Sample Rate- and Frequency Offset Detector

 - still under construction -

Chapter overview

1. Introduction
2. One-time calibration of the sampling rate
3. Continuous calibration of the sampling rate
4. Continuous detection (and -possibly- correction) of a frequency offset / "drift"
5. The Goertzel filters (optionally used for high-res frequency measurement)
   1. The narrow-band 'Scope' display (spectrum showing the output from the Goertzel filters)
   2. CPU load caused by the Goertzel filters (and how to reduce it)
   3. Periodic reference signals (like 'Alpha' / RSDN-20)
6. Frequency Calibration Sources
7. Interpreter Commands to control and monitor the frequency calibrators

Appendix: Soundcard clock drift measurements, Algorithm for the continuous sample rate correction , MSK Carrier Phase Detection .

See also: Spectrum Lab's main index , circuit window , phase- and amplitude monitors .

Introduction

This chapter is only important for phase- and precise frequency measurements. You don't the functions explained in this chapter for most 'normal' applications like audio frequency analysis.

To improve the accuracy of frequency- and phase readings, it is possible to reduce the influence of "drifting" soundcard sample rates by permanently monitoring the frequency and phase of an external reference signal.

( This is different from the 'normal' sample rate calibration table on the audio settings screen, where the sample rate is only calibrated once but not permanently)

With the permanent frequency calibration, you can (almost) eliminate the effect of a drifting VFO in an external receiver.

Some frequency reference sources are listed in one of the following paragraphs.

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One-time calibration of the sampling rate (pre-calibration)

With the following steps, you can calibrate the sampling rate once. This is enough for most applications.

1. Select a nominal sample rate which is high enough to detect the "reference signal" of your choice. Most modern cards seem to work better with 48000 samples/second, rather than 44100 . These sampling rates are sufficient for most applications.
2. Use a relatively high FFT resolution, for example 262144 points, in the settings for the main spectrum display.
3. Make sure the spectrum/waterfall cursor readout operates in peak detecting mode.
4. With the peak-detecting cursor in the spectrum graph or the waterfall, measure the frequency of the reference signal.
   Move the mouse close to the peak frequency. The "peak indicator" circle in the spectrum plot should jump to the peak.
   For example, the 'cursor' function will show a value of 15623.2345 Hz (this is an interpolated value, the resolution is much higher than the FFT bin width ! The interpolation algorithm was suggested by DF6NM, thanks Markus ... it really does an amazing job !)
5. Enter the "correct" and the "measured" frequency in the calibrator fields of the audio settings dialog. Then click "Calibrate". The program calculates the new sampling rate and shows it in the calibration table. If you think it's reasonable, click "Apply" to make the new value effective.
6. Move the mouse to the peak of the reference signal again and check the displayed frequency (again, in 'peak'-mode). It should be very close to the true frequency of the reference signal, like 15625.0001 Hz for the "TV-sync" example.

Notes:

• The mentioned accuracy in the sub-milliHertz-region is realistic, if the soundcard in your PC has a crystal oscillator, and has been running for a few hours. If the frequency of the soundcard's oscillator drifts too fast, try the continuous calibration routine which is explained in the next chapter. Don't calibrate immediately after powering on the system - see soundcard frequency drift measurements in the appendix.
• The calibration table is saved in the machine-depending configuration file MCONFIG.INI in the installation directory. It is not part of a user configuration file (SETTINGS.INI; *.USR; etc). So, if someone sends you a test setup file via e-mail, your calibration does not get lost.
• There are different entries in the calibration table for some 'nomimal' sampling rates (like 11025, 22050, 44100, 48000, 96000  Hz). Because it is very likely that all rates are derived from the same clock oscillator, it's ok to do the calibration procedure for the highest sampling rate only, divide the calibrated result by two or four, and enter the result manually in the table. This way you can calibrate 11025 samples/second with the 15625 Hz TV sync 'indirectly'. But beware, some soundcards are known to be very far off the nominal sampling rate; in recent years (2010) many soundcards work better at 48 kHz than at 44.1 kHz .

Continuous calibration of the sample rate

For 'very demanding' applications like phase measurements, or spectrograms with extreme frequency resolution (mHz range), it may not be sufficient to "calibrate" the soundcard's sampling rate only once. Instead, the SR (sample rate) may have to be monitored continuously against a stable reference, so any SR drift can be eliminated.

To achieve this, select Components ... Sampling Rate Detector from SL's main menu, or select one of the preconfigured settings (from the Quick Settings menu) which automatically activate this function (for example, the Very Slow Morse modes like "QRSS600").

A control panel like this one will pop up :

Most important: When selecting one of the preconfigured sources from the 'Reference Freq.' combo, the program will automatically adjust other parameters on this panel, as required. The screenshot above shows a typical configuration using a VLF transmitter with MSK modulation (minimum shift keying). The other controls on this panel are explained in a later chapter (you will usually not need to modify them, at least not if you picked one of the pre-configured references from the list).

