Digital Signal Processing Reference
In-Depth Information
Figure 18.7
Detailed block diagram of the functional unit for adapting signal spectrum
estimations to the specific sampling nonuniformities of a signal sample value subset
To realize how this could be done, the impact of phase-shifting of the sampling
pulse sequences on the aliasing conditions has to be taken into account. The point
is that conditions for frequency overlapping or aliasing essentially depend not
only on the sampling frequency but also on the sampling phase. Therefore the
estimates of signal components in the frequency domain differ depending on the
phase shift of the corresponding periodic sampling instant process. The fact that
the phase angle of the signal, downconverted due to aliasing, depends on the
phase of the sampling point process is exploited in order to eliminate the aliases
at the stage of aggregating the data. The particular
z
sets of the Fourier coefficient
estimates, obtained by processing the signal sample value
z
subsets, are used to
calculate the final alias-free characteristics of the input signal spectrum.
18.4.2 Adapting the Estimation for Each Signal Sample
Value Subset
Adapting the estimation of the Fourier coefficients for each signal sample value
subset is performed as described in Section 18.2. Once the pattern of the missing
sampling points determined by the pseudo-random number generator used to form
the sampling pulse sequence is known, all coefficients of matrix
C
are calculated
for each signal sample value subset. They are then used to eliminate the errors
due to the described cross-interference caused by sampling point skipping.
In general, in this approach to the considered adaptation process, the number
of signal components might exceed the number of signal sample values of a
particular periodic sampling subset. Then an iterative procedure has to be used to
adapt the calculation of particular sets of Fourier coefficient estimates to sampling
nonuniformities for each signal sample value subset, as shown in Figure 18.7.
Apparently the differences between the true and estimated values of Fourier
coefficients are errors. While there are various error components caused by
