A sliding Goertzel algorithm

LMS-based notch filter for the estimation of sinusoidal signals in noise

This paper presents a new computational algorithm for the Fourier transform at arbitrary frequencies. This algorithm, if an input signal has r frequencies, can be implemented by one FIR filter composed of r second-order digital notch filters (2-DNF's; H_{p}(z) = 1 - 2 \cos (2\pif_{p}/f_{s}) z^{-1} + z^{-2} ), and r second-order digital resonators (2- DR's; H' p (z)= 1/H p (z)) where frequencies f p (p = 1, ..., r) are arbitrary and f s is a sampling frequency. This algorithm is referred to as the notch Fourier transform (NFT). This NFT algorithm has the following main advantages, 1) It can be applied to the input signal composed of arbitrary frequencies. 2) In advance of the end of one period of the signal, Fourier coefficients can be computed. 3) Although we can analyze the input signal composed of r arbitrary frequencies by solving simultaneous equations, the amount of processing in the NFT is smaller by the order of magnitude N where N = 2r is the number of sample data. At every sampling time after one block of data, the NFT can compute all Fourier coefficients with the number of multiplications proportional to N. But for the exact computation of Fourier coefficients, we must know the signal frequencies in advance.

Notch Fourier transform

Reproduction accuracy of a digital signal, representing for example stereo audio signals, is improved by transmitting sample data which have been encoded to form transmission signals. The transmission signals are arranged in consecutive frames, each frame including a plurality of information packets, and each information packet including N bits. The number of information packets in a frame is determined by the ratio of the product of the transmission bit-rate and the number of samples represented in the frame, to the product of the number of bits in a packet and the sampling frequency. The transmission signals are recorded in a record carrier, or are transmitted in real time. In a digital stereo audio signal embodiment, the samples may be sub-band encoded or transform encoded. The transmission signal may include an indicator signal indicating a combination of certain samples, or scale factor signals for specific components of the sampled signal.

Decoding of an encoded wideband digital audio signal in a transmission system for transmitting and receiving such signal

The main purpose of this paper is to introduce a fast method for gene prediction in DNA sequences based on the period-3 property in exons. First, the symbolic DNA sequences were converted to digital signal using the electron ion interaction potential method. Then, to reduce the effect of background noise in the period-3 spectrum, we used the discrete wavelet transform at three levels and applied it on the input digital signal. Finally, the Goertzel algorithm was used to extract period-3 components in the filtered DNA sequence. The proposed algorithm leads to decrease the computational complexity and hence, increases the speed of the process. Detection of small size exons in DNA sequences, exactly, is another advantage of the algorithm. The proposed algorithm ability in exon prediction was compared with several existing methods at the nucleotide level using: (i) specificity - sensitivity values; (ii) receiver operating curves (ROC); and (iii) area under ROC curve. Simulation results confirmed that the proposed method can be used as a promising tool for exon prediction in DNA sequences.

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A fast algorithm for exonic regions prediction in DNA sequences.

It is shown that for nonrecursive digital filters in the first canonic form the hardware requirements are proportional to the output rate. Using a low output rate, a relatively simple receiver for multifrequency-code (MFC) signals can be achieved. Linear phase bandpass pairs with a 90° phase difference are used to eliminate the input signal phase dependence. Narrow linear phase bandpass filters with even and odd symmetric impulse response are compared with filters with no phase constraints. It turns out that linear phase filters are almost as good as filters without phase constraints and that 8 bits are enough for the filter coefficients. Some aspects of the design of a digital receiver for PCM-encoded MFC signals are discussed.

F. Braun

Papers

Nonrecursive digital filters for detecting multifrequency code signals