An Adaptive Resolution Computationally Efficient Short-Time Fourier Transform (original) (raw)

A Signal Driven Adaptive Resolution Short-Time Fourier Transform

2009

The frequency contents of the non-stationary signals vary with time. For proper characterization of such signals, a smart time-frequency representation is necessary. Classically, the STFT (short-time Fourier transform) is employed for this purpose. Its limitation is the fixed timefrequency resolution. To overcome this drawback an enhanced STFT version is devised. It is based on the signal driven sampling scheme, which is named as the cross-level sampling. It can adapt the sampling frequency and the window function (length plus shape) by following the input signal local variations. This adaptation results into the proposed technique appealing features, which are the adaptive time-frequency resolution and the computational efficiency.

Improved resolution short time Fourier transform

2011 7th International Conference on Emerging Technologies, 2011

Short time Fourier transform is simple and yet effective tool for computing time frequency representations. However, its performance greatly depends upon shape and size of window employed. Longer windows give good frequency resolution while shorter windows give good time resolution. In this paper, we present a novel method to improve the resolution of short time Fourier transform by combining short time Fourier transforms of different window lengths.

Adaptive Time-Frequency Resolution for Analysis and Processing of Audio

Filter banks with fixed time-frequency resolution, such as the Short-Time Fourier Transform (STFT), are a common tool for many audio analysis and processing applications allowing effective implementation via the Fast Fourier Transform (FFT). The fixed time-frequency resolution of the STFT can lead to the undesirable smearing of events in both time and frequency. In this paper, we suggest adaptively varying STFT time-frequency resolution in order to reduce filter bank-specific artifacts while retaining adequate frequency resolution. Several strategies for systematic adaptation of time-frequency resolution are proposed. The introduced approach is demonstrated as applied to spectrogram displays, noise reduction, and spectral effects processing.

High Resolution Time-Frequency Analysis of Non-stationary Signals

Proceedings of the 4th International Conference of Control, Dynamic Systems, and Robotics (CDSR'17), 2017

Time-frequency representations of signals are very important analysis tools which are required in various fields of science and engineering. Observations of most dynamic systems provide non-stationary signals where frequency properties vary in time. There are vast amounts of studies on the development of new time-frequency representations in the literature. Some methods provide better resolutions in time or frequency, or some providing improvements on both resolutions but with the cost of complexity and observation of cross-terms. Currently all methods provide somewhat balanced solutions when compared to their trade-off observables; computation cost, complexity, and performances. Further,their performances are greatly limited by the Heisenberg-Gabor limit. In this work, threedimensional time-frequency distribution (3D-TFD), three dimensional short-time Fourier transform (3D-STFT) are proposed, and the resolution improvement metric vector is defined. They are used to fuse the independent measurements of high resolution time and frequency. A heuristic practical approach is proposed as a proof-of-concept, and tested on a short duration pulse of constant frequency. It is observed that only two layers of 3D-STFT could be sufficient to obtain both high time and high frequency resolutions. Higher resolutions in both axes are obtained simultaneously. This novel method can be used in feature extraction, detection and other analysis applications. A more detailed study is planned as a future work.

GUI Based Time-Frequency Analysis by Short-Time Fourier Transform

—Analysis and application of Short-time Fourier Transform (STFT) in real world cannot be overemphasized. STFT which works by computing Discrete Fourier Transform of several signal segment (window length); it is this DFTs of non-stationary signal over many-number of segments that is called STFT. This project compares and contrasts the matlab in-built library STFT function with our own developed/modified function. Parameters such as window length, hop-size. nfft points, and the choice of window were explored. Variation of these parameters allows us to understand the concept and logic behind STFT algorithm and computation. Associated STFT techniques and concept such Spectrogram and Graphical User Interface (GUI) are also part of this project work.

