blip BPSK demodulation

This post is going to demonstrate the demodulation of a BPSK signal by a blind phase locking algorithm called the blip Fourier transform. Binary Phase Shift Keying (BPSK) is a simple modulation scheme that adjusts the phase of a sine wave carrier by 180° depending on bit values. In PSK modulation all the information is encoded in the phase of the signal unlike Frequency Shift Keying (FSK) which modulates the frequency. The phase tracking blip Fourier transform is a new feature in the recently released baudline 1.08 version and you can read more about it in the on-line manual section about transforms.


Setup

1. Record or load a BPSK modulated signal into baudline.
2. In the Input Channel Mapping window set the transform to blip Fourier and the space to phase.
3. Zoom the spectrogram timebase axis down to the bit level.
4. Set the Windowing to Gaussian and adjust the beta value to taste.
5. View, measure, explore, ...

blip Fourier phase
The spectrogram display of the blip Fourier transform in phase space.

The carrier is at 1000 Hz and the modulated bits of the BPSK signal are clearly visible. The discontinuities represent 180° phase transitions and not absolute phase. Other interesting features are the fractal like structure that surrounds the carrier and the fabric of the noise floor to the right which is composed of interwoven phase worms. The elements of phase space are rich and quite literally complex in nature.


periodicity bars
Baudline's periodic bars are used to measure the periodicity of the phase transitions. Fine adjustment for exact alignment was accomplished with the up and down arrow keys. The bars aligned on the 180° phase transitions represent the modulated symbols. Click on the spectrogram image for a full size version that will show the periodicity bars in full detail.


Note the overlaid delta 0.016 second period value.


baud rate
The delta selected measurement window displays a higher accuracy period value and a convenience 1 / period = Hz calculation. In BPSK there are only two possible phases (0° and 180°) so the symbol rate equals the baud rate (1 bit/symbol) which the periodicity bars measured to be 63 Hz or 63 baud.


demodulated bits
Use the spectrogram's periodicity bars as a symbol clocking aid to manually demodulate the bit stream. Reading off the delta phase transitions corresponds to the bit string: 010100110010110100011010 or it's inversion 101011001101001011100101 since the true starting bit is unknown. The decoding of the meaning of these 24 bits is left as an exercise for the reader.


Conclusion
The remarkable revelation is that the blip Fourier transform has no a priori knowledge of the carrier frequency, baud rate, or even the PSK modulation scheme. It simply is blind phase locking and allowing a visual demodulation of the signal. Demodulating the actual bits from a BPSK signal is just a byproduct and a neat trick.

Phase consists of half of the spectrum. Half. Previous analysis tools have discarded this phase information and focused solely on magnitude. Use the baudline signal analyzer and see the other half of what you've been missing.

blip Fourier preview

This post is a quick preview of the blip Fourier transform that is going to be in the upcoming 1.08 version of baudline. The new blip Fourier transform utilizes a blind phase locking algorithm to enhance the spectral display in both magnitude and phase spaces. This does two valuable things. First, the spectral resolution is enhanced in the magnitude space which is ideal for observing amplitude beating while deep zooming down to the sample level. Second, spinning phase in now locked which allows the phase space to contain visibly useful information.


Setup
For this demonstration two instances of baudline's Tone Generators were used to create a sine wave on the left channel and an FM modulated triangle wave on the right channel. This multiple channel manipulation was done with CoreAudio but JACK could of accomplished the same test system.



Next the x * y multiplication operation in the Input Mapping window was used to mix the left and right channels to create a single modulated channel.


The new synthesized channel was then run through the Waveform window, the Fourier transform, and both the magnitude and phase spaces of the blip Fourier transform.


Waveform
The time domain samples are displayed in the Waveform window. The FM sweep and the AM beats are visible.



Fourier magnitude
The frequency domain is displayed with the Spectrogram window using the standard Fourier transform. The main FM triangle shape is visible.


Note that the timebase is 1/64X so this is fairly deep zoom with each spectral slice representing less than 3 samples.


blip Fourier magnitude
The same spectrogram display and magnitude space as above but with the blip Fourier transform. Note the sharper edges, grid on the FM triangle, and the enhanced detail in the noise floor.


The grid pattern is not a DSP artifact but in fact amplitude beats which are a unique feature of the signal.


blip Fourier phase
This is the same spectrogram display of the blip Fourier transform as above but of the phase space. This means that the spectrogram's color axis and the spectrum's vertical axis are not dB magnitude but instead represent phase in radians (±pi). The main signal features are the same but the blind phase locking creates interesting patterns that show how the phase is changing.


The diamond/triangular shaped blocks are not beats in this view space but phase modulation (PM) created by the x*y operation. The second harmonic of the FM triangle shape has a similar phase structure. Beneath that are folded aliasing and other distortion products. It appears that the fabric of phase space is a layered summation of signals with the most prominent on top. The zebra-like ripples around the main signal elements have a rich complexity and will be studied further in a future blog post.


Conclusion
The blip Fourier transform is an enhanced view into the frequency domain that has many powerful uses. The phase and fine sample details of signals can be explored and analyzed in ways previously not possible. As amazing as the blip transform's blind phase locking algorithm is, it is not without its faults since the process does create some additional distortion which lowers the system SNR. So the blip Fourier transform is great for deep low-level zooming and fine structure examination but it is not suitable for weak signal work. It is not a replacement for the Fourier transform but instead an additional transform for the DSP toolbox.