## Discrete Wavelet Transform Filter Bank Implementation (part 2)

Following the previous blog entry: http://www.dsprelated.com/showarticle/115.php

Difference between DWT and DWPT

Before getting to the equivalent filter obtention, I first want to talk about the difference between DWT(Discrete Wavelet Transform) and DWPT (Discrete Wavelet Packet Transform). The latter is used mostly for image processing.

While DWT has a single "high-pass" branch that filters the signal with the h1 filter, the DWPT separates branches symmetricaly: this means that one...

## Matlab Programming Contest

November 10, 2010

Every 6 months Mathworks hosts an online Matlab programming contest.  If you love or hate Matlab check out the contest.  The group does a really good job putting together the puzzles.  The contest runs for a week and starts today at noon EST (10 Nov 2010).

If you are an experienced Matlab programmer or new to Matlab it is worth checking out.  Even if you do not intend on submitting solutions.  Also, the problems / puzzles only require the base Matlab...

## Discrete Wavelet Transform Filter Bank Implementation (part 1)

October 27, 20101 comment

UPDATE: Added graphs and code to explain the frequency division of the branches

First of all, a 'quick and dirty' simplified explanation of the differences between DFT and DWT:

The DWT (Discrete Wavelet Transform), simply put, is an operation that receives a signal as an input (a vector of data) and...

## Least-squares magic bullets? The Moore-Penrose Pseudoinverse

Hello,

the topic of this brief article is a tool that can be applied to a variety of problems: The Moore-Penrose Pseudoinverse.While maybe not exactly a magic bullet, it gives us least-squares optimal solutions, and that is under many circumstances the best we can reasonably expect.

I'll demonstrate its use on a short example. More details can be found for example on Wikipedia, or the Matlab documentation...

## Fitting Filters to Measured Amplitude Response Data Using invfreqz in Matlab

This blog post has been moved to the code snippet section and can now be found HERE.  Please update your bookmark.  Thanks!

## Radio Frequency Distortion Part II: A power spectrum model

October 11, 20101 comment
Summary

This article presents a ready-to-use model for nonlinear distortion caused by radio frequenfcy components in wireless receivers and linear transmitters. Compared to the similar model presented in my earlier blog entry, it operates on expectation values of the the power spectrum instead of the signal itself: Use the signal-based model to generate distortion on a signal, and the one from this article to directly obtain the power spectrum much more efficiently.In...

## Accelerating Matlab DSP Code on the GPU

Intrigued by GPUs, I've spent a few days testing out Jacket, an interface that lets you accelerate MATLAB (my favorite, if frustrating language) on NVIDIA GPUs. It's definitely got some caveats. But it was really easy to accelerate my code. And the results were impressive. So I thought I'd put up a few simple DSP-related benchmarks I created and ran on my laptop (a Macbook Air with NVIDIA GeForce 9400M graphics card). The m-files for the two functions I benchmarked (2D FFT and 2D...

## 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

## Correlation without pre-whitening is often misleading

White Lies

Correlation, as one of the first tools DSP users add to their tool box, can automate locating a known signal within a second (usually larger) signal. The expected result of a correlation is a nice sharp peak at the location of the known signal and few, if any, extraneous peaks.

A little thought will show this to be incorrect: correlating a signal with itself is only guaranteed to give a sharp peak if the signal's samples are uncorrelated --- for example if the signal is composed...

## Instantaneous Frequency Measurement

I would like to talk about the oft used method of measuring the carrier frequency in the world of Signal Collection and Characterization world. It is an elegant technique because of its simplicity. But, of course, with simplicity, there come drawbacks (sometimes...especially with this one!).

In the world of Radar detection and characterization, one of the key characteristics of interest is the carrier frequency of the signal. If the radar is pulsed, you will have a very wide bandwidth, a...

## Part 11. Using -ve Latency DSP to Cancel Unwanted Delays in Sampled-Data Filters/Controllers

This final article in the series will look at -ve latency DSP and how it can be used to cancel the unwanted delays in sampled-data systems due to such factors as Nyquist filtering, ADC acquisition, DSP/FPGA algorithm computation time, DAC reconstruction and circuit propagation delays.

Some applications demand zero-latency or zero unwanted latency signal processing. Negative latency DSP may sound like the stuff of science fiction or broken physics but the arrangement as...

## Matlab Programming Contest

November 10, 2010

Every 6 months Mathworks hosts an online Matlab programming contest.  If you love or hate Matlab check out the contest.  The group does a really good job putting together the puzzles.  The contest runs for a week and starts today at noon EST (10 Nov 2010).

If you are an experienced Matlab programmer or new to Matlab it is worth checking out.  Even if you do not intend on submitting solutions.  Also, the problems / puzzles only require the base Matlab...

## Coefficients of Cascaded Discrete-Time Systems

March 4, 2018

In this article, we’ll show how to compute the coefficients that result when you cascade discrete-time systems.  With the coefficients in hand, it’s then easy to compute the time or frequency response.  The computation presented here can also be used to find coefficients of mixed discrete-time and continuous-time systems, by using a discrete time model of the continuous-time portion [1].

## Compute the Frequency Response of a Multistage Decimator

Figure 1a shows the block diagram of a decimation-by-8 filter, consisting of a low-pass finite impulse response (FIR) filter followed by downsampling by 8 [1].  A more efficient version is shown in Figure 1b, which uses three cascaded decimate-by-two filters.  This implementation has the advantages that only FIR 1 is sampled at the highest sample rate, and the total number of filter taps is lower.

The frequency response of the single-stage decimator before downsampling is just...

## 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...

## Generating Partially Correlated Random Variables

IntroductionIt is often useful to be able to generate two or more signals with specific cross-correlations. Or, more generally, we would like to specify an $\left(N \times N\right)$ covariance matrix, $\mathbf{R}_{xx}$, and generate $N$ signals which will produce this covariance matrix.

There are many applications in which this technique is useful. I discovered a version of this method while analysing radar systems, but the same approach can be used in a very wide range of...

## FREE Peer-reviewed IEEE signal processing courses

April 26, 20111 comment

The IEEE signal processing society is offereing FREE peer reviewed courses, though not many, they are peer reviewed and span differenet topics like; wavelets, speech analysis, and statistical detection.

Enjoy

http://cnx.org/lenses/ieeesps/endorsements?b_start:int=0&-C=

## The Phase Vocoder Transform

February 12, 2019
1 Introduction

I would like to look at the phase vocoder in a fairly abstract'' way today. The purpose of this is to discuss a method for measuring the quality of various phase vocoder algorithms, and building off a proposed measure used in [2]. There will be a bit of time spent in the domain of continuous mathematics, thus defining a phase vocoder function or map rather than an algorithm. We will be using geometric visualizations when possible while pointing out certain group theory...

## An Efficient Lowpass Filter in Octave

November 6, 2019

This article describes an efficient linear-phase lowpass FIR filter, coded using the Octave programming language. The intention is to focus on the implementation in software, but references are provided for those who wish to undertake further study of interpolated FIR filters [1]- [3].

The input signal is processed as a vector of samples (eg from a .wav file), which are converted to a matrix format.   The complete filter is thus referred to as a Matrix IFIR or...

## A Markov View of the Phase Vocoder Part 1

January 8, 2019
Introduction

Hello! This is my first post on dsprelated.com. I have a blog that I run on my website, http://www.christianyostdsp.com. In order to engage with the larger DSP community, I'd like to occasionally post my more engineering heavy writing here and get your thoughts.

Today we will look at the phase vocoder from a different angle by bringing some probability into the discussion. This is the first part in a short series. Future posts will expand further upon the ideas...