Don't forget to set the Enabled checkmark.  It can be used to disable the correction temporarily (in the presence of heavy noise aka QRN). If you only want to measure your soundcard's momentary sampling rate (but not let SpecLab adjust other processing stages based on the measured sample rate), set the 'Measure Only' checkmark. If your receiver is a software defined radio with quadrature output, set the checkmark I/Q input (in that case, the Q channel will be tapped at the 'Right' input, for example L1 = Inphase, and R1 = Quadrature phase input).

After a few seconds, the SR detector has acquired enough samples to calculate the first 'true' sampling rate (see principle below if you're interested to know how it works). If the reference signal is strong enough, and a few other 'signal-valid' criteria are fulfilled, the Status field (at the bottom of the control panel) will turn green.

The 'History' in the lower part of the panel shows the sample rate's deviation (in ppm) from the nominal value, intended as an aid to compare the stability of different soundcards (the ppm values can be copied and pasted somewhere else through the windows clipboard, remember CTRL-C and CTRL-V..) . If the history shows a very 'jumpy' behaviour, the clock crystal of your soundcard may be too close to a heat source, or near a cooling fan. This may render the soundcard useless for some applications - also see soundcard drift measurements at the end of this document (it contains an example of a 'good' (low-drift) and a 'poor' (rapidly drifting) soundcard.

The proper operation of the SR detector can be monitored on the integrated 'Scope' window (not to be confused with SL's input monitors, and the time domain scope). For example, if a 'healthy' MSK signal is being received, the Scope will show something like this:

If the reference is an MSK signal, the scope shows the spectrum of the squared baseband signal. There should be two peaks in the spectrum, symmetrically around the (invisible) 'carrier frequency', spaced by the bit frequency. For example, an MSK broadcaster transmitting 200 bits per second will produce a line 100 Hz below the center frequency, and another line 100 Hz above the center. Both lines (peaks) are labelled in the scope display; one with the offset from the center, the other with the difference between both peaks in bits/second. This indicator is typically very close to the nominal bitrate (see screenshot); if not, you may be tuned to a false signal.

If the reference is a coherent 'carrier' (like the AM carrier of a time signal transmitter, or a longwave broadcaster), the scope will look simpler - ideally, it only shows the carrier, way above the noise level:

Details about the 'Scope' follow in a later chapter .

Principle

The sample rate calibrator is a sofware implementation of...

• old algorithm : a numerical controlled oscillator (NCO) with two outputs, 90° phase difference ("I/Q output"),
  a complex multiplier ("I/Q" mixer), the reference signal is multiplied with the NCO's outputs like in an "image cancelling zero-IF receiver",
  and a chain of low-pass filters and decimators, with adjustable bandwidths.
• new algorithm (2010-03): a bank of Goertzel filters, each filter observes a narrow frequency band,
  and emits a complex frequency bin every 10 to 30 seconds which is then processed as in the old algorithm (see details in the appendix).
• a phase meter for the decimated I/Q-samples (or the Goertzel filter with the maximum output).
  By comparing the phase in the current and the previous complex sample, the momentary frequency can be calculated with a much higher resolution than the measuring time (a few seconds) would allow in a simple 'frequency counter'.

The phase meter produces a new reading every second (or, for the Goertzel filters, every 10 seconds). From the difference of phase values, the new deviation of the sampling rate is calculated, and the 'calibrated' sampling rate (which is an input parameter for some other function blocks) will be is slowly adjusted. Many (but not all) function blocks in SpecLab will benefit from this 'measured' sampling rate. For example, if the main spectrum analyser uses extremely long FFTs (with decimation) to achieve a milli-Hertz resolution, you will need this continuous calibration. A test showed that the clock frequency of the audio device in a notebook PC could be 'shifted' by 1.5 ppm within half an hour, just by cooling the notebook's underside with a fan (a 10 kHz signal was off by 15 mHz - see soundcard clock drift in the appendix). In many cases the permanently running sampling rate 'calibrator' eliminates the need for an external A/D converter (clocked with an oven-controlled or GPS-disciplined oscillator) !
Another example: With an E-MU 0202 (external audio device capable of 192 kSamples/second), it was possible to compare the carrier phases of several VLF transmitters, using the German DCF 77 (time signal transmitter on 77.5 kHz) as an ultra-stable frequency reference.

There are some additional function blocks in the frequency calibrator which detect the presence and the quality of the reference signal. This prevents the 'calibrated' sample rate from running away if the reference signal is bad or even missing. The 'pulling range' for the calibrated sampling rate can be adjusted by the user.

