nstant and varying . As a rule of thumb, it is of no use to select the order of larger than half the number of tones taken into account during computations. Fig. 4.31 shows the total number of terms generated by SymbolicHTM, summed over all computed HTM elements, versus the order of u and the number of tones taken 4.3 AUTOMATED SYMBOLIC LPTV SYSTEM ANALYSIS Frequency (Hz) (a) Symmetric bandpass filter H1 (s) Frequency (Hz) (b) Asymmetric bandpass filter H1 (s) Figure 4.29: Input-output HTM elements of the overall receiver for (a) a symmetric and (b) an asymmetric bandpass filter H (s). The crosses, circles and squares respectively represent the HTM elements H0,1 (jw), Ho,o(jw) and H0,2 (jw). 4.3.8 Application 2: Receiver stage with feedback across the mixing element Order of Nr. of Tones Figure 4.30: Accuracy of the symbolic expression for H0,1(s) versus the or- der of u and the number of tones (2K+1) taken into account in generating the expression. Note that the direction of the Z-axis has been reversed. Order of u Nr. of Tones Figure 4.31: The total number of terms generated versus the order of and the number of tones (2K+1) taken into account in generating the HTM ex- pressions. The CPU time spent per term equals on average 4e-3 seconds. 4.4 CONCLUSIONS AND DIRECTIONS FOR FURTHER RESEARCH into account. On average, the CPU time spent to generate a single term equals 4e-3 seconds. It is the number of terms which determines the computational cost of the SymbolicHTM algorithm. As can be seen, the number of generated terms quickly rises with the order of , especially when a large number of tones is taken into account. In this second example, it took 0.15 sec to compute results up to 2nd order in while taking 7 tones into account. This time increases up to a couple of seconds for both and K becoming large. Fig. 4.30, however, shows that these extra terms often do not contribute to the accuracy of the HTM elements of interest. This means that much time is spent on computing terms that are insignificant and hence of n