A set of sum-cosine window functions
01 Jun 1985-International Journal of Electronics (Taylor & Francis Group)-Vol. 58, Iss: 6, pp 969-974
TL;DR: A set of windows, called sum-cosine windows, whose first side-lobe level varies from −39-30 to − 67-66dB, while the peak sidelobe offers −39 to − 6312dB attenuation are presented, resulting in easy implementation compared to the near-optimum windows proposed by Kaiser.
Abstract: This paper presents a set of windows, called sum-cosine windows, whose first side-lobe level varies from −39-30 to − 67-66dB, while the peak sidelobe offers −39-30 to − 6312dB attenuation The asymptotic decay rate of the sidelobe envelope ranges from 12dB per octave to 36dB per octave However, the main-lobe width of these windows falls in between Hamming and Blackman windows and Black-man windows and the optimum windows, proposed by Harris and Nuttall The distinct advantage of these windows is their simple form, resulting in easy implementation, compared to the near-optimum windows proposed by Kaiser
Citations
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Patent•
11 Sep 2012
TL;DR: A signal processor for providing a processed version of an input signal in dependence on the input signal comprises a windower configured to window a portion of input signal, or of a pre-processed version thereof, in depending on a signal processing window described by signal processing windows values for a plurality of window value index values as mentioned in this paper.
Abstract: A signal processor for providing a processed version of an input signal in dependence on the input signal comprises a windower configured to window a portion of the input signal, or of a pre-processed version thereof, in dependence on a signal processing window described by signal processing window values for a plurality of window value index values, in order to obtain the processed version of the input signal. The signal processor also comprises a window provider for providing the signal processing window values for a plurality of window value index values in dependence on one or more window shape parameters.
8 citations
TL;DR: The locust slice images have all the features such as strong self-similarity, piecewise smoothness and nonlinear texture structure.
Abstract: The locust slice images have all the features such as strong self-similarity, piecewise smoothness and nonlinear texture structure. Multi-scale interpolation operator is an effective tool to descri...
3 citations
15 May 2009
TL;DR: In this article, a new method for obtaining series of window functions is introduced, which is sum of sinc sum functions (S-SUMF), which is a form of frequency response expression of digital filters.
Abstract: A new method for obtaining series of window functions is introduced. A novel form of frequency response expression of digital filters is deduced which is sum of sinc sum functions. One of the remarkable characteristics of the form is that weights(coefficients of terms) of window functions can be directly calculated according to the expression. An example for how to find a window function is illustrated in detail. An instance of series of window functions is tabled with both window weights and filter performances. Stopband attenuation of filters is from 32db to 63db with the gap about 3db. With same performances of stopband attenuation and transition width both the order and passband ripple of filters using the new method is little better than that using Kaiser window if passband attenuation is smaller than 50db and little worse if bigger than 52db. The obtained window functions are as simple as Blackman window function. The outstanding feature of the new approach is that it can provide a very efficient way to find series of window functions with both good performances and easy calculation.
2 citations
Cites methods from "A set of sum-cosine window function..."
...Further about window method, all existed windows that have been tried to find are all based on the approach of window frequency responses[6-11], of which the edge of the mainlobe or the height of sidelobes in frequency domain must be small....
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01 Jan 2017
TL;DR: A comprehensive review and extension of conventional approaches for perceptual coding of arbitrary multichannel audio signals with particular emphasis to use cases ranging from two-channel stereophonic to six-channel 5.1-surround setups with or without the application-specific constraint of low algorithmic coding latency.
Abstract: The increasing number of simultaneous input and output channels utilized in immersive
audio configurations primarily in broadcasting applications has renewed industrial
requirements for efficient audio coding schemes with low bit-rate and complexity. This
thesis presents a comprehensive review and extension of conventional approaches for
perceptual coding of arbitrary multichannel audio signals. Particular emphasis is given
to use cases ranging from two-channel stereophonic to six-channel 5.1-surround setups
with or without the application-specific constraint of low algorithmic coding latency.
Conventional perceptual audio codecs share six common algorithmic components,
all of which are examined extensively in this thesis. The first is a signal-adaptive filterbank,
constructed using instances of the real-valued modified discrete cosine transform
(MDCT), to obtain spectral representations of successive portions of the incoming discrete
time signal. Within this MDCT spectral domain, various intra- and inter-channel
optimizations, most of which are of linear predictive nature, are employed as a second
step to minimize spectral, temporal, and/or spatial redundancy. These processing steps
are succeeded by a psychoacoustically motivated and controlled quantization process,
with optional simple parametric extensions such as noise substitution or related forms
of MDCT coefficient exchange, in order to reach the desired coding bit-rate. The fourth
component comprises lossless entropy coding of the quantized spectral coefficients and
parameters as well as the compilation of all entropy coded data into a transmittable bitstream.
Components five and six, finally, represent low-bit-rate methods for improved
high-frequency regeneration for audio bandwidth extension and downmix-based stereo
or surround coding, which generally do not operate in the MDCT domain but require an
additional pair of complex-valued pseudo-quadrature mirror filter (QMF) banks around
the MDCT core infrastructure. The auxiliary filter-banks are shown to notably increase
both the algorithmic codec complexity and latency, rendering their usage for low-delay
communication applications difficult, especially on battery-powered mobile devices.