Some parts of the calibration algorithm are explained in the appendix. The monitoring display (to check if the SR detector operates properly) is explained here .

chapter overview

Settings for the sample rate calibrator in Spectrum Lab

There is a special control window for the sample rate detector ( / compensator ) in Spectrum Lab.  To get there, select "View/Windows".."Sample Rate Calibrator" from Spectrum Lab's main menu, or click on the "SR calib" function block in the circuit diagram. It's not really a 'calibration', but this function allows to compensate the soundcard's sample rate drift permanently. See

Controls for the 'Sample Rate Detector'

Enabled

Must be checked to activate the sample rate calibrator

Measure Only

Used during development or for "testing purposes". If this checkbox is marked, the sample rate is measured, but the other components in Spectrum Lab are not affected (they keep using the constant 'calibrated' sample rate from the table on the audio settings panel).

Use Goertzel

This option replaces the older phase meter algorithm with a set of Goertzel filters. This allows detection of a reference signal over a wider frequency range, and monitoring a narrow part of the spectrum (with a few dozen spectrum lines) on a special 'Scope' display.

Source Channel

Defines where the reference signal is taken from. Choices are 'LEFT input' or 'RIGHT input' if the program runs in stereo mode.

Reference Frequency (Hz):

The known frequency of the reference signal (as it should be). Please note that the sample rate detector uses audio, or "baseband" frequencies but not "radio" frequency. A number of predefined frequency references can be picked from this list, too. Picking one of the references from the list may automatically change some other parameters (like the mode/algorithm field) .

Min. Reference Amplitude

If the strength of the reference signal is less than this value, the sample rate calibration will be temporarily disabled (important if you use 15625 Hz as reference and someone turns the TV off !). A typical value is -80 dBfs, wich means "80 dB below the maximum level which can be handled by the ADC). Keep the amplitude of the reference signal as low as possible (typically about -60 dBfs) to leave enough headroom for other signals you want to measure.
The current (measured) signal strength is displayed in the lower part of the control window.

Periodicity

Rarely used, and only works with the Goertzel option. The only known use was for the Russian 'Alpha' VLF transmitters, which do not send a continuous signal but a periodic sequence which repeats 0.2777777 times each seconds.
This periodicity causes multiple spectral lines (separated 0.2777777 Hz from each other), which the calibrator must know to avoid 'locking' on the false line (because the strongest 'Alpha' line is not always the one with the nominal frequency). If you pick one of the 'Alpha' frequencies in the Reference Frequency list, the Periodicity field (in Hz) will be automatically filled. For normal (continuous wave) reference signals, leave this field empty.

Update Cycle :

Number of seconds per measuring interval. Longer intervals (10 or even 30 seconds) are preferred because they allow frequency measurements with better accuracy. On the other hand, if the soundcard's sampling rate drifts rapidly (as can often be seen with internal soundcards), shorter intervals (less than 10 seconds) can give better results, because even "short excursions" of the sampling rate will be compensated.

Observed Bandwidth

Defines the width of the frequency window for the sample rate. A typical value is 0.5 Hz (for a 15625 Hz reference). If the bandwidth is too low, the phase meter may not "see" the reference signal if the sample rate is too far off. If the bandwidth is set too high, the phase meter gets less immune to noise. If a the calibrator uses a bank of Goertzel filters (to observe the band), the CPU load depends on the observed bandwidth, because the larger the bandwidth, the more Goertzel filters must run in parallel (each Goertzel filter has a bandwidth of approximately 0.1 Hz).

Max. offset (from calibrated sample rate)

The initial value for the ADC's sample rate is taken from a table in SpecLab's 'audio settings'. The deviation between the sample rate in the table and the result of the calibration procedure must not exceed a certain value, like this:
Sample Rate from calibration table in the 'audio settings':  44103 Hz
Max Deviation: 5 ppm  -> true calibrated sample rate = 44103 Hz +/- 5 ppm = 44103 +/- 0.2 Hz = 44102.8 .. .44103.2 Hz.
(Note: this has nothing to do with the 'nominal sample rate' 44100 Hz, so you should do a first 'coarse' calibration for your soundcard before activating this function. The reason why only a small 'deviation' range should be used is to have a good starting value for the narrow-band phase meter. )
A typical soundcard oscillator drift, after booting up a "cold" PC, can be found in the appendix . For PCs operated indoors, or at a relatively 'constant' temperature, 5 ppm should be sufficient.

Current sample rate

Displays the currently calculated sample rate. You cannot edit this field, but copy its contents into the clipboard. Mark the text with the mouse and press CTRL-C to copy into the windows clipboard. You can then insert the copied value as a "very good starting point" into the calibration table in SpecLab's audio settings screen.

Displayed values on 'Sample Rate Detector' control panel

Depending on the mode / algorithm settings ( phase meter / MSK demodulator / Goertzel filters), the following values may be displayed on the SR detector's control panel :

SampR : start = <freq> Hz  + / - <dev> ppm

Shows the initial sampling rate (usually taken from the 'calibration' table on the audio settings panel), and the currently measured offset in ppm (parts per million).

