Aliasing on Downsampling

While the filter bank of Fig.9.36 gives good stopband rejection, there is still a significant amount of aliasing when the bands are critically sampled. This happens because the transition bands are aliased about their midpoints. This can be seen in Fig.9.36 by noting that aliasing ``folding frequencies'' lie at the crossover point between each pair of bands. An overlay of the spectra of the downsampled filter-bank outputs, for an impulse input, is shown in Fig.9.37.

Figure 9.38 shows the aliased spectral signal bands (prior to inverse STFT) for a step input (same filter bank). (This type of plot looks ideal for an impulse input signal because the spectrum is constant, so the aliased bands are also constant.) Note the large slice of dc energy that has aliased from near the sampling rate to near half the sampling rate in the top octave band. The signal and error spectra are shown overlaid in Fig.9.39. In this case, the aliasing causes significant error in the reconstruction.

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About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.