The complex-domain coding tools can be regarded as pre- and post-processors to the
MDCT core-coder, and it is demonstrated that most algorithmic details of these tools can
be integrated directly into the MDCT architecture. Moreover, algorithms for respective
encoder-side calculation of the modified spectral coefficients and the associated coding
parameters, i. e., analysis, are derived which allow the decoder-side reconstruction, i. e.
synthesis, to remain real-valued. More specifically, exclusive utilization of the MDCT can
be maintained in the decoder, while the modulated complex lapped transform (MCLT),
whose real part is the MDCT and whose imaginary part is represented by the modified
discrete sine transform (MDST), may be employed in the encoder for best audio quality.
Phase-related details of the conventional complex-valued coding algorithms, which are
difficult to realize using only real-valued transformation, are substituted by an intensity
downmix-based but subjectively acceptable encoder-side pre-processing operation.
The characteristics of state-of-the-art MDCT filter-bank designs are the second focus
of this thesis. Continuing the above investigation of parametric stereo/surround coding
methods, an extension of the MDCT coding paradigm, applying sine modulation by way
of the MDST instead of the traditional cosine modulation in some channels, is described.
Time domain aliasing cancelation (TDAC) compliant transitions between the MDCT and
MDST instances, for perfect reconstruction (PR) in the absence of spectral quantization,
are discussed. When used in a signal-adaptive fashion, this so-called “kernel switching”
method leads to significant coding quality gains on input material with an inter-channel
phase difference (IPD) around ±90°. Thereafter, a so-called “ratio switching” approach
is presented. Its purpose is the signal-adaptive variation of the inter-transform overlap
ratio based on the input’s instantaneous harmonicity and temporal flatness. To this end
the definition of the extended lapped transform (ELT), whose overlap ratio exceeds that
of the MDCT and MDST, is modified to allow transitions to and from the latter two transforms
with PR, i. e., proper TDAC. Using the modified ELT (MELT) with a newly designed
window function on tonal quasi-stationary waveform portions, e. g., recordings of single
instruments, while resorting to the MDCT or MDST on noise-like and/or non-stationary
parts, is shown to yield small but significant improvements in overall coding quality.
For low-delay use cases, where the additional look-ahead due to increased transform
overlap ratio is undesirable, long-term predictive (LTP) coding as an alternative to ratio
switching is examined as a third and final topic. After reviews of conventional time- and
frequency-domain approaches, a new MDCT-domain algorithm with low parameter rate
(one periodicity value per time unit) and complexity (a fraction of that of the prior art)
is proposed. Supporting intra- and inter-channel prediction, this frequency-domain predictor
(FDP) offers coding gains which are close, and orthogonal, to those of the MELT.
The work concludes with comparative objective and subjective evaluation of the presented
contributions, when integrated into the MPEG-D USAC based MPEG-H 3D Audio
codec. Objective assessment reveals large savings in delay and decoder complexity, and
blind subjective testing indicates that, in terms of audio quality, the modified MPEG-H
codec matches or outperforms the respective state of the art in both general-purpose
and low-delay applications. Most importantly, for both stereo and 5.1-surround channel
configurations, more consistent audio quality across the different types of input signals,
with fewer observed negative outliers, is achieved in comparison to the state of the art.
2 citations
Patent•
08 Mar 2011
TL;DR: A signal processor for providing a processed version of an input signal in dependence on the input signal comprises a windower configured to window a portion of input signal, or of a pre-processed version thereof, in depending on a signal processing window described by signal processing windows values for a plurality of window value index values as discussed by the authors.
Abstract: A signal processor for providing a processed version of an input signal in dependence on the input signal comprises a windower configured to window a portion of the input signal, or of a pre-processed version thereof, in dependence on a signal processing window described by signal processing window values for a plurality of window value index values, in order to obtain the processed version of the input signal. The signal processor also comprises a window provider for providing the signal processing window values for a plurality of window value index values in dependence on one or more window shape parameters.
1 citations
References
More filters
01 Jan 1978
TL;DR: A comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared is included, and an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.
Abstract: This paper makes available a concise review of data windows and their affect on the detection of harmonic signals in the presence of broad-band noise, and in the presence of nearby strong harmonic interference. We also call attention to a number of common errors in the application of windows when used with the fast Fourier transform. This paper includes a comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared. Finally, an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.
7,130 citations
TL;DR: Correct plots of Harris' windows are presented and additional windows with very good sidelobes and optimal behavior under several different constraints are derived.
Abstract: Some of the windows presented by Harris [1] are not correct in terms of their reported peak sidelobes and optimal behavior. We present corrected plots of Harris' windows and also derive additional windows with very good sidelobes and optimal behavior under several different constraints. The temporal weightings are characterized as a sum of weighted cosines over a finite duration. The plots enable the reader to select a window to suit his requirements, in terms of bias due to nearby sidelobes and bias due to distant sidelobes.
1,024 citations
[...]
TL;DR: In this paper, a simple window that yields 6 dB improvement in the first sidelobe gain with almost no loss in the maximum sidclobe gain, compared with that of Kaiser's near optimum zeroth-order Bessel window, is developed.
Abstract: A simple window that yields 6 dB improvement in the first sidelobe gain, with almost no loss in the maximum sidclobe gain, compared with that of Kaiser's near optimum zeroth-order Bessel window, is developed. The main-lobe energy of Kaiser's window is about 0.00078% more than that of the new window. The distinct advantage of the window is its very simple form similar to that of a Hamming window.
8 citations