• Proceedings of the IEEK Conference
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• 2002.06e
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• pp.9-12
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• 2002

The problem of sub-Nyquist nonuniform sampling for the perfect reconstruction of signals with time-varying spectral contents is studied. The signals are assumed to have a known instantaneous bandwidth in time-frequency domain. As the function of time, the nonuniform sampling pattern of a given signal, that is, the instantaneous sampling frequency is determined by the observation of instantaneous bandwidth based on time-frequency analysis. The proposed sampling pattern guarantees the perfect reconstruction of nonuniform sampled signals under Nyquist-sampling rate in average.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.351-358
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• 2007

For an entire function f whose Fourier transform has a compact support confined to $[-{\pi},\;{\pi}]$ and restriction to ${\mathbb{R}}$ belongs to $L^2{\mathbb{R}}$, we derive a nonuniform sampling theorem of Lagrange interpolation type with sampling points ${\lambda}_n{\in}{\mathbb{R}},\;n{\in}{\mathbb{Z}}$, under the condition that $$\frac{lim\;sup}{n{\rightarrow}{\infty}}|{\lambda}_n-n|<\frac {1}{4}$.

• Speech Sciences
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• v.12 no.2
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• pp.153-170
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• 2005

The sub-Nyquist nonuniform sampling (SNNS) and the perfect reconstruction (PR) formula are proposed for the development of a systematic method to obtain minimal representation of a speech signal. In the proposed method, the instantaneous sampling frequency (ISF) varies, depending on the least upper boundary of spectral support of a speech signal in time-frequency domain (TFD). The definition of the instantaneous bandwidth (IB), which determines the ISF and is used for generating the set of samples that represent continuous-time signals perfectly, is given. Also, the spectral characteristics of the sampled data generated by the sub-Nyquist nonuniform sampling method is analyzed. The proposed method doesn't generate the redundant samples due to the time-varying property of the instantaneous bandwidth of a speech signal.

• The Journal of the Acoustical Society of Korea
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• v.14 no.5
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• pp.89-93
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• 1995

To reduce the redundancy within samples that resulted from uniform sampling method, nonuniform sampling or nonredundant-sample coding methods can be considered. However, it is well known that when conventional nonuniform sampling methods are applied directly to speech signal, the required amount of data is comparable to or mure than that by uniform sampling method like PCM. To overcome this problem, a new nonuniform sampling method is proposed, in which nonuniform sampling is applied to the low-pass filtered speech signal and higher band is compensated by 8 colored Gaussian random noise with various noise levels. By this method, speech signal waveform can be encoded by 1.8 times larger compression ratio than the conventional nonuniform sampling method.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.379-385
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• 2014

For a bandlimited function with polynomial growth on the real line, we derive a nonuniform sampling expansion using a special bandlimited function which has polynomial decay on the real line. The series converges uniformly on any compact subsets of the real line.

• The Journal of the Acoustical Society of Korea
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• v.16 no.6
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• pp.110-114
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• 1997

When applying the nonuniform sampling to noisy speech signal, the required data rate increases to be comparable to or more than that by uniform sampling such as PCM. To solve this problem, we have proposed the waveform coding method, multiband nonuniform waveform coding(MNWC), applying the nonuniform sampling to band-separated speech signal[7]. However, the speech quality is deteriorated when it is compared to the uniform sampling method, since the high band is simply modeled as a Gaussian noise with average level. In this paper, as a good method to overcome this drawback, the high band is modeled as one of 16 codewords having different center frequencies. By doing this, with maintaining high speech quality as MOS score of average 3.16, the proposed method achieves 1.5 times higher compression ratio than that of the conventional nonuniform sampling method(CNSM).

• The Journal of the Acoustical Society of Korea
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• v.11 no.4
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• pp.36-44
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• 1992

To reduce the redundancy within samples that resulted from uniform sampling method, nonuniform sampling or nonredundant-sample coding methods can be considered. But it is well-known that when conventional nonuniform sampling methods are applied directly to speech signal, the amount of data required is comparable to or more than that required by uniform sampling method like PCM. To overcome this problem, we consider properties of speech signal in the sense of perception, and suggest a nonuniform sampling method at the maxima and minima of speech wave. To analyze the performance of the suggested method, compression ratio is considered. We show that compression ratio can be improved by silence detection, which can't be implemented by conventional methods based on uniform sampling. As experimental results, compression ratios of 1.54 without silence detection and 2.88 with silence detection for 8kHz 8-bit PCM signals are obtained.

• Journal of the Korean Institute of Intelligent Systems
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• v.24 no.1
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• pp.28-32
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• 2014

For a signal such as speech showing piece-wise linear shape in a very short time period, a nonuniform sampling method based on the inflection point detection (IPD) is proposed to reduce data rate. The method exploits the geometrical characteristics of signal further than the existing local maxima/minima detection (MMD) based sampling method. As results, the reconstructed signal by the interpolation of the IPD based sampled data resembles the original speech more. Computer simulation shows that the proposed IPD based method produces about 9~23 dB improvement over the existing MMD method. To show the usefulness of the IPD technique, it is applied to speech coding, and compared to the continuously variable slope delta modulation (CVSD). The nonuniformly sampled data is binary coded with one bit flag set "1". Noninflection samples are not sent, but only flag bits set 0 are sent. The method shows 0.3 ~ 9 dB SNR and 0.5 ~ 1.3 mean opinion score (MOS) improvements over the CVSD.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.16 no.2 s.93
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• pp.120-127
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• 2005

The design method of the transversal filter using continuously cascaded directional couplers is presented. The coupler can be treated for a continuously varying nonuniform coupled transmission line. The design method is based on the optimum extraction of desired coupling factor by the control of null positions which are inherent to the coupling spectra pattern. In the optimization process, the improved Woodward-Lawson sampling method is applied to easily synthesize the distributed delay and weighting elements for transversal filter properties. For application, the microstrip transversal filter is fabricated and optimum dielectric overlay is introduced for the mode phase velocity compensation for non-TEM coupler nodes by using SDA(Spectral Domain Approach). Experiment results confirm the validity of the proposed method.

• The Journal of the Acoustical Society of Korea
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• v.20 no.1
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• pp.13-20
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• 2001

Adaptive digital filters with long impulse response such as acoustic echo canceller and active noise controller suffer from slow convergence and computational burden. Subband techniques and multirate signal processing have been recently developed to improve the problem of computational complexity and slow convergence in conventional adaptive filter. Any FIR transfer function can be realized as a serial connection of interpolators followed by subfilters with a sparse impulse response. In this case, each interpolator which is related to the column vector of Hadamard matrix has band-pass magnitude response characteristics shifted uniformly. Subband technique using Hadamard transform and decimation of subband signal to reduce sampling rate are adapted to system modeling and acoustic noise cancellation In this paper, delayless subband structure with nonuniform bandwidth has been proposed to improve the performance of the convergence speed without aliasing due to decimation, where input signal is split into subband one using tree-structured filter bank, and the subband signal is decimated by a decimator to reduce the sampling rate in each channel, then subfilter with sparse impulse response is transformed to full band adaptive filter coefficient using Hadamard transform. It is shown by computer simulations that the proposed method can be adapted to general adaptive filtering.