We analyze the effect of window choice on the zero-padding method and corrected quadratically interpolated fast Fourier transform using a harmonic signal in noise at both high and low signal-to-noise ratios (SNRs) on a theoretical basis. Then, we validate the theoretical analysis using simulations. The theoretical analysis and simulation results using four traditional window functions show that the optimal window is determined depending on the SNR; the estimation errors are the smallest for the rectangular window at low SNR, the Hamming and Hanning windows at mid SNR, and the Blackman window at high SNR. In addition, we analyze the simulation results using the signal-to-noise floor ratio, which appears to be more effective than the conventional SNR in determining the optimal window.

Adaptive noise cancellation using adaptive filters is a known method for removing noise that interferes with signal measurements. The adaptive noise canceller performs filtering based on the current situation through a windowing process. The shape of the window function determines the tracking performance of the adaptive noise canceller with respect to the fluctuation of the property of the unknown system that noise (reference signal) passes. However, the shape of the window function in the field of adaptive filtering has not yet been considered in detail. This study mathematically treats the effect of the window function on the adaptive noise canceller and proposes an optimization method for the window function in situations where offline processing can be performed, such as biomedical signal measurements. We also demonstrate the validity of the optimized window function through numerical experiments.

The sliding discrete Fourier transform (DFT) is a well-known algorithm for obtaining a few frequency components of the DFT spectrum with a low computational cost. However, the conventional sliding DFT cannot be applied to practical conditions, e.g., using the sine window and the zero-padding DFT, with preserving the computational efficiency. This paper discusses the extension of the sliding DFT to such cases. Expressing the window function by complex sinusoids, a recursive algorithm for computing a frequency component of the DFT spectrum using an arbitrary sinusoidal window function is derived. The algorithm can be easily extended to the zero-padding DFT. Computer simulations using very long signals show the validity of our algorithm.

This letter proposes a new transceiver for OFDM systems based on Smooth Local Trigonometric Transform (LTT). In our transceiver, the transmitter is realized by first modulating the original serial data using a constellation mapper, then feeding the results into the inverse LTT modulator. Unlike the conventional DFT-OFDM system, which always uses the roll cosine function as its window function, the proposed system needs no additional window function for the reason that LTT transform includes a bell-shaped window function by itself. Moreover, each LTT-OFDM symbol has a much more rapid attenuation rate outside of the spectral bandwidth and better spectrum convergence. In the receiver, the original data is recovered by demodulating the received data using forward LTT. Comparative simulation results from the conventional DFT-OFDM system, the system we proposed, and the recently proposed DCT based OFDM system are discussed in terms of bit error rate (BER).

The speech noise reduction system based on the frequency domain adaptive line enhancer using a windowed modified DFT (MDFT) pair is presented. The adaptive line enhancer (ALE) is effective for extracting sinusoidal signals blurred by a broadband noise. In addition, it utilizes only one microphone. Therefore, it is suitable for the realization of speech noise reduction in portable electronic devices. In the ALE, an input signal is generated by delaying a desired signal using the decorrelation parameter, which makes the noise in the input signal decorrelated with that in the desired one. In the present paper, we propose to set decorrelation parameters in the frequency domain and adjust them to optimal values according to the relationship between speech and noise. Such frequency domain decorrelation parameters enable the reduction of the computational complexity of the proposed system. Also, we introduce the window function into MDFT for suppressing spectral leakage. The performance of the proposed noise reduction system is examined through computer simulations.

The discrete-time short-time Fourier transform (STFT) is known as a useful tool for analyzing and synthesizing signals. This paper introduces an extention of the well-known STFT to a general form which is more suitable for high resolutional signal analysis. A channel frequency division scheme is developed for realizing arbitrary bandwidth and center frequency so as to improve resolution performance. It is based on a nonuniform filter bank structure with integer decimation and interpolation factors. A design example of the generalized STFT using symmetric windows is given.

This paper describes the general conditions for perfect signal reconstruction in adaptive blocksize MDCT. MDCT, or modified Discrete Cosine Transform, is a method in which blocks are laid to overlap each other. Because of block overlapping, some consideration must be paid to reconstructing the signals perfectly in adaptive blocksize schemes. The perfect reconstruction conditions are derived by considering the reconstruction signals, on a segment by segment basis. These conditions restrict the analysis/synthesis windows in the MDCT formula. Finally, this paper evaluates two examples of window sets, including windows used in the ISO MPEG audio coding standard.