Each time I need to do something with audio, one dimensional signal processing in general, or images, I need to go through my collection of Python scripts to help me remember once again which library to use to save and load them. To make this easier…
When you are designing a modem, you’ll typically make heavy use of simulations. Much of the design work is concentrated on the algorithmic part of the device, especially in these days of Software-Defined Radio (SDR), where the actual electronics might…
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…
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…
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…
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…
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…
After explaining how amplitude modulation and frequency modulation work, which are both analog modulation schemes, I’d now like to give an example of a digital modulation techique. A basic, but very relevant, example of a digital modulation scheme is…
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…