A windowed sinc filter outperforms a moving-average filter in the frequency domain. In part 2 of this series, we described a type of convolution filter called the moving-average filter, and we demonstrated that it is effective at removing Gaussian white noise in the time domain but performs poorly in the frequency domain. Q: Do all […]
How to use convolution to implement filters: part 2
A moving-average filter can address white noise in the time domain but performs poorly in the frequency domain. In part 1 of this series, we defined convolution, denoted by the * symbol, and looked at a simple geometrical example of how it operates to produce a new function y(t) from two given functions, f(t) and […]
How to use convolution to implement filters: part 1
Convolution is used in a variety of signal-processing applications, including time-domain-waveform filtering. In a recent series on the inverse fast Fourier transform (FFT), we concluded with a mention of convolution and its application to filtering. Convolution Q: What is convolution? A: Convolution, denoted by * symbol, combines two functions to form a third function in […]
How to calculate and apply the inverse discrete Fourier transform: part 4
In part 3 of this series, we used the inverse fast Fourier transform (IFFT) to create 100-Hz time-domain waveforms of various amplitudes and phases. We can also use the IFFT to create waveforms containing multiple frequencies. If you look closely at Figure 1 in part 1 of this series, you’ll notice that the time-domain waveform […]
How to calculate and apply the inverse discrete Fourier transform: part 3
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 calculate and apply an inverse FFT: part 1
The inverse Fourier transform (inverse FFT or iFFT) reverses the operation of the Fourier transform and derives a time-domain representation from a frequency-domain dataset. In early 2024, EE World published a series on the Fourier transform, which can convert a time-domain signal to the frequency domain (Figure 1, red arrow). The process is reversible (Figure […]
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 […]