Reference signal strength, quality, and / or currently measured frequency :

If the 'simple phase meter' is used, this line shows the signal strength after narrow-band filtering and the signal to signal-plus-noise ratio ( "S/(S+N)" ). The S/(S+N) value compares the amplitude of the narrow-band filtered value against a medium-bandwidth value, usually ten times the narrow-band value.
If the Goertzel filters (DFT) is used, this line shows the frequency of the reference signal (i.e. the "strongest peak" in the observed frequency range), and the signal strength in dBfs (dB "over full scale", thus always negative).

Error Integral (only active when using the Goertzel filters) :

Shows the summed-up products of frequency difference ("measured" sampling rate minus "predicted" sampling rate) from each measuring cycle, multiplied by the measuring interval time in seconds. Thus the unit of this 'integral' has no unit (it can be considered Hertz * seconds, though). If the sampling rate doesn't drift at all, or drifts at a constant, linear rate, the "predicted" sample rate (for the end of the next measuring cycle) will be equal to the "measured" sampling rate, and the SR Error Integral will be zero.
Note: Long-term phase observations (for ionospheric studies, etc; using the pam function) only make sense if the error integral stays almost zero; i.e. the drift must be very low or at least predictable. Internal soundcards are usually not suited for such long-term phase measurements, but some external audio devices (especially USB devices in "large boxes") are.
Internally, the a fraction of the error integral is used to steer the 'predicted sampling rate' (until the end of the next measuring cycle) to minimize slow drifting effects in long-term phase measurements. The error integral can be reset (cleared) by clicking the 'Apply' button on the Sample Rate Detector panel - it simply restarts the detector, which includes "forgetting" old values.

Rbw: Receiver Bandwidth (in Hertz)

Depends on the mode, but is usually dictated by the update cycle .

Decimation (only displayed when NOT using the Goertzel filters) :

Shows the scheme how the high audio sample rate and ADC bandwidth (like 44100 samples/second and 22050 Hz bandwidth) is reduced in chain of decimator stages down to the phase meter's sample rate and bandwidth (like 1 sample/second and 0.5 Hz bandwidth). Every decimator stage can reduce sample rate and bandwidth either by 2 or by 3, the total decimation ratio is also shown here. With a large decimation ratio, you can use signals buried in the noise as reference !

Phase angle (only displayed when NOT using the Goertzel filters) :

Shows the actual value of the phase meter (reference signal - oscillator). The displayed value should be constant, only a small phase jitter is unavoidable (usually below 0.5 °).

Status:

If this panel is green, everything is ok; otherwise the text shows what may be wrong, for example:
"SR range exceeded"
"S/(S+N) ratio too bad"
"Reference signal too weak", etc.

chapter overview

Continuous detection (+"calibration?") of a frequency offset

The frequency offset detector works similar like the sample rate detector (see previous chapter). The result from the frequency measurement is not used to determine the (corrected) sample rate. Instead, the frequency difference (deviation) between a reference frequency and the measured frequency is calculated. This can be used to...

• compensate a slowly drifting oscillator in an external receiver
• measure small changes in the frequency between a well-known "reference" signal and an unknown "received" signal
• correct the frequency error for the display by subtracting it from the frequency shift for the complex FFT.
• steer the VFO (in SpecLab's test circuit) to compensate the offset in the time domain

(Note: The detection of the soundcard's sampling rate AND the frequency offset detector can run simultaneously, but you need two different reference signals then. For example: one reference signal at 15.625 kHz to "calibrate" the sampling rate, and another like 1000 Hz to detect the frequency drift in your shortwave receiver. To calibrate your receiver, the 2nd reference signal must be produced in your receiver, of course. Details below).

To activate the frequency offset detector from SpecLab's main menu, select

"View/Windows" ... "Frequency Offset Detector".

A small control window opens, where the following parameters can be set:

Enabled:

Must be checked to start the F.O. calibrator.

Source channel:  

Select the LEFT or RIGHT input channel of the soundcard (unlike other function blocks in SpecLab, this one cannot be connected to any signal in the signal processing chain !).
If the input (into SpecLab) is a complex aka "I/Q"-signal, set the source to "BOTH inputs (complex)". In that case the frequency offset detector can process positive as well as negative input frequencies.

Reference Frequency (Hz):

The known frequency of the reference signal (as it should be). Please note that the frequency offset detector uses audio, or "baseband" frequencies but not "radio" frequency. So, in this field, enter the AUDIO (or "downconverted") frequency. A number of predefined frequency references can be picked from this list, too. Picking one of the references from the list may automatically change some other parameters (like the mode/algorithm field) .

Min Reference Amplitude (dB):

The detector will be passive if the amplitude of the reference signal is below this value. This prevents "running away" if the reference fails.

Max Offset (Hz):

This is the maximum "pulling range" for the detector. In most cases, this field will be set to the same value as the "observed bandwidth" below.

Observed bandwidth (Hz):

This is the bandwidth of phase meter (which is used internally used to measure the frequency offset; unless the Goertzel filters are in use). If your receiver may be "off" by +/-0.5 Hz, set the 'observed bandwidth' to 1.0 (!) Hz. Otherwise the detector may not be able to "see" the initial frequency of the reference signal and never lock on it.

