## A Pitch Dependent Time-Frequency Response for Periodic Signals (1998)

### BibTeX

@MISC{Kramer98apitch,

author = {Michael L. Kramer and Douglas L. Jones},

title = {A Pitch Dependent Time-Frequency Response for Periodic Signals},

year = {1998}

}

### OpenURL

### Abstract

Although several kernel design methods have been proposed for improved time-frequency responses (TFRs) for various signal classes, the family of simple periodic signals has not been specifically considered. Many signals, such as speech and music, which are analyzed using timefrequency techniques exhibit a strong periodic structure. Here we develop an improved TFR designed for periodic functions, under the assumption that the fundamental period of the signal is known or can at least be accurately estimated. 1 Introduction Bilinear distributions are often preferred over linear representations, such as the STFT, for their high time-frequency resolution [1]. Although the simplicity and efficiency of the STFT makes it a very common choice as a general-purpose TFR, (and its squared magnitude, the spectrogram, has long been used for speech analysis) its resolution capabilities are limited. Specifically, for accurate frequency representation, the analysis window must contain several periods of...

### Citations

142 |
Time-Frequency Distributions: A Review
- Cohen
- 1989
(Show Context)
Citation Context ...o. N00167-94-M-7133, and by the Office of Naval Research, contract no. N00014-95-1-0674. If we further restrict our choice of possible representations to a member of the shift-invariant Cohen's class =-=[2]-=-, the problem of finding the best TFR for the periodic signals of interest becomes a matter of finding an appropriate kernel which exploits the periodicity of the signal. The fundamental problem with ... |

21 |
A resolution comparison of several time-frequency representations
- Jones, Parks
(Show Context)
Citation Context ...nal is known or can at least be accurately estimated. 1 Introduction Bilinear distributions are often preferred over linear representations, such as the STFT, for their high time-frequency resolution =-=[1]-=-. Although the simplicity and efficiency of the STFT makes it a very common choice as a general-purpose TFR, (and its squared magnitude, the spectrogram, has long been used for speech analysis) its re... |

6 |
The aliasing problem in discrete-time Wigner distributions
- Claasen, Mecklenbrauker
- 1983
(Show Context)
Citation Context ...a scaling of the �� variably by two to avoid non-integer samples. Doing so results in aliasing which can be circumvented by using the analytic representation of the signal (positive frequencies on=-=ly) [7]-=-. Since most periodic signals of interest are real this does not pose a problem. The second implementation obstacle is the availability of x(n) for all n. Because we may desire a real-time system, we ... |

3 |
Transient analysis of speech signal using the Wigner time frequency representation,” ICASSP May 89,Glasgow
- Velez
(Show Context)
Citation Context ...ow-pass kernels excessively attenuate the desirable auto-terms falling outside the support of \Phi(`; �� ). A technique for handling the periodicity of speech signals was proposed by Velez and Abs=-=her [4]-=- and involves choosing a window for the pseudo-Wigner distribution (PWD) to have length just greater than the maximum expected pitch period. This is done in order to limit the number of periods includ... |

3 |
The Wigner distribution -- a tool for time--frequency analysis, Part I: Continous signals
- Claasen, auker
- 1980
(Show Context)
Citation Context ...ility of x(n) for all n. Because we may desire a real-time system, we must window the signal prior to computing W x (t; !). The resulting distribution is referred to as the pseudo-Wigner distribution =-=[6], an-=-d its discretized version is given as DPW x (n; k) = L 2 X m=\Gamma L 2 x(n +m)x (n \Gamma m)w(m)w (\Gammam)e \Gammaj 2�� M mk ; (13) where, for our purposes, w(n) is a symmetric window of length ... |

2 |
McGonegal, "A comparative performance study of several pitch detection algorithms
- Rabiner
- 1976
(Show Context)
Citation Context ...wledge of the period, T , of the driving impulse train, so this period must then be accurately estimated for the local region of interest. The pitch can be estimated by a number of well-known methods =-=[5]-=-, so for now we consider the signal to have a known (i.e., accurately estimated) local periodicity of T . Because kernel design is often easiest in the correlative domain, we focus on designing an app... |

1 |
Adaptive Time-Frequency Analysis and Synthesis
- Kramer
- 1995
(Show Context)
Citation Context ...ined within this region of support will be insufficient to exhibit this periodicity, because 1 All integrals and discrete summations are from \Gamma1 to 1 unless otherwise stated. See the appendix in =-=[3]-=- for derivations of equations in this paper. when too few pitch periods are included, a very fine frequency periodicity will become blurred and often undetectable. Because X(!) is also periodic, the i... |