## Modeling Anti-Alias Filters

September 26, 2021

Digitizing a signal using an Analog to Digital Converter (ADC) usually requires an anti-alias filter, as shown in Figure 1a.  In this post, we’ll develop models of lowpass Butterworth and Chebyshev anti-alias filters, and compute the time domain and frequency domain output of the ADC for an example input signal.  We’ll also model aliasing of Gaussian noise.  I hope the examples make the textbook explanations of aliasing seem a little more real.  Of course, modeling of...

## Sampling bandpass signals

Sampling bandpass signals 1.1 Introduction

It is known [1], [3] that bandpass signals can be sampled with a sampling frequency which is lower than the sampling frequency according to the sampling theorem.

## A Narrow Bandpass Filter in Octave or Matlab

The design of a very narrow bandpass FIR filter, coded in either Octave or Matlab, can prove challenging if a computationally-efficient  filter is required. This is especially true if the sampling rate is high relative to the filter's center frequency. The most obvious filter design methods, using either window-based or Remez ( Parks-McClellan ) functions, can easily result in filters with many thousands of taps.

The filter to be described reduces the computational effort (and thus...

## Second Order Discrete-Time System Demonstration

Discrete-time systems are remarkable:  the time response can be computed from mere difference equations, and the coefficients ai, bi of these equations are also the coefficients of H(z).  Here, I try to illustrate this remarkableness by converting a continuous-time second-order system to an approximately equivalent discrete-time system.  With a discrete-time model, we can then easily compute the time response to any input.  But note that the goal here is as much to...

## Design IIR Butterworth Filters Using 12 Lines of Code

While there are plenty of canned functions to design Butterworth IIR filters [1], it’s instructive and not that complicated to design them from scratch.  You can do it in 12 lines of Matlab code.  In this article, we’ll create a Matlab function butter_synth.m to design lowpass Butterworth filters of any order.  Here is an example function call for a 5th order filter:

N= 5 % Filter order fc= 10; % Hz cutoff freq fs= 100; % Hz sample freq [b,a]=...

## Use Matlab Function pwelch to Find Power Spectral Density – or Do It Yourself

In my last post, we saw that finding the spectrum of a signal requires several steps beyond computing the discrete Fourier transform (DFT)[1].  These include windowing the signal, taking the magnitude-squared of the DFT, and computing the vector of frequencies.  The Matlab function pwelch [2] performs all these steps, and it also has the option to use DFT averaging to compute the so-called Welch power spectral density estimate [3,4].

## 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,...

## Design IIR Bandpass Filters

In this post, I present a method to design Butterworth IIR bandpass filters.  My previous post [1] covered lowpass IIR filter design, and provided a Matlab function to design them.  Here, we’ll do the same thing for IIR bandpass filters, with a Matlab function bp_synth.m.  Here is an example function call for a bandpass filter based on a 3rd order lowpass prototype:

N= 3; % order of prototype LPF fcenter= 22.5; % Hz center frequency, Hz bw= 5; ...

This article shows how to implement a Butterworth IIR lowpass filter as a cascade of second-order IIR filters, or biquads.  We’ll derive how to calculate the coefficients of the biquads and do some examples using a Matlab function biquad_synth provided in the Appendix.  Although we’ll be designing Butterworth filters, the approach applies to any all-pole lowpass filter (Chebyshev, Bessel, etc).  As we’ll see, the cascaded-biquad design is less sensitive to coefficient...

## Digital PLL's -- Part 1

1. Introduction

Figure 1.1 is a block diagram of a digital PLL (DPLL).  The purpose of the DPLL is to lock the phase of a numerically controlled oscillator (NCO) to a reference signal.  The loop includes a phase detector to compute phase error and a loop filter to set loop dynamic performance.  The output of the loop filter controls the frequency and phase of the NCO, driving the phase error to zero.

One application of the DPLL is to recover the timing in a digital...

## Time Machine, Anyone?

Abstract: 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 :-).

Introduction

## Plotting Discrete-Time Signals

A discrete-time sinusoid can have frequency up to just shy of half the sample frequency.  But if you try to plot the sinusoid, the result is not always recognizable.  For example, if you plot a 9 Hz sinusoid sampled at 100 Hz, you get the result shown in the top of Figure 1, which looks like a sine.  But if you plot a 35 Hz sinusoid sampled at 100 Hz, you get the bottom graph, which does not look like a sine when you connect the dots.  We typically want the plot of a...

## TCP/IP interface (Matlab/Octave)

Communicate with measurement instruments via Ethernet (no-toolbox-Matlab or Octave)

Purpose

Measurement automation is digital signal processing in a wider sense: Getting a digital signal from an analog world usually involves some measurement instruments, for example a spectrum analyzer. Modern instruments, and also many off-the-shelf prototyping boards such as FPGA cards [1] or microcontrollers [2] are able to communicate via Ethernet. Here, I provide some basic mex-functions (compiled C...