Actual Peak Frequency:

Shows the "main peak frequency" within the detector's bandwidth. Can be used for high-precision frequency measurements, but depends a bit on the signal/noise ratio (within the detector's bandwidth).

Averages:

Can be used to suppress unstable reference signals, and reduce the effect of pulse-type noise. "50" means, the "average offset value" is calculated from the last 50 values from the phase meter. Practical values are 50...200. If the displayed average frequency offset appears to be "too noisy" (see below), increase the number of averages. If the detector reacts too slow, reduce this number.

Avrg Offset:

Shows the current output of the detector, which can optionally be used to enhance the accuracy of the main spectrum analyser (when running in "complex FFT mode with frequency shift"), and in the time domain scope (when used as a "phase meter"). The frequency error measured with the frequency offset detector can be "subtracted" by the local oscillator which sets the "center frequency" of the FFT and the scope's phase meter.

In the lower part of the window, some other values are displayed which were used during program development. One of them is the "signal / (signal+noise)" ratio, which is a crude indicator for the reference signal's quality. If the quality is very poor, the "result" of the frequency offset detector freezes, and the detector's "status" indicator turns yellow or even red (which can also be seem on the circuit window).

RED = "Reference signal too weak"

YELLOW = "Signal to noise ratio of reference signal too bad"

To calibrate a drifting receiver, you must find a way to feed a add a weak but very stable reference signal to the antenna input, which produces a suitable audio tone in the output. Use your imagination - and an oven controlled crystal oscillator, and a chain of dividers/multipliers, or a programmable DDS generator.

chapter overview

Goertzel Filters (for the continuous sample rate calibrator)

Depending on the checkmark 'use Goertzel' on the configuration tab, a bank of Goertzel filters is used to calculate a complex DFT (discrete fourier transform) over a narrow frequency range. Each filter measures a frequency for 30 seconds, with a frequency bin width of approximately 0.033 Hz (the effective bandwidth is a bit more due to the Hann window).

One of the Goertzel filters will (hopefully) catch the 'peak' of the reference signal - ideally in the center frequency bin. The phase angle in the output of the filter with the maximum amplitude will be compared with the previous value (from the same frequency bin). This phase difference (between the most recent complex and the previous value) is used to calculate the 'measured' frequency of the reference signal, with a much higher resolution than the DFT's frequency bin with (which, as noted above, is about 0.1 Hz). Along with the phase angle, the program can determine the frequency to a few micro-Hertz (!) even though the measuring interval is only 10 seconds.

The result of this calculation, along with the narrow-band spectrum of the observed frequency range, is displayed on the 'Scope' tab in the Sample Rate Calibrator window.
Displaying the 'measured' frequency with so many digits is usually 'overkill', but it helps to check devices with oven-controlled or temperature compensated oscillators. But the reference signal must have a very good SNR (like the signal in the screenshot below) for the micro-Hertz digit to be useful. The device under test was an E-MU 0202 at 48000 samples/s .

The 'Scope' tab (in the sample rate calibrator's control window)

While the Goertzel filters are running, the graph on the 'Scope' window shows the narrow-band spectrum around the reference signal. The last result of the frequency measurement, and the magnitude of the reference signal are shown near the peak in the graph.

The old graphs (from previous spectrograms) slowly fade out on the display. This is not a bug but a feature ;-) ... it helps to discover intermittent noise, dropouts, or "slowly drifting" signals without the need for a spectrogram display. The most recent curve is yellow, while older curves fade to brown, and finally disappear after a couple of minutes. Peaks which look 'smeared' on the display are not stable in amplitude or frequency.

CPU load caused by the Goertzel filters (and how to reduce it)

Depending on how the calibrator is configured, it may cause a significant extra CPU load on your system. For example, if the sample rate calibrator shall observe a 1.5 Hz wide band with 33 mHz resolution (per frequency bin), there will be 45 (!) Goertzel filters running in parallel, each at 48 kSamples/second. On a 1.6 GHz Centrino CPU, this example used 12 % CPU time (from one CPU).

Fortunately, in a normal environment, the soundcard's oscillator will drift less than one ppm (parts per million) after warm-up, so you will get along with a much smaller 'observed bandwidth' - which reduces the CPU load caused by the Goertzel algorithm. See the soundcard drift tests in the appendix to get an idea about the really required bandwidth : If the soundcard's sampling rate has been properly pre-calibrated, the observed bandwidth only needs to be a few ppm (parts per million) of the reference frequency.

Periodic reference signals (with multiple lines in the spectrum)

For certain reference sources (see next chapter), it is necessary to use very narrow bandwidth for each filter (DFT frequency bin). For example, the Russian VLF 'Alpha' navigation beacons (or RSDN-20) send short 'beeps' every 3.6 seconds, which results in a spectrum of individual lines spaced 0.277777 Hz, as explained in an article at www.vlf.it by Trond Jacobsen. With a 10-second measuring interval it is just possible to see the individual lines in the spectrum, but a larger measuring interval is recommended - especially when looking at a typical 'onboard' audio device's clock frequency drift (see appendix: soundcard clock drift measurements ).

