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A Short Course on Frame Theory
Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012
Veniamin I. Morgenshtern, Helmut Bölcskei
In the critically sampled case, 1/T = 2B, the ideal lowpass filter of bandwidth BT with the transfer function specified in (20.63) is the only filter that provides perfect reconstruction of the spectrum x̂(f) of x(t) according to (20.62) (see Figure 20.6). In the oversampled case, there is, in general, an infinite number of reconstruction filters that provide perfect reconstruction. The only requirement the reconstruction filter has to satisfy is that its transfer function be constant within the frequency range −BT ≤ f ≤ BT (see Figure 20.7). Therefore, in the oversampled case one has more freedom in designing the reconstruction filter. In A/D converter practice this design freedom is exploited to design reconstruction filters with desirable filter characteristics, like, e.g., rolloff in the transfer function.
Digital audio principles
Published in Francis Rumsey, Desktop Audio Technology, 2003
The basic D/A conversion process is shown in Figure 2.34. Audio sample words are converted back into a staircase-like chain of voltage levels corresponding to the sample values. This is achieved in simple convertors by using the states of bits to turn current sources on or off, making up the required pulse amplitude by the combination of outputs of each of these sources. This staircase is then ‘resampled’ to reduce the width of the pulses before they are passed through a low-pass reconstruction filter whose cut-off frequency is half the sampling frequency. The effect of the reconstruction filter is to join up the sample points to make a smooth waveform. Resampling is necessary because otherwise the averaging effect of the filter would result in a reduction in the amplitude of high-frequency audio signals (the so-called ‘aperture effect’). Aperture effect may be reduced by limiting the width of the sample pulses to perhaps one-eighth of the sample period. Equalisation may be required to correct for aperture effect.
Conversion
Published in John Watkinson, An Introduction to Digital Video, 2012
Figure 3.7 shows that all practical sampling systems consist of a pair of filters, the anti-aliasing filter before the sampling process and the reconstruction filter after it. It should be clear that the results obtained will be strongly affected by the quality of these filters which may be spatial or temporal according to the application.
Medical image interpolation based on 3D Lanczos filtering
Published in Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 2020
Thiago Moraes, Paulo Amorim, Jorge Vicente Da Silva, Helio Pedrini
As can be observed from the overall results, the proposed 3D Lanczos resampling method presented satisfactory results for the majority of the medical images tested in this work. As rationale for its superiority, we highlight some advantages of the Lanczos filter (Turkowski 1990): (i) the sinc filter is a theoretically optimal reconstruction filter for band-limited signals; (ii) it allows a proper compromise in terms of aliasing, sharpness and ringing effects; (iii) it allows a choice between preservation of abrupt transition in the data and smoother interpolation.