General Bug Fixes

• Memory corruption problems within the AtOne application framework on which AtSpec is built. 
• A memory leakage problem with AtSpec graphs that shows up if you repeatedly open and close graphs. 
• Graph PDF B always displays the same result as graph PDF A. 
• Online help additions and modifications. 
• Installer problem in the shareware versions of AtSpec in which AtSpec prematurely expires when installed in a sub directory that has white space in the name (such as "program files"). 
• The rectangular analysis window cannot be persisted between sessions. 

Driver Bug Fixes and Enhancements

• Input Impedance Driver does not scale impedance according to the reference resistor. 
• Input Impedance Driver gives erroneous impedance results when using some sound cards, particularly at the high frequency end of the spectrum. 
• Sound Blaster Driver has a single sample phase error when using some sound cards. 
• General improvements in the robustness of the Signal Generator and Input Driver software. 
• Synchronous test signal generation ability added to the signal generator and noise generator drivers. 

The Advantages of using Synchronous Test Signals in Analysis

The effect of leakage on spectrum analysis is twofold. In the first instance leakage will limit the spectral resolution of any measurements made. The governing factor is the characteristic lobe width of the applied window. Secondly the presence of leakage will limit the rate of convergence of any spectrum analysis estimates. Both effects combined will make certain types of analysis less accurate than could be possible using a synchronous test signal. 

Synchronous Test Signals

So what is a synchronous test signal? A synchronous test signal can be defined as a signal that is harmonically related to the spectrum analysis window with an integral number of periods of the test signal fitting exactly into the spectrum analysis window. Recall that when a rectangular window is used the lobe width is at a minimum but the leakage is greatest. However, should the signal under test be periodic with an integral number of periods exactly fitting into the analysis window then no leakage occurs and the resulting spectrum estimate exactly represents the sample domain signal being analysed. This property is demonstrated in Figure 1 which shows the measured power spectrum of an square wave approximation measured using a rectangular window with and without the square wave being harmonically related to the window. When not periodically related the spectrum energy leaks out into adjacent bands obscuring the noise floor. On the other hand, when the signal is periodically related the leakage effect vanishes and the signal harmonics and intermodulation products are clearly visible. 
 

You could then well ask why is this any better than using a superior windowing function such as the Blackman window? The reason is frequency resolution. By using a rectangular window and a synchronous test signal we obtain results that have the leakage rejection of using a Blackman window and the lobe width of the rectangular window. In fact, for the harmonic components of the synchronous test signal there is absolutely no leakage with all the energy lying in the appropriate frequency bin. This is clearly demonstrated in Figure 2, showing the main harmonic of the signal in Figure 1 measured by a rectangular window and a Blackman window. 
 

It is clear that the rectangular window has superior resolution to the Blackman window. In fact the majority of the signal energy is contained in a single frequency bin for the rectangular window case as opposed to five bins in the case of the Blackman window. The noise floor either case is comparable. 

Convergence of Estimates

Another area where this approach is superior to asynchronous test signals is in the convergence of analysis. Generally speaking, spectrum analysis results using synchronous test signals will converge within far fewer averages than the alternative case of an asynchronous signal, with the components associated with the test signal converging in typically one or two averages. Figure 3 shows a comparison of the spectrum estimate of a synchronous and asynchronous pseudo white noise signal when the average count is 8. In this case it is clear that the synchronous case has very little variance with the estimate corresponding to a smooth line, whereas the asynchronous case has a much larger variance which can only be reduced by taking more averages. 
 

Also In the case of pseudo noise signals (which have a finite period) reduction in the variance of the estimate by increased number of averages is only possible while the number of averages multiplied by the window length in samples is less than the pseudo noise period in samples. Thus for short sequence length pseudo noise signals the reduction of variance through averaging is somewhat limited. Therefore for these types of pseudo noise test signals it makes sense to force them to be synchronous. 

How do I Generate Synchronous Test Signals?

Generating synchronous test signals with AtSpec is a simple operation with either the signal generator or noise generator output devices.  Both driver allow you to control the period of the realized waveform through the Resolution setting.  With the resolution drop down box setting (in the Configure Driver dialog) set to the current analyzer resolution the signal generator signal will be synchronous.  The only other point to remember is that the analyzer windowing setting (in the Analyzer Options dialog) should be set to rectangular.  These settings are illustrated in Figure 4. 
 

In summary, the use of synchronous test signals provides a means for acurately measuring the response of linear systems, whether frequency response analysis or distortion analysis.  In frequency response analysis a synchronous pseudo noise signal is used and in distortion analysis a synchronous sinusoid is used.  We encourage you to investigate the use of synchronous test signals and the advantages that they provide. 
 

Version 2.0 features and enhancements news letter

Paavo Jumppanen
Author of AtSpec Spectrum Analyzer