DSP Archives | Page 6 of 15

July 12, 2021 DSP

Generating Signals and Viewing the Spectrum

One of the most common questions DSP beginners have is how to generate the signals (particularly, sinusoids) and view their spectrum. They have a rough idea what time domain and frequency domain are about but struggle to construct the first few lines of code that open the gates towards a deeper understanding of signals. For this reason, I produce below an Octave (or Matlab) code that you can simply copy and paste to view and modify the results. Keep in mind that the code has been written for an explanation purpose, not conciseness or optimization. As you progress towards developing

September 5, 2022 DSP

Specifications of a Radio Receiver

When designing a radio receiver, a system architect has to deal with the issues such as dynamic range, noise floor and sensitivity of a radio receiver [1]. The ultimate purpose is computing a power budget to ensure that a minimum amount of signal power is available at the receiver during operation. This is not much different than how a country assigns an available budget into different sectors such as defense, education and health. Dynamic Range Dynamic range is the ratio of the largest signal level to the smallest signal level that the system can process in analog and digital stages.

March 25, 2024 DSP / Miscellaneous

Why the Constant e Arises in Complex Plane as a Rotation

In the tutorial on how complex numbers arose, we asked three questions. The first two were answered in the same article while the answer to the third question, repeated below, is explained here. Why is the expression $e^{i \theta}$ a rotation of 1 by $\theta$ radians on a unit circle? Is it possible to make sense out of a number like $2.71828^{\sqrt{-1}\cdot\theta}$? The constant e is a special number discovered by Jacob Bernoulli while studying compound interests. It appears in many other forms as well which are all related to each other but that topic is a complete account in

(Top) An 8-PSK waveform. (Bottom) Two constellation diagrams: one at the Tx shown by thick red lines and the other at the Rx for a phase offset of 17 degrees shown by dotted purple lines

December 8, 2020 DSP

I/Q Signals 101: Neither Complex Nor Complicated

Dec 04, 2020 If you are an absolute beginner looking for a really intuitive understanding of I/Q signals, read the introductory guide on I/Q signals from the ground up. The article below explains this idea from a communication systems perspective. There was a recent discussion on GNU Radio mailing list in regards to the simplest possible intuition behind I/Q signals. Why is I/Q sampling required? Question: The original question from Kristoff went like this: “… when you mention `GNU Radio complex numbers’, you also have to mention I/Q signals, which is a topic that is very difficult to explain in

Signal frequency and analysis frequency are not the same, resulting in DFT leakage and spectrum sampling away from the peak. The spectrum shown here is oversampled by 3 through 3x zero-padded FFT

October 16, 2026 DSP

Peak Interpolation for Sub-Bin Accuracy in Radar and Communications

In signal processing applications, one frequently encounters the problem of estimating the frequency of a complex sinusoid embedded in noise. For example, a DSP engineer will encounter this problem in the delayed echo of an FMCW radar that directly translates into target range, or in carrier frequency estimation of a wireless communication system after timing synchronization has already been achieved (see Chapter 6 for details of how modulation removal exposes the underlying complex sinusoid). Beyond communications and radar, this frequency estimation is also heavily relied upon in digital pitch tracking, speech synthesis, active and passive sonar detection, Doppler ultrasound and