Signal Processing

How to Create a Fractional-Delay Filter

Figure 1. Impulse response (left) and frequency response (right) of a 0.3 samples fractional delay filter with 21 coefficients.

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…

Tom Mon, 06/17/2019 - 09:43
Mapping Bits to a Constellation

Figure 2. Bit mapping for QPSK.

Before information can be transmitted using a digital modulation scheme, the information bits have to be mapped to the constellation. Each point in the constellation is known as a symbol, making the full collection of symbols a kind of alphabet of the modulation scheme. For most digital modulation schemes…

Tom Mon, 05/06/2019 - 09:57
What is a Constellation Diagram?

Figure 1. QPSK constellation.

A constellation diagram is a diagram that shows how the information in a digital modulation scheme such as phase shift keying (PSK) is represented in a modulated carrier. This article is a bit of an experiment; instead of introducing the constellation diagram by simply presenting it…

Tom Mon, 03/25/2019 - 12:54
What is an Analytic Signal?

Figure 1. Spectra of cosine (left) and complex exponential (right).

An analytic signal is a signal without negative frequency components. This might seem a strange concept if you’re not used to it, but analytic signals are used in signal processing, for example in modems for telecommunications. Let’s start from…

Tom Mon, 02/25/2019 - 09:56

I’m working on a series of articles on modems. It’ll be a loose collection of posts, and not a true multi-part article such as the one on tomography. Modem technology is not widely known and/or understood, even by a technical audience. However…

Tom Wed, 02/13/2019 - 10:52
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…

Tom Mon, 02/26/2018 - 13:01
The Phase Response of a Filter

Figure 2. Frequency (left) and phase (right) response of a moving-average filter.

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…

Tom Thu, 02/08/2018 - 17:39