT_BUFSIZES=1.

If you add your own functions to csdr, you have to initialize the buffers before doing the processing. Buffer size will be stored in the global variable the_bufsize.

Example of initialization if the process generates N output samples for N input samples:

if(!sendbufsize(initialize_buffers())) return -2;

Example of initalization if the process generates N/D output samples for N input samples:

if(!initialize_buffers()) return -2;
sendbufsize(the_bufsize/D);

Example of initialization if the process allocates memory for itself, and it doesn't want to use the global buffers:

getbufsize(); //dummy		
sendbufsize(my_own_bufsize);

Example of initialization if the process always works with a fixed output size, regardless of the input:

if(!initialize_buffers()) return -2;
sendbufsize(fft_size);

Testbench

csdr was tested with GNU Radio Companion flowgraphs. These flowgraphs are available under the directory grc_tests, and they require the gr-ha5kfu set of blocks for GNU Radio.

[sdr.js] (#sdrjs)

sdr.js is libcsdr compiled to JavaScript code with Emscripten. Nowadays JavaScript runs quite fast in browsers, as all major browser vendors included JavaScript JIT machines into their product. You can find a great introductory slideshow here on the concept behind Emscripten and asm.js.

The purpose of sdr.js is to make SDR DSP processing available in the web browser. However, it is not easy to use in production yet. By now, only those functions have wrappers that the front-end of OpenWebRX uses.

To compile sdr.js, first get Emscripten. (It turns out that there is an emscripten package in Ubuntu repositories.)

To install and build dependencies (for now, only FFTW3):

make emcc-get-deps

To compile sdr.js (which will be created in the sdr.js subdirectory):

make emcc

You can test sdr.js by opening sdr.html. It contains a test for firdes_lowpass_f for this time.

To remove sdr.js and the compiled dependencies:

make emcc-clean

[Licensing] (#licensing)

Most of the code of libcsdr is under BSD license.
However, before the implementation of some algoritms, GPL-licensed code from other applications have been reviewed. In order to eliminate any licesing issues, these parts are placed under a different file. However, the library is still fully functional with BSD-only code, altough having only less-optimized versions of some algorithms.
It should also be noted that if you compile with -DUSE_FFTW and -DLIBCSDR_GPL (as default), the GPL license would apply on the whole result.