Sum of Two Equal-Frequency Sinusoids

Rick Lyons
4 comments

The sum of two equal-frequency real sinusoids is itself a single real sinusoid. However, the exact equations for all the various forms of that single equivalent sinusoid are difficult to find in the signal processing literature. Here we provide those equations.


Using the DFT as a Filter: Correcting a Misconception

Rick Lyons
1 comment

I have read, in some of the literature of DSP, that when the discrete Fourier transform (DFT) is used as a filter the process of performing a DFT causes an input signal's spectrum to be frequency translated down to zero Hz (DC). I can understand why someone might say that, but I challenge that statement as being incorrect. Here are my thoughts.


Negative Group Delay

Andor Bariska
2 comments

Dispersive linear systems with negative group delay have caused much confusion in the past. Some claim that they violate causality, others that they are the cause of superluminal tunneling. Can we really receive messages before they are sent? This article aims at pouring oil in the fire and causing yet more confusion :-).


Implementing Simultaneous Digital Differentiation, Hilbert Transformation, and Half-Band Filtering

Rick Lyons
2 comments

Recently I've been thinking about digital differentiator and Hilbert transformer implementations and I've developed a processing scheme that may be of interest to the readers here on dsprelated.com.


A New Contender in the Digital Differentiator Race

Rick Lyons

This blog proposes a novel differentiator worth your consideration. Although simple, the differentiator provides a fairly wide 'frequency range of linear operation' and can be implemented, if need be, without performing numerical multiplications.


The World's Most Interesting FIR Filter Equation: Why FIR Filters Can Be Linear Phase

Rick Lyons
8 comments

This article discusses a little-known filter characteristic that enables real- and complex-coefficient tapped-delay line FIR filters to exhibit linear phase behavior. That is, this article answers the question: What is the constraint on real- and complex-valued FIR filters that guarantee linear phase behavior in the frequency domain?


Correcting an Important Goertzel Filter Misconception

Rick Lyons

Correcting an Important Goertzel Filter Misconception


Complex Down-Conversion Amplitude Loss

Rick Lyons
2 comments

This article illustrates the signal amplitude loss inherent in a traditional complex down-conversion system. (In the literature of signal processing, complex down-conversion is also called "quadrature demodulation.")


Convolution DSP tutorial

RC Kim
3 comments

Tutorial on convolution and basic DSP.


Specifying the Maximum Amplifier Noise When Driving an ADC

Rick Lyons
3 comments

I recently learned an interesting rule of thumb regarding the use of an amplifier to drive the input of an analog to digital converter (ADC). The rule of thumb describes how to specify the maximum allowable noise power of the amplifier.