Filter Design

Apply a Filter Twice for Greatly Improved Performance

Figure 3. Impulse response of the filter of Figure 1 convolved with itself.

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…

Submitted on 26 February 2018

How to Create a Configurable Filter Using a Kaiser Window

Figure 3. Frequency response of a low-pass filter with a Kaiser window; A=60.

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…

Submitted on 26 December 2016

The Transition Bandwidth of a Filter Depends on the Window Type

Figure 1. Low-pass filter with Blackman window, r=4.0 (filter has 41 taps).

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…

Submitted on 6 December 2016

The Moving Average in the Financial Sector

Figure 4. Impulse (left), step (middle), and frequency (right) responses for Spencer’s 15-point moving average.

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…

Submitted on 29 February 2016