The inverse transform can create a time-domain waveform where no waveform has been before. In part 2 of this series, we used the discrete Fourier transform to convert a waveform from the time domain to the frequency domain, operated on the frequency-domain data, and used the inverse transform to reconstruct the altered time-domain waveform. That’s […]
How to calculate and apply an inverse FFT: part 2
In part 1 of this series, we looked at the formula for the inverse discrete Fourier transform and manually calculated the inverse transform for a four-point dataset. Then, we used Excel’s implementation of the inverse fast Fourier transform (IFFT) to verify our work. Could we try something more realistic? Sure. We can take a signal […]
How to determine noise figure: part 4
Two incompatible definitions of noise factor can lead to confusion, which you can alleviate by understanding where the differences lie.
How to determine noise figure: part 3
Noise factor and noise figure as defined in an IEEE standard can be derived from a two-port device’s equivalent noise temperature. In part 1 and part 2 of this series we discussed several ways to indicate the noise performance of a device under test (DUT). We first introduced the concept of noise factor based on […]
How to determine noise figure: part 2
The relationship between noise and temperature prompted a precursor of the IEEE to promulgate an alternative definition of noise figure in 1959. In part 1 of this series, we described the work of the Danish-American radio engineer Harald Friis, who described noise factor F of a device or system as the ratio of the input-power […]
How to determine noise figure: part 1
A noise figure consolidates the effects of various noise types to provide a single specification for the noise performance of a component or system. In electronic circuits and systems, noise is an undesirable, inevitable disturbance in currents and voltages. Noise has many underlying fundamental causes. Thermal noise, also known as Johnson–Nyquist noise, results from random […]
How to interpret a QAM display: part 3
Error vector magnitude characterizes actual QAM signals’ deviations from their ideal locations due to nonlinearity and phase noise. In part 1 of this series, we discussed quadrature amplitude modulation (QAM), which results from summing orthogonal amplitude-modulated cosine and sine waves of the same frequency. In part 2, we looked at assigning bit sequences to QAM […]
How to interpret a QAM display: part 2
Sixteen unique 16-QAM symbols can each convey a unique 4-bit sequence. In part 1 of this series, we discussed quadrature amplitude modulation (QAM), which results from summing amplitude-modulated cosine and sine waves of the same frequency. We also looked at the constellation diagram, which a test instrument such as an oscilloscope or vector signal analyzer […]
How to interpret a QAM display: part 1
A constellation diagram plots a quadrature amplitude modulation (QAM) signal’s in-phase and quadrature components. The EE World article “Should I use a spectrum, signal, or vector network analyzer?” in part 3 mentioned that vector-signal analyzers (VSAs) can display modulation-domain and frequency-domain information. Other instruments incorporating digital signal processing (DSP) capabilities, including oscilloscopes, can provide insights into […]
Should I use a spectrum analyzer, signal analyzer, or vector network analyzer? Part 4
A vector network analyzer can fully characterize components by deriving their scattering parameters. In earlier parts of this series, we looked at analog spectrum analyzers (part 1 and part 2) and vector signal analyzers (part 3), both of which monitor unknown signals, whether emanating from a system, device under test (DUT), or an enemy’s transmitter […]
