There's No End to It -- Matlab Code Plots Frequency Response above the Unit Circle

Reference [1] has some 3D plots of frequency response magnitude above the unit circle in the Z-plane.  I liked them enough that I wrote a Matlab function to plot the response of any digital filter this way.  I’m not sure how useful these plots are, but they’re fun to look at. The Matlab code is listed in the Appendix.

This post is available in PDF format for easy...

Exact Near Instantaneous Frequency Formulas Best at Zero Crossings

July 20, 2017
Introduction

This is an article that is the last of my digression from trying to give a better understanding of the Discrete Fourier Transform (DFT). It is along the lines of the last two.

In those articles, I presented exact formulas for calculating the frequency of a pure tone signal as instantaneously as possible in the time domain. Although the formulas work for both real and complex signals (something that does not happen with frequency domain formulas), for real signals they...

Exact Near Instantaneous Frequency Formulas Best at Peaks (Part 2)

Introduction

This is an article that is a continuation of a digression from trying to give a better understanding of the Discrete Fourier Transform (DFT). It is recommended that my previous article "Exact Near Instantaneous Frequency Formulas Best at Peaks (Part 1)"[1] be read first as many sections of this article are directly dependent upon it.

A second family of formulas for calculating the frequency of a single pure tone in a short interval in the time domain is presented. It...

How to Find a Fast Floating-Point atan2 Approximation

Context Over a short period of time, I came across nearly identical approximations of the two parameter arctangent function, atan2, developed by different companies, in different countries, and even in different decades. Fascinated with how the coefficients used in these approximations were derived, I set out to find them. This atan2 implementation is based around a rational approximation of arctangent on the domain -1 to 1:

Multimedia Processing with FFMPEG

November 16, 2015

FFMPEG is a set of libraries and a command line tool for encoding and decoding audio and video in many different formats. It is a free software project for manipulating/processing multimedia data. Many open source media players are based on FFMPEG libraries.

FFMPEG is developed under Linux but it can be compiled under most operating systems including Mac OS, Microsoft Windows. For more details about FFMPEG please refer

Understanding and Implementing the Sliding DFT

Introduction

In many applications the detection or processing of signals in the frequency domain offers an advantage over performing the same task in the time-domain.   Sometimes the advantage is just a simpler or more conceptually straightforward algorithm, and often the largest barrier to working in the frequency domain is the complexity or latency involved in the Fast Fourier Transform computation.   If the frequency-domain data must be updated frequently in a...

Handling Spectral Inversion in Baseband Processing

The problem of "spectral inversion" comes up fairly frequently in the context of signal processing for communication systems. In short, "spectral inversion" is the reversal of the orientation of the signal bandwidth with respect to the carrier frequency. Rick Lyons' article on "Spectral Flipping" at http://www.dsprelated.com/showarticle/37.php discusses methods of handling the inversion (as shown in Figure 1a and 1b) at the signal center frequency. Since most communication systems process...

Computing FFT Twiddle Factors

Some days ago I read a post on the comp.dsp newsgroup and, if I understood the poster's words, it seemed that the poster would benefit from knowing how to compute the twiddle factors of a radix-2 fast Fourier transform (FFT).

Then, later it occurred to me that it might be useful for this blog's readers to be aware of algorithms for computing FFT twiddle factors. So,... what follows are two algorithms showing how to compute the individual twiddle factors of an N-point decimation-in-frequency...

Python scipy.signal IIR Filtering: An Example

May 19, 2013
Introduction

In the last posts I reviewed how to use the Python scipy.signal package to design digital infinite impulse response (IIR) filters, specifically, using the iirdesign function (IIR design I and IIR design II ).  In this post I am going to conclude the IIR filter design review with an example.

Previous posts:

Delay estimation by FFT

Given x=sig(t) and y=ref(t), returns [c, ref(t+delta), delta)] = fitSignal(y, x);:Estimates and corrects delay and scaling factor between two signals Code snippet

This article relates to the Matlab / Octave code snippet: Delay estimation with subsample resolution It explains the algorithm and the design decisions behind it.

Introduction

There are many DSP-related problems, where an unknown timing between two signals needs to be determined and corrected, for example, radar, sonar,...

Understanding and Implementing the Sliding DFT

Introduction

In many applications the detection or processing of signals in the frequency domain offers an advantage over performing the same task in the time-domain.   Sometimes the advantage is just a simpler or more conceptually straightforward algorithm, and often the largest barrier to working in the frequency domain is the complexity or latency involved in the Fast Fourier Transform computation.   If the frequency-domain data must be updated frequently in a...

A Differentiator With a Difference

Some time ago I was studying various digital differentiating networks, i.e., networks that approximate the process of taking the derivative of a discrete time-domain sequence. By "studying" I mean that I was experimenting with various differentiating filter coefficients, and I discovered a computationally-efficient digital differentiator. A differentiator that, for low fequency signals, has the power of George Foreman's right hand! Before I describe this differentiator, let's review a few...

Accurate Measurement of a Sinusoid's Peak Amplitude Based on FFT Data

There are two code snippets associated with this blog post:

Flat-Top Windowing Function for the Accurate Measurement of a Sinusoid's Peak Amplitude Based on FFT Data

and

Testing the Flat-Top Windowing Function

This blog discusses an accurate method of estimating time-domain sinewave peak amplitudes based on fast Fourier transform (FFT) data. Such an operation sounds simple, but the scalloping loss characteristic of FFTs complicates the process. We eliminate that complication by...

Linear-phase DC Removal Filter

This blog describes several DC removal networks that might be of interest to the dsprelated.com readers.

Back in August 2007 there was a thread on the comp.dsp newsgroup concerning the process of removing the DC (zero Hz) component from a time-domain sequence [1]. Discussed in that thread was the notion of removing a signal's DC bias by subtracting the signal's moving average from that signal, as shown in Figure 1(a).

Figure 1.

At first I thought...

Computing the Group Delay of a Filter

I just learned a new method (new to me at least) for computing the group delay of digital filters. In the event this process turns out to be interesting to my readers, this blog describes the method. Let's start with a bit of algebra so that you'll know I'm not making all of this up.

Assume we have the N-sample h(n) impulse response of a digital filter, with n being our time-domain index, and that we represent the filter's discrete-time Fourier transform (DTFT), H(ω), in polar form...