For that reason, if you select one of the three active Alpha frequencies in the list, the program will automatically adjust some other parameters .. including the 'Periodicity' field because the decoder needs to know that, in this case, the reference signal is not a continuous wave, and the output of the Goertzel filters will produce multiple lines in the spectrum which all belong to the same signal. But the SNR may be poor, and the signals may suffer from phase changes caused by Ionospheric reflection, so don't expect too much accuracy (in comparison with a local, continuous wave reference).

The algorithm will first scan the spectrum for the largest peak, and -starting there- looks for other peaks which match the periodicity criterium (0.277777 Hz spacing for the Alpha VLF transmitters). The result may look like this on the scope panel:

The main peak is marked with the measured frequency (under the assumption that the soundcard still runs at the initial sampling rate), all weaker peaks which obviously belong to the reference signal are marked with relative frequencies as multiples of the nominal periodicity ('spacing' in frequency). For example, '-3.9994' shown in the graphics means 'this peak is 3.9994 times 0.2777777 Hz below the strongest peak', etc. Only peaks which are spaced at (almost) integer multiples of the periodicity are involved in further processing. Peaks below the threshold amplitude (*) are discarded, as well as peaks on obviously 'wrong' frequencies, or peaks which are 10 dB weaker than the main peak. If none of the peaks is close enough to the expected reference frequency, the program uses the measured periodicity value (if 'close enough' to 0.277777 Hz) to find out which peak is the right one. Unfortunately, at the moment this requires a very good SNR (signal to noise ratio) ... so it's more or less a wild guess at the moment ... but this may be improved by 'intelligent averaging' in a future release of the software.

(*) the threshold amplitude, in dBfs, is indicated as a green horizontal line in the scope display

chapter overview

Frequency Reference Sources

Here are a few possible frequency reference sources to calibrate the ADC's sample rate. Some of them are listed in the 'Reference Frequency' combo of the sample rate calibrator, so you don't need to type in the frequencies yourself..

• The output from an ovenned crystal oscillator (OCXO), divided down into the audio frequency range. Such 'large canned oscillators' can be found on hamfests or auctions, since they are widely used in wireless communication equipment. 5 or 10 MHz are common frequencies for such oscillators.
• The 1-pulse-per-second output of a good GPS receiver with little jitter. Spectrum Lab can lock to a harmonic of this 1-Hz-signal because the 'observed frequency range' can be set to a very narrow bandwidth. Of course, you will need to pre-calibrate the soundcard's sampling rate (with another source) to pick the right 1-Hz harmonic !
• The divided-down carrier frequency of a longwave time-code transmitter like MSF (60kHz), DCF77 (77.5kHz), or similar. Use a PLL cuircuit to recover a 'clean' carrier signal, then (for example) divide 77.5kHz by 31 or 60kHz by 24. The result should be a very stable 2500 Hz signal which can be fed into the soundcard. If you have a soundcard which supports 192 kHz sampling, you don't need any hardware because the soundcard should be able to receive 77.5 kHz directly with a few meters of wire.
• Some Navy transmitters in the VLF spectrum (17 to 24 kHz, or up to 90 kHz if the soundcard permits) can be used as a reference signal, if they use MSK modulation (minimum shift keying), and don't insert more-or-less arbitrary phase jumps in the transmitted signal. At least some of those "broadcasters" seem to have their carriers locked to atomic clocks or GPS standards - in that case, and it they are not too far away (i.e. within "groundwave distance"), they can be used as references for the soundcard sampling rate correction. Most of the European transmitters can be picked from the 'Reference' combo list on the 'Sampling Rate Detector' control panel. So far, the system was only tested with DHO38 (MSK200 on 23.4 kHz), because that transmitter was close enough for groundwave reception (even during nighttime). Beware, DHO38 used to be off air once or twice a day.
• Some longwave broadcasters (like the BBC's Droitwich transmitter on 198 kHz) use Rubidium standards for their carrier signal. In western europe, use a simple PLL oscillator, and divide the signal down with a cheap CMOS circuit (only required if you don't use a software defined radio like SDR-IQ or Perseus, which can be tuned to any frequency in the LF, MF, or HF spectrum).
• Any of the  Russian 'Alpha' (aka RSDN-20) VLF transmitters on  11 to 14 kHz; their exact frequencies can be picked from the 'reference frequencies' combo. When doing that, the 'Periodicity' field will automatically be set to 0.277777 Hz (= the repetition frequency of the "beeps", 1 / 3.6 seconds). Some details on using the Alpha beacons as a frequency reference can be found in the chapter about the Goertzel-filter-based calibrator.
• The line sync signal of some TV broadcasting stations.
  In EUROPE (and, most likely, countries with 50 Hz AC mains): Frequency exactly 15625 Hz. While we still had terrestrial "analog" TV transmitters, the german "ZDF" derived their TV sync signals from a high-precision standard clock.
  In the US (and other countries using 60 Hz AC mains), the line sync frequency is ideally 15734.2657343 Hz (for NTSC, colour, 4.5 MHz sound subcarrier divided by 286).
  Update: It is questionable if the TV sync frequency still has this precision, now that everything (in Europe, even terrestrial transmissions) are digital. The sync frequencies *may* be generated by a cheap computer-grade crystal in the set-top box of your TV, so in case of doubt use one of the other sources...
• The stereo pilot tone of a few FM broadcasting stations. Not many FM stations have their 19 kHz pilot tone locked to an atomic clock, at least not in Germany.
• Any other reference can be used, as long as it can be processed with the audio card. If the ADC supports a sample rate of 44100 Hz, the reference signal can be everything between 16 Hz ... 22 kHz.

