An analytical expression for the standard deviation of Total Harmonic Distortion (THD) estimation is derived. It applies to the case where the estimator uses sine fitting. It is shown that, in common circumstances, it is inversely proportional to the actual value of THD, the signal-to-noise ratio and the square root of the number of samples. The proposed expression is validated both with numerical simulations and an experimental setup using a Monte Carlo procedure.
This paper deals with the amplitude estimation in the frequency domain of low-level sine waves, i.e. sine waves spanning a small number of quantization steps of an analog-to-digital converter. This is a quite common condition for high-speed low-resolution converters. A digitized sine wave is transformed into the frequency domain through the discrete Fourier transform. The error in the amplitude estimate is treated as a random variable since the offset and the phase of the sine wave are usually unknown. Therefore, the estimate is characterized by its standard deviation. The proposed model evaluates properly such a standard deviation by treating the quantization with a Fourier series approach. On the other hand, it is shown that the conventional noise model of quantization would lead to a large underestimation of the error standard deviation. The effects of measurement parameters, such as the number of samples and a kind of the time window, are also investigated. Finally, a threshold for the additive noise is provided as the boundary for validity of the two quantization models
The Multi-Tone (MT) signal with uniform amplitudes can be used for DAC testing. This paper shows an easier way to generate a MT signal using several impulse signals. The article also analyzes qualities of methods for testing the dynamic parameters of Digital to Analog Converters using an impulse signal. The MT, Damped Sine Wave (DSW) and Sinx/x (SINC) signals will be used as the source for these tests. The Effective Number of Bits (ENOB) and Signal to noise and distortion (SINAD) are evaluated in the frequency domain and they are modified using the Crest Factor (CF) correction and compared with the standard results of the Sine Wave FFT test. The first advantage of the test using an impulse signal is that you need fewer input parameters to create the band signal for testing the DAC. The second one is to reduce the testing time using a band signal in comparison with multiple tests using a single sine wave.