Short-time fourier transform: two fundamental properties and an optimal implementation

IEEE Transactions on Signal Processing, 2003

Shift and rotation invariance properties of linear time-frequency representations are investigated. It is shown that among all linear time-frequency representations, only the short-time Fourier transform (STFT) family with the Hermite-Gaussian kernels satisfies both the shift invariance and rotation invariance properties that are satisfied by the Wigner distribution (WD). By extending the time-bandwidth product (TBP) concept to fractional Fourier domains, a generalized time-bandwidth product (GTBP) is defined. For mono-component signals, it is shown that GTBP provides a rotation independent measure of compactness. Similar to the TBP optimal STFT, the GTBP optimal STFT that causes the least amount of increase in the GTBP of the signal is obtained. Finally, a linear canonical decomposition of the obtained GTBP optimal STFT analysis is presented to identify its relation to the rotationally invariant STFT.

Adaptive system identification using time-varying Fourier transform

2009 Second International Conference on the Applications of Digital Information and Web Technologies, 2009

In this paper, we introduce a time-varying shorttime Fourier transform (TV-STFT) for representing discrete signals. We derive an explicit condition for perfect reconstruction using time-varying analysis and synthesis windows. Based on the derived representation, we propose an adaptive algorithm that controls the length of the analysis window to achieve a lower mean-square error (MSE) at each iteration. When compared to the conventional multiplicative transfer function approach with a fixed length analysis window, the resulting algorithm achieves faster convergence without compromising for higher steady state MSE. Experimental results demonstrate the effectiveness of the proposed approach.

An Improved S-Transform for Time-Frequency Analysis

2009 IEEE International Advance Computing Conference, 2009

The time-frequency representation (TFR) has been used as a powerful technique to identify, measure and process the time varying nature of signals. In the recent past S-transform gained a lot of interest in time-frequency localization due to its superiority over all the existing identical methods. It produces the progressive resolution of the wavelet transform maintaining a direct link to the Fourier transform. The S-transform has an advantage in that it provides multi resolution analysis while retaining the absolute phase of each frequency component of the signal. But it suffers from poor energy concentration in the timefrequency domain. It gives degradation in time resolution at lower frequency and poor frequency resolution at higher frequency. In this paper we propose a modified Gaussian window which scales with the frequency in a efficient manner to provide improved energy concentration of the S-transform. The potentiality of the proposed method is analyzed using a variety of test signals. The results of the study reveal that the proposed scheme can resolve the time-frequency localization in a better way than the standard S-transform.

Signal estimation from modified short-time Fourier transform

IEEE Transactions on Acoustics, Speech, and Signal Processing, 1984

An algorithm to estimate a signal from its modified short-time Fourier transform (STFT) is presented. This algorithm is computationally simple and is obtained by minimizing the mean squared error between the STFT of the estimated signal and the modified STFT. Using this algorithm, an iterative algorithm to estimate a signal from its modified STFT magnitude is also developed. The iterative algorithm is shown to decrease, in each iteration, the mean squared error between the STFT magnitude of the estimated signal and the modified STFT magnitude. The major computation involved in the iterative algorithm is the discrete Fourier transform computation, and the algorithm appears to be real-time implementable with current hardware technology. The algorithm developed has been applied to the time-scale modification of speech. The resulting system generates very high-quality speech, and appears to be better in performance than any existing method.

A resolution comparison of several time-frequency representations

IEEE Transactions on Signal Processing, 1992

Two signal components are considered "resolved" in a time-frequency representation when two distinct peaks can be observed. The time-frequency resolution limit of two Gaussian components, alike except for their time and frequency centers, are determined for the Wigner distribution, the pseudo-Wigner distribution, the smoothed Wigner distribution, the squared magnitude of the short-time Fourier transform, and the Choi-Williams distribution. The relative performance of the various distributions depends on the signal. The pseudo-Wigner distribution is best for signals of this class with only one frequency component at any one time, the Choi-Williams distribution is most attractive for signals in which all components have constant frequency content, and the matched filter short-time Fourier transform is best for signal components with significant frequency modulation. A relationship between the short-time Fourier transform and the cross-Wigner distribution is used to argue that, with a properly chosen window, the short-time Fourier transform or the cross-Wigner distribution must provide better signal component separation than the Wigner distribution.