## Introduction of C Programming for DSP Applications

Appendix C of the book : Real-Time Digital Signal Processing: Implementations, Application and Experiments with the TMS320C55X

## An Introduction To Compressive Sampling

This article surveys the theory of compressive sensing, also known as compressed sensing or CS, a novel sensing/sampling paradigm that goes against the common wisdom in data acquisition.

## Introduction to Compressed Sensing

Chapter 1 of the book: "Compressed Sensing: Theory and Applications".

## C++ Tutorial

This tutorial is for those people who want to learn programming in C++ and do not necessarily have any previous knowledge of other programming languages. Of course any knowledge of other programming languages or any general computer skill can be useful to better understand this tutorial, although it is not essential. It is also suitable for those who need a little update on the new features the language has acquired from the latest standards. If you are familiar with the C language, you can take the first 3 parts of this tutorial as a review of concepts, since they mainly explain the C part of C++. There are slight differences in the C++ syntax for some C features, so I recommend you its reading anyway. The 4th part describes object-oriented programming. The 5th part mostly describes the new features introduced by ANSI-C++ standard.

## Computing FFT Twiddle Factors

In this document are two algorithms showing how to compute the individual twiddle factors of an N-point decimation-in-frequency (DIF) and an N-point decimation-in-time (DIT) FFT.

## Generating Complex Baseband and Analytic Bandpass Signals

There are so many different time- and frequency-domain methods for generating complex baseband and analytic bandpass signals that I had trouble keeping those techniques straight in my mind. Thus, for my own benefit, I created a kind of reference table showing those methods. I present that table for your viewing pleasure in this document.

## How Discrete Signal Interpolation Improves D/A Conversion

Earlier this year, for the Linear Audio magazine, published in the Netherlands whose subscribers are technically-skilled hi-fi audio enthusiasts, I wrote an article on the fundamentals of interpolation as it's used to improve the performance of analog-to-digital conversion. Perhaps that article will be of some value to the subscribers of dsprelated.com. Here's what I wrote: We encounter the process of digital-to-analog conversion every day—in telephone calls (land lines and cell phones), telephone answering machines, CD & DVD players, iPhones, digital television, MP3 players, digital radio, and even talking greeting cards. This material is a brief tutorial on how sample rate conversion improves the quality of digital-to-analog conversion.

## Understanding the 'Phasing Method' of Single Sideband Demodulation

There are four ways to demodulate a transmitted single sideband (SSB) signal. Those four methods are: synchronous detection, phasing method, Weaver method, and filtering method. Here we review synchronous detection in preparation for explaining, in detail, how the phasing method works. This blog contains lots of preliminary information, so if you're already familiar with SSB signals you might want to scroll down to the 'SSB DEMODULATION BY SYNCHRONOUS DETECTION' section.