chapter overview

Interpreter commands for the frequency calibrators

fo_cal.xxxx = commands and functions for the frequency offset calibrator:

• fo_cal.avrg
  Average frequency offset (difference between "measured" frequency and "known reference" frequency ).
  A positive offset means "the measured frequency is TOO HIGH". So to correct a "measured" frequency, subtract fo_cal.avrg from the measured value before you display it (but beware: Do NOT subtract fo_cal.avrg if the FFT frequency bins have already been corrected as explained here ).
• fo_cal.delta_phi
  Phase angle difference between to consecutive phase calculations. Should ideally be zero. Mainly used for program development.
• fo_cal.fc
  Current center frequency which has been measured by the frequency offset calibrator. Should ideally be the same value as the "known reference frequency". You may (ab-)use this function for a precise measurement of a single frequency. Example: To measure the exact mains frequency ("hum"), set the "Reference audio frequency" to 50.000 Hz, the "observed bandwidth" to 0.5 Hz, and the max. offset also to 0.5 Hz (all these values on the control panel of the Frequency Offset Detector).

sr_cal.xxxx = commands and functions for the sampling rate calibrator:

• sr_cal.avrg
  Average sampling rate measured by the sampling rate calibrator. This value is also displayed in the calibrator's control window. You may use it for your own application.
• sr_cal.ampl
  Measured amplitude of the reference signal, converted into dBfs (decibel over full scale, thus always a negative value).
• sr_cal.delta_phi
  Phase angle difference between to consecutive calculations. Should ideally be zero. Mainly used for program development.
• sr_cal.fc
  Measured reference signal frequency. Calculated by the sampling rate calibrator, under the assumption that the sampling rate was constant since the calibrator was started. Should ideally be the same value as the "known reference frequency". Useful for plotting the audio device's oscillator drift, if a drift-free frequency reference (OCXO, GPS) is available.
• sr_cal.fr
  Returns the configured reference frequency (nominal frequency, constant), as configured in the 'Reference Frequency' field .

See also: Example for plotting the soundcard's frequency deviation (in ppm) and the drift rate (in ppm / minute),  Interpreter command overview, circuit window, main index .

See also: Spectrum Lab's main index .

Appendix

Soundcard clock drift measurements

The following drift rate (red graph in the diagram below) and frequency offset (green)  graphs were made with an internal audio device in a notebook PC (Thinkpad Z61m, internal "SoundMax HD Audio"). The graph starts a few minutes after booting the PC. Before that, the PC had cooled off for several hours. The reference signal (10 MHz OCXO divided down to 10 kHz) had been running for a couple of days. The soundcard's final sampling rate was calibrated earlier (in the calibration table).

Sampling rate drift test (Thinkpad, internal audio device)

Each horizontal division is 15 minutes wide. At 09:10, the notebook's cooling fan started to run, causing the 'bent' curve. The green graph shows the deviation of the sampling rate; vertical scale range for this channel is +/- 0.5 ppm (parts per million - see formula at the end of this chapter). The same order of clock deviation can be expected when measuring frequencies without the continuous sampling rate calibrator.

Next test candidate: An E-MU 0202 USB (external audio device in a quite large box). The initial sampling rate deviated from the final value by over 2 ppm, so during the 'early' warm-up phase, the trend is only visible on a broader scale (in cyan colour). 5 minutes after start, the calibrator's tracking algorithm was able to measure and eliminate the drift (because of the large initial drift rate, and the 30-second frequency measuring intervals for the Goertzel filters). It's obvious that the curves are less 'jumpy' than with the internal soundcard, thanks to the absence of a cooling fan in the box.

