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Digital Principles
Published in John Watkinson, The Art of Digital Video, 2013
Rather than simply truncate the impulse response in time, it is better to make a smooth transition from samples that do not count to those that do. This can be done by multiplying the coefficients in the filter by a window function that peaks in the centre of the impulse. Figure 3.42 shows some different window functions and their responses. The rectangular window is the case of truncation, and the response is shown at I. A linear reduction in weight from the centre of the window to the edges characterizes the Bartlett window (II), which trades ripple for an increase in transition-region width. At III is shown the Hamming window, which is essentially a raised cosine shape. Not shown is the similar Hamming window, which offers a slightly different trade-off between ripple and the width of the main lobe. The Blackman window introduces an extra cosine term into the Hamming window at half the period of the main cosine period, reducing Gibb's phenomenon and ripple level, but increasing the width of the transition region. The Kaiser window is a family of windows based on the Bessel function, allowing various trade-offs between ripple ratio and main lobe width. Two of these are shown in IV and V. The drawback of the Kaiser windows is that they are complex to implement.
Digital principles
Published in John Watkinson, The Art of Digital Audio, 2013
Rather than simply truncate the impulse response in time, it is better to make a smooth transition from samples which do not count to those that do. This can be done by multiplying the coefficients in the filter by a window function which peaks in the centre of the impulse. Figure 3.45 shows some different window functions and their responses. The rectangular window is the case of truncation, and the response is shown at I. A linear reduction in weight from the centre of the window to the edges characterizes the Bartlett window II, which trades ripple for an increase in transition-region width. At III is shown the Hanning window, which is essentially a raised cosine shape. Not shown is the similar Hamming window, which offers a slightly different trade-off between ripple and the width of the main lobe. The Blackman window introduces an extra cosine term into the Hamming window at half the period of the main cosine period, reducing Gibb's phenomenon and ripple level, but increasing the width of the transition region. The Kaiser window is a family of windows based on the Bessel function, allowing various tradeoffs between ripple ratio and main lobe width. Two of these are shown in IV and V.
Filters and transforms
Published in John Watkinson, Convergence in Broadcast and Communications Media, 2001
Rather than simply truncate the impulse response in time, it is better to make a smooth transition from samples which do not count to those that do. This can be done by multiplying the coefficients in the filter by a window function which peaks in the centre of the impulse. Figure 3.11 shows some different window functions and their responses. The rectangular window is the case of truncation, and the response is shown at I. A linear reduction in weight from the centre of the window to the edges characterizes the Bartlett window II, which trades ripple for an increase in transition-region width. At III is shown the Hann window, which is essentially a raised cosine shape. Not shown is the similar Hamming window, which offers a slightly different trade-off between ripple and the width of the main lobe. The Blackman window introduces an extra cosine term into the Hamming window at half the period of the main cosine period, reducing Gibb’s phenomenon and ripple level, but increasing the width of the transition region. The Kaiser window is a family of windows based on the Bessel function, allowing various tradeoffs between ripple ratio and main lobe width. Two of these are shown in IV and V.
Construction of intelligent multi-construction management platform for bridges based on BIM technology
Published in Intelligent Buildings International, 2023
We use the filterDesigner tool provided by MATLAB to design a low-pass filter and a band-pass filter using the window function method (Kaiser window). In MATLAB, the Kaiser window is implemented as a built-in function called ‘kaiser.’ The function takes two arguments: the length of the window and a parameter called the ‘beta’ value, which controls the shape of the window. The beta value determines the trade-off between the width of the main lobe of the window and the magnitude of the side lobes. Designing both a low-pass filter and a band-pass filter using the Kaiser window approach allows for flexibility in filtering out unwanted frequencies from a signal while preserving the frequencies of interest. The filter designer tool provided by MATLAB simplifies this process by providing a user-friendly interface for designing and implementing these filters. The passband of the low-pass filter is 110KHz, the passband gain is ldB, the stopband is 150KHz, and the stopband gain is −30 dB. The center frequency of the bandpass filter is 100KHz, the passband is 40KHz, the passband gain is 1 dB, the stopband is 120KHz, the stopband gain is −30 dB, and the sampling frequency is 1 MHz. Taking the band-pass filter as an example, Figure 3 shows the magnitude-frequency response of the designed band-pass filter, Figure 4 shows the phase-frequency response of the designed band-pass filter, and Figure 5 shows the group delay response curve of the designed band-pass filter.