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Aliasing frequency calculator

Abstract: this application note provides a fast and easy-to-use tool to determine the true position of the mirror signal and the position of the overlapping frequency, as well as the harmonic frequency in the typical spectrum. The obtained data are used to analyze the dynamic characteristics of analog-to-digital converter (ADC) and digital to analog converter (DAC). This calculation tool is based on Excel tables and can be downloaded through the links provided in the application notes

this Excel based, easy-to-use overlapping frequency calculator provides a fast method to locate fundamental harmonics in the first Nyquist band of the data sampling system. This calculator has nothing to do with the sampling process. The system can work in Nyquist sampling, oversampling or undersampling. This tool is very useful for determining the overlapping spectrum of ADC and DAC in the first Nyquist band

this application note discusses the method of calculating the aliasing frequency in the first Nyquist band, including detailed instructions for the use of the overlapping frequency calculator. In addition, in order to enhance understanding, this paper briefly discusses the concepts of aliasing frequency and Nyquist frequency in Brinell, Richter, etc., which are common optional durometers for data sampling systems or specific data converters

aliasing frequency and Nyquist frequency

as we all know, there is frequency aliasing in the data sampling system. When a signal is sampled with a clock lower than the Nyquist frequency, frequency aliasing will occur, where the Nyquist frequency is twice the signal bandwidth. In the real world, the signal spectrum includes fundamental harmonics, as well as noise in and out of the frequency band. The inherent nonlinearity of the system and the nonlinearity of the sampling process will produce the harmonic result of the fundamental wave in the output waveform, which is the original balanced bridge wave component. For all higher harmonics higher than fsamp/2, fsamp is the sampling frequency, and the aliasing frequency will enter the first Nyquist band (Fig. 1a, 1b)

figure 1a Aliasing phenomenon in time domain

Fig. 1b Aliasing in the frequency domain

the fast Fourier transform (FFT) spectrum of discrete time-domain signals can be divided into infinite fsamp/2 bands, namely the Nyquist band. The spectrum between DC and fsamp/2 is the first Nyquist band. The spectral components repeat in different Nyquist bands. Note: the even order Nyquist band is the mirror image of the odd order Nyquist band (Figure 2)

Figure 2 Schematic diagram of multiple Nyquist bands

frequency aliasing of ADC and DAC

aliasing in ADC is generated by the sampling/holding (t/h) process of input stage analog signal. In the field of digital signal processing (DSP), t/h process is equal to the convolution of the spectrum of pulse sequence (determined by the sampling clock) and the analog input spectrum. Convolution results in periodic spectra in different Nyquist bands. When the input signal contains spectral components greater than the Nyquist frequency (fsamp/2), adjacent Nyquist bands will overlap each other, resulting in frequency aliasing

The aliasing in the DAC is generated by the zero order hold (ZOH) process of discrete-time sampling in the output stage (the zero order hold is used to avoid code related pulse interference). In the practical application of DSP in electronic universal tensile machine, the zero order holding process is equal to the convolution of sin (x)/x spectrum (expressed as a rectangular function, used to hold discrete-time samples) and the spectrum (amplitude change) of DAC core output pulse sequence. In addition, like ADC, the periodic output spectrum of different Nyquist bands is the result of convolutionfrom a mathematical point of view, if there is no frequency aliasing, all frequency components lower than fsamp/2 will appear in the spectrum. However, due to frequency aliasing, any harmonic component (fharm) higher than fsamp/2 will also appear as the mirror frequency, and the frequency is: | k x fsamp fharm | where k = 1, 2, 3, etc

the following calculation is used to calculate different harmonics in the first Nyquist band. The State Administration of market supervision also relies on the national professional Metrology Technical Committee for temperature, biology, medicine, ionizing radiation, clinical medicine and so on:

fnyq = fsamp/2

fHARM = N x fFUND;//N is an integer

If (fHARM lies in an odd Nyquist zone) then

fLOC = fHARM % fFUND;//% is the modulus operator

fLOC = fFUND - (fHARM % fFUND);

where fnyq is the Nyquist frequency, fsamp is the sampling frequency, FFund is the fundamental frequency of the signal, fharm is the harmonic frequency of the signal, and floc is the position of the harmonic component in the first Nyquist frequency band

use a simple electronic calculator to calculate the position (floc) of different harmonic frequencies (fharm). First, you must determine the number of iterations. To simplify this process, you can download the overlap frequency Calculator Excel table

the overlap frequency calculator requires two input variables: the sampling frequency fsamp and the signal fundamental frequency FFund. Through these two variables, the calculator can calculate the Nyquist frequency (fnyq), the absolute value of different harmonic frequencies (fharm), and the different harmonics of the first Nyquist band in the overlapping spectrum. An example of calculating the overlap frequency is given in Table 1

table 1 Overlap frequency calculation (input fsamp=500.000000, FFund =29.)

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