Sampling rate drift test (E-MU 0202, USB audio device)

To measure and plot the soundcard oscillator's drift, the interpreter function "sr_cal.fc" were used, and SL's plot window . The expression 1E6*(sr_cal.fc-sr_cal.fr)/sr_cal.fr calculates the current frequency deviation in ppm (parts per million).
To measure the drift rate (in ppm per minute), calculate the drift (frequency error in ppm) periodically, and subtract the previous result from the current result every minute. This can be achieved in the Conditional Actions table ("DriftRate = Drift - OldDrift", which is not true maths but it works for this purpose). The 60 second timebase is provided by one of SL's programmable timers. Example (copied from the conditional actions in the configuration 'SoundcardDriftTest.usr') :

Nr	IF.. (event)	THEN.. (action)
1	initialising	Drift=0 : DriftRate=0 : OldDrift=0 : timer0.start(60) : REM timer will run off after 60 seconds
2	timer0.expired	Drift=1E6*(sr_cal.fc-sr_cal.fr)/sr_cal.fr : DriftRate=Drift-OldDrift : OldDrift=Drift : timer0.start(60)

The values of 'Drift' (in ppm) and 'DriftRate' (in ppm / minute) are plotted in the watch window. The sample application (SoundcardDriftTest.usr) is contained in the SL installer.

(Old algorithm, Rev date 2002-04-18, only uses one complex oscillator, one complex multiplier, and a long chain of decimators):

The example explained here uses a reference frequency f_ref = 15625 Hz (TV line sync)

1. NCO frequency for the I/Q mixer
   theoretically: f_ref  = 15625 Hz (this is the 'Reference Frequency' entered by the user)
   practically :  f_nco =   f_ref * k,  where k = true sample rate / assumed sample rate,
   because the program only THINKS it mixes the input signal with f_ref, but in fact -due to the sample rate error- the true NCO frequency is different !
   Here for example: k = f_sample_assumed / f_sample_true = 44101 Hz / 44100 Hz,
   so f_nco = 15625 Hz * 44101/44100 = 15625.35431 Hz. The NCO is initially programmed for '15625.0 Hz' because the program does not know the true sample rate (this is what we're looking for !)
2. Frequency at the output of the I/Q mixer (not decimated)
   f_mix = (f_ref - f_nco) = f_ref - f_ref*k = f_ref * (1-k) = 15625 Hz * (1-44101 / 44100) = -0.3543 Hz
   (dont bother about the negative frequency, we are processing I/Q samples)
3. Accumulation of the phase (from f_mix_decimated, observed over the measuring interval)
   Measuring interval: t_meas = decimation_ratio / true sample rate = 16384 / 44101 Hz
   Phase deviation: delta_phi = 360° * t_meas * f_mix = -47.3866°
   (the phase deviation is what the software actually measures. It does not know the true sample rate !)
4. Calculation of the 'calibrated' sample rate.
   known:  delta_phi, f_ref, decimation_ratio, f_sample_assumed
   wanted:  k (correction factor), f_sample_true
   delta_phi = 360° * t_meas * f_mix
                  = 360° * (decimation_ratio * f_mix)  / f_sample_true
                  = 360° * decimation_ratio * (f_ref  - f_ref * f_sample_true / f_sample_assumed) / f_sample_true
   -> ... ->
   f_sample_true = f_sample_assumed / ( 1 + delta_phi * f_sample_assumed / (360° * decimation_ratio * f_ref) )

Note that the NCO frequency is not reprogrammed with the new "true value" of f_ref !

(New algorithm, Rev date 2010-03-30, uses a bank of Goertzel filters to calculate a DFT for a few frequencies):

< ToDo >: Describe how the phase information in the complex DFT can be used to measure the frequency with a resolution of a few microhertz, using a 30 second measuring interval...

MSK Carrier Phase Detection

To detect the 'carrier phase' of an MSK signal (without demodulating or decoding it), the complex, downconverted (analytic or "baseband") signal is squared. This produces two discrete lines in the spectrum, symmetrically around the carrier frequency.

For example, DHO38 is first multiplied with an complex NCO (numerically controlled oscillator, with sine- and cosine output) at 23400 Hz, then decimated until the sampling rate is about 1.5 to 3 times the bitrate. In the decimated, complex (analytic) signal, the two lines appear like 'sidebands', separated -100 Hz and +100 Hz from the carrier signal (which is now at 0 Hz, ideally).

The squared baseband signal is then passed through a DFT (discrete fourier transform, possibly an FFT = Fast Fourier Transform). To avoid locking on false signals, the amplitudes in the complex frequency bins (at the two "expected" baseband frequencies) are compared with their neighbours, and the phases in the complex bins are compared with the previous DFT (in reality, this step is a bit more complicated because the signals are not perfectly centered in their FFT bins.. some phase angle fiddling is required for this reason).

Compared to a continuous wave signal, the MSK carrier phase detection requires a larger SNR (go figure..) because the observed signal bandwidth (or, the equivalent receiver bandwidth) is larger. For comparison, measuring the carrier phase of DHO38 requires approximately a 300 (!) Hz filter bandwidth. For phase coherent time signal transmittes like DCF77, the observed bandwidth may be less than a Hz.

Note: The same principle is also used in the phase- and amplitude monitors (when configured for MSK).

Last modified: 2010-03-30