With fractional delay, I mean a delay of a fraction of a sampling period. Introducing a delay of an integer number of samples is easy, since you can do that by simply skipping a number of samples, or buffering them if you don’t want to…
I’d like to add another trick to your digital filter toolbox: when you apply any filter in both directions on your input signal, the combined filtering operation is zero phase. As you know from…
Say that you have implemented a low-pass FIR filter with the correct cut-off frequency and transition band, but that you are not quite happy with the suppression of frequencies in the stop band. A straightforward trick to put in your toolbox is that you can double the suppression by…
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 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…
When researching what to include in The Moving Average as a Filter and Variations on the Moving Average, I came across a lot of references to applications in the financial sector. This is not my forte, but, just for fun, I gave a few of the moving averages that are used there the same treatment as the filters in…