12/5/15
Over View
This GRC project is a utility program that can be used to study both the architecture of typical SSB DSPs and use as a SSB DSP design tool for custom DSPs. Associated with the utility are flow graphs for Weaver method SSB demodulators (receivers), Phasing or Hartley method demodulators and, a Phasing method variant, the Polyphase demodulator. The .grc file for each of the modulators can be loaded separately and, with <copy> and <paste> operations, placed in the utility work space for study and executed for operation. The operational aspects of this utility are based on a stimulus – response paradigm. Detailed analysis of the DSP signal flows are left for independent study. Additional examples of SSB DSP flow graphs, including modulators (transmitters) are included under the
Miscellaneous DSP Projects menu.
Background
There are two recognized approaches for SSB DSP designs: the Phasing method, and the Quadrature Mixer method. The filter method of SSB

signal processing, common in analog SSB circuits, will not be discussed.
The familiar Phasing SSB method is also known as the ‘Hartley method’, named after the engineer who first described the mathematics of this approach. The Polyphase method is a variation of the Phasing method.
The contemporary DSP terminology for this same Phasing method is the
‘complex bandpass filter’ method. The contemporary name reflects the modern DSP implementation using complex digital data type.
The widely used Quadrature Mixer SSB method, popularly known as the
‘Weaver method’ or the ‘third method’, owes its names to the engineer who first described the mathematics and patented this process in 1960.
Contemporary terminology for this method is the ‘complex multiplier’ method. This contemporary name reflects the combination of the modern DSP implementation that also uses complex digital data type and the modern term ‘multiplier’ instead of the classic term ‘mixer’.
Overview of The Utility
The utility consists of a single GRC work space that contains DSP blocks for signal and broad band noise stimulus sources and audio output and
FFT displays for the response sinks. In addition, 5 separate .grc flow graph files are provided: two for the Phasing, two for the Weaver, and one for the Polyphase SSB demodulator DSPs. The Phasing and Weaver flow graphs are rendered both in their modern ‘complex’ digital data type representation and in the classic ‘real’ digital data type

representation. The Polyphase flow graph is rendered only in the ‘real’ digital data type representation.
The Flow Graph
The Baseband Utility GRC flow graph appears visually quite simple. The stimulus and response DSP blocks are located along the far left edge of the GRC workspace. The large empty area in the center and right side of the workspace is the location where the selected .grc flow graph will be placed with <copy> and <paste> commands.
Figure 1 depicts the flowgraph for this utility.

Figure 2 depicts a screen view of the GRC GUI that appears once a DSP flow graph has been placed in the Baseband Utility work space and the flow graph is executed. The example GUI screen view is that of the
Polyphase SSB DSP demodulator.
Fig 2: GRC SSB DSP Utility - GRC GUI

Figure 3 depicts the flow graph for the ‘complex’ Weaver SSB DSP demodulator.
Fig. 3: ‘complex’ Weaver Method SSB DSP Demodulator Flow Graph

Figure 4 depicts the ‘real’ Weaver method SSB DSP demodulator.
Fig 4: ‘real’ Weaver Method SSB DSP Demodulator Flow Graph

Figure 5 depicts the ‘complex’ Phasing method SSB DSP demodulator.
Fig. 5: ‘complex’ Phasing Method SSB DSP Demodulator Flow Graph

Figure 6 depicts the ‘real’ Phasing method SSB DSP demodulator.
Fig. 6: ‘real’ Phasing Method SSB DSP Demodulator Flow Graph

Figure 7 depicts the ‘real’ Polyphase method SSB DSP demodulator.
Fig. 7: ‘real’ Polyphase SSB DSP Demodulator Flow Graph
Using the Utility
It is useful to study the individual .grc file SSB DSP flow graphs and compare the flow graphs to outside published DSP resource material.
One can visualize the specific DSP elements of a particular method and

anticipate the operation of the DSP. Visualization of the flow graphs helps to understand the text book descriptions and underlying DSP mathematics.
To study the actual operation of any one of the DSPs, load the SSB DSP
Utility and load the .grc file for SSB method you want to execute into separate GRC windows. <copy> and <paste> the SSB DSP flowgraph into the SSB DSP Utility workspace window. Next, complete the
‘stimulus in’ and the ‘response out’ flow graph connections and execute the SSB DSP Utility. If you use a tone to test with USB, input a positive frequency signal, e.g. 1000 Hz. To test with LSB, input a negative frequency signal e.g. -1500 Hz. The SSB DSP operation is displayed in the GUI.
The one exception to these instructions is the Polyphase SSB DSP demodulator flow graph. That flow graph is intended be executed without using the SSB DSP Utility. The flow graph has built in stimuli and response inputs and outputs and need not use the SSB DSP Utility to operate. See Additional Thoughts below.
Additional Thoughts
The operating parameters for these DSPs can be altered directly in the flow graph for study, performance optimization, and design simulation.
It is very useful to be able to design a SSB DSP in a simplified

environment, such as the SSB DSP Utility, isolated from a larger more complex DSP application. The SSB designed in the utility can be copied and pasted into the larger DSP to function with in that more complex application.
SSB modulators (transmitters) are constructed by simply substituting the ‘stimulus in’ connection for the ‘response out’ connection and visa versa. The modulator action can be confirmed by simulation with the utility.
The flow graph for the Polyphase SSB DSP demodulator is a special case. That flow graph is sufficiently novel that alterations of its rendition could be confusing. The flow graph is a minimally modified version of the flow graph as published by the author Theodor Prosch,
DL8PT. The article, A Minimalist Approximation of the Hilbert
Transform, was originally published in QEX magazine,
September/October 2012, pages 25 – 31. The article includes a table of coefficient sets for the IIR Filters that provide for varying levels of sideband suppression. In this example, the coefficients were entered for the highest level of sideband suppression, -77 dB. Two signal sources as well as a noise source serve as inputs to help visualize the operation of this SSB DSP.
The interpretation of the ‘real’ Weaver SSB demodulator will test your understanding of ‘complex’ vs ‘real’ signal processing. The operation of the ‘complex’ Weaver SSB demodulator is plainly seen and intuitive

when using the noise source stimulus. This intuitive result is the product of ‘complex’ signal processing. The mathematics of ‘complex’ signal processing does not permit expression of the ‘image’ or suppressed sideband. That is not the case with ‘real’ signal processing.
The spectrum of any ‘real’ signal expresses both the upper and lower sideband, the positive and negative frequencies. The Weaver demodulator can be viewed as ‘folding’ and inverting the unwanted sideband ‘underneath’ (in the same lowpass baseband) as the wanted sideband. Using the ‘real’ signal version of the SSB DSP both sidebands are viewed at all times on the FFFT, but only the wanted sideband is actually output. Here is where the audio output response can help clarify the DSP operation. The audio tone will sum and difference about the 1.5 kHz complex signal source with sideband selection.
Somewhat confusing in simulation and worthy of study.
Other stimuli can be substituted for the broadband noise source in the utility. For example, an audio frequency signal source, or multiple sources, can be used as stimuli for a more discrete spectrum analysis.
The computer microphone input, via an Audio Source DSP block, can be used as the stimulus and speakers or headphones can be used to monitor voice input.
Another interesting application of the utility is the ‘closed loop’ test.
The ‘closed loop’ configuration pairs the operation of a full modulator/demodulator system for analysis. To set up a ‘closed loop’ test it is only necessary to directly connect, within the flow graph, the output of any one of the modulators to the input of any demodulator.

The flow graph will execute and display the ‘closed loop’, modulator to demodulator response. Another example of a ‘closed loop’ configuration is presented under the Test and Measurement menu.
The .grc Files
.grc file for Baseband Stimulus Response Utility
Baseband Stimulus-Response Utility.grc
.grc file for Complex Phasing SSB DSP demod
Complex Phasing SSB DSP demod.grc
.grc file for Complex Weaver SSB DSP demod
Complex Weaver SSB DSP demod.grc
.grc file for Polyphase SSB DSP demod
Polyphase SSB DSP demod.grc
.grc file for ‘real’ Weaver SSB DSP demod
'real' Weaver SSB DSP demod.grc
.grc file for ‘real’ Phasing SSB DSP demod
'real' Phasing SSB DSP demod.grc

Once downloaded, these files can be opened with your GRC application for inspection and operation.