Lecture Notes on Elliptic Filter Design

Sophocles J. Orfanidis
1 comment

Elliptic filters, also known as Cauer or Zolotarev filters, achieve the smallest filter order for the same specifications, or, the narrowest transition width for the same filter order, as compared to other filter types. On the negative side, they have the most nonlinear phase response over their passband. In these notes, we are primarily concerned with elliptic filters. But we will also discuss briefly the design of Butterworth, Chebyshev-1, and Chebyshev-2 filters and present a unified method of designing all cases. We also discuss the design of digital IIR filters using the bilinear transformation method.


Optimizing the Half-band Filters in Multistage Decimation and Interpolation

Rick Lyons
1 comment

This article discusses a not so well-known rule regarding the filtering in multistage decimation and interpolation by an integer power of two.


The DFT Magnitude of a Real-valued Cosine Sequence

Rick Lyons
5 comments

This article may seem a bit trivial to some readers here but, then again, it might be of some value to DSP beginners. It presents a mathematical proof of what is the magnitude of an N-point discrete Fourier transform (DFT) when the DFT's input is a real-valued sinusoidal sequence.


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.


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.")