The article Why use Symmetrical FIR Filters with an Odd Length? mentiones that symmetrical FIR filters are linear phase. In this follow-up article, I simply want to show you what the phase response of these filters actually looks like…
In my articles on filter design I mostly focus on a rather specific subset of all possible filters, namely symmetrical FIR filters with an odd number of coefficients. Each of these properties (1. FIR, 2. symmetrical, and 3. an odd number of coefficients) was chosen for…
This article shows how to plot the frequency response of the filters that I describe in my articles on filter design. For the specific case of a filter, the frequency response tells you exactly how each frequency is altered. The example code is…
This article explains how to create a windowed-sinc filter with a Kaiser (or Kaiser-Bessel) window. The windowed-sinc filters in previous articles typically had two parameters, the cutoff frequency and the transition bandwidth (or rolloff). With a Kaiser window, there is a third input parameter, the ripple. For the specific case of the Kaiser window, the same…
This article contains more detailed information on setting the transition bandwidth (or roll-off) from How to Create a Simple Low-Pass Filter. That article suggest to use, as the filter length N, an odd number close to 4/b, where b is the required transition bandwidth. This is a good basic rule. However, in…
This is part three of an article that describes the signal path of a radio meteor. The next step is sampling. At the point of sampling, there is a difference between a real-world BRAMS system and the simulation that produced the illustrations in this series of articles. In the real system…
This is part two of an article that describes the signal path of a radio meteor. At the antenna of the receiver, the reflected signal is combined with a (much smaller) directly received signal. At first sight this might seem unimportant, since the amplitude of the direct component is typically much less than…
This is part one of a rather basic article that describes the complete signal path of a radio meteor, from the sinusoidal carrier wave that is initially transmitted, to the spectrogram that is typically used as the final result in the receiving chain. I have presented this material at…
In digital communications, the measure of the signal to noise ratio of a signal is Eb/N0. Why is that? To figure it out, let’s start from the classical SNR, which is the ratio of the average signal power S to the average noise power N, given by…
This article presents spectral reversal, a technique to turn a low-pass filter into a high-pass filter. Spectral reversal is an alternative for spectral inversion, as described in How to Create a Simple High-Pass Filter. Starting from the cutoff frequency…