# Understanding Linear Regression

May 17, 2006
The CNT-90 timer/counter/analyzer employs linear regression techniques for improved measurement resolution. The inclination of the regression line corresponds to the estimated average period time of the input signal (T*), and is calculated as: ...

The CNT-90 timer/counter/analyzer employs linear regression techniques for improved measurement resolution. The inclination of the regression line corresponds to the estimated average period time of the input signal (T*), and is calculated as:

where:

xk = the number of cycles in sample k;

yk = the time-stamping value in sample k; and

n = the number of samples in the measurement

The uncertainty (variance) of the inclination T* is:

where:

s(y) = the normal root-mean-square (RMS) resolution, tRES, for an individual time stamp and s(x) = the standard deviation of an approximate rectangular distribution,

(xk = x0 + kN/n i.e.,

s(x) ≈ Σ = N/2(3)0.5

for large values of n, which leads to the relative resolution in period or frequency:

s(T*)/T* = s(f*)/f* = 0.52tRES>/0.5>

### Wideband Peak & Average Power Sensor with 80 Msps Sample Rate

Aug. 16, 2024
Mini-Circuits’ PWR-18PWHS-RC power sensor operates from 0.05 to 18 GHz at a sample rate of 80 Msps and with an industry-leading minimum measurement range of -40 dBm in peak mode...

### Turnkey Solid State Energy Source

Aug. 16, 2024
Featuring 59 dB of gain and output power from 2 to 750W, the RFS-G90G93750X+ is a robust, turnkey RF energy source for ISM applications in the 915 MHz band. This design incorporates...