Ahmad I. Abu-El-Haija

Improving performance of digital sinusoidal oscillators by means of error feedback circuits

A few structures for digital sinusoidal oscillators have been proposed, together with the design methods used for such structures. Because of the finite wordlength effects, these structures produce high roundoff errors which change both the amplitude and frequency of the generated sinusoidal signal. This makes it difficult to design an oscillator which generates a sinusoidal waveform with a particular frequency and amplitude. It is shown in this paper that if we add to the direct form digital oscillator a circuit which saves the quantization error and feeds it back for consideration at subsequent iterations, roundoff errors are considerably reduced, and the frequency and amplitude of the generated waveform are very close to those expected by theory. Formulas are derived for the resulting errors and simulation results are given, showing that a significant improvement is obtained by error feedback.

Digital Oscillator Having Low Sensitivity and Roundoff Errors

A digital oscillator structure is proposed which has very low sensitivity and roundoff errors, particularly for low frequencies. The oscillator coefficient implemented is a normalized scaled value of the twos complement of the original coefficient, such that all bits represented are significant. The signal is scaled where appropriate to keep the overall transfer function unchanged. Multipliers used in the proposed structure have the same width as that in the direct form digital oscillator, although the performance is significantly improved.

Digital filter structures having low errors and simple hardware implementation

Sensitivity and roundoff errors can seriously limit the application of recursive digital filters in practice, particularly when the filters have poles near z = + 1 . A filter structure, based on digital incremental computers is proposed, which has low sensitivity, good error characteristics, and simple hardware implementation for pole locations close to z = + 1 . Expressions for the roundoff errors are derived and compared to those for conventional structures. A design procedure is suggested to implement the new filter structure given the transfer function. Simulation results are presented.

A digital receiver for Dual Tone Multifrequency (DTMF) signals

A new digital receiver for Dual Tone Multifrequency (DTMF) signals is proposed in this paper. This receiver is equivalent to the optimal analog receiver. The received DTMF signal is passed through two group filters and eight very narrow bandpass tone filters. The outputs of the group filters are used to compute thresholds, while those of the tone filters are used to compute norm-sums for blocks of 80 samples. These norm-sums are compared to a theoretical expected norm-sum based on the estimated signal peak by a threshold estimation stage. The proposed receiver has a very low probability of error even when the incoming signal is severely buried in noise. It is implemented using TMS32010 assembly language and examined in real time.

Fast and accurate measurement of power system frequency

A simple, fast and accurate method is presented for the measurement of the power system frequency. The method is based upon counting the number of strips (or samples) between zero crossings during one complete cycle of the sinusoidal waveform. Since the number of strips is usually not an integer, an estimate is derived that is very close to the actual value. The frequency is directly calculated front the number of strips. The measurement can be performed in at most 25 ms for a 60-Hz frequency, and at most 30 ms for a 50-Hz frequency. If the sinusoidal signal is sampled at 8 kHz for the purpose of measurement, the proposed method achieves accuracy in measuring the frequency of about 0.0001-0.0004 Hz.

A structure for digital notch filters

Narrow-band digital notch filters have their poles near the unit circle. As the sampling rate is increased, the poles move towards z = +1. Implementing such filters requires long registers to overcome the sensitivity and roundoff errors. A filter structure based on digital incremental computers is proposed which has low sensitivity and round-off errors, and simple hardware implementation. The filter structure can be directly used on differentially pulse-code modulated signals. Hardware multipliers are not required as the poles approach z = +1 , and excellent results can be obtained using multipliers with very short word lengths, or with small size read-only memories.

Recursive digital sine wave oscillators using the TMS32010 DSP

Digital sine wave oscillators are implemented in this paper using the TMS32010 digital signal processor (DSP), specifically the TMS32010 Evaluation Module kit (EVM) and the Analog Interface Board (AIB). These oscillators are based on solutions of the second-order difference equation and its modifications. the considered oscillator structures are: the direct form, modified direct form, first-order error feedback, and second-order error feedback. The parameters of these oscillators are implemented in 32 bits to reduce the harmonic distortion, improve the frequency resolution, and generate very low frequencies while maintaining a large number of samples per cycle. the performance of the implemented oscillators is evaluated and compared with that of the look-up table (LUT) methods. The numerical results obtained indicate the superiority of our oscillator structures over other oscillators using LUT, or TMS320 series.<<ETX>>

Frequency determination of weak sinusoids buried in noise

A simple method for estimating the frequency of a sinusoidal signal highly contaminated with noise is described in this paper. The proposed method uses digital signal processing techniques such as least squares smoothing, numerical integration, windowing, and sampling rate reduction for filtering out the noise with only simple computational needs. The frequency is estimated by counting the number of maxima and minima of the resulting signal. For sinusoidal signals which can be sampled at a high rate relative to the Nyquist limit, this method is particularly attractive, and gives good estimates even for very low values of signal-to-noise ratio (SNR).

Fast detection of amplitude and frequency of sinusoidal signals using calculus of finite differences

A novel digital method for the fast and simultaneous detection of amplitude and frequency of sinusoidal signals is presented. First and second derivatives of the input signal are evaluated numerically using the calculus of finite differences, from which the desired parameters are measured. The measurement can be accomplished using a few samples of the sinusoidal waveform; and more samples can be considered to improve accuracy.

A Digital Incremental Oscillator: Generation of Sinusoidal Waveform in DPCM

Based on the concept of incremental computations, a digital oscillator structure is proposed which consists of two incremental integrators and one incremental multiplier. Models for these elements are developed and detailed analyses are made showing that the errors of the proposed structure are extremely low compared with the direct-form one. The proposed oscillator structure can be implemented without a hardware multiplier and can generate sinusoidal waveforms in the differential pulse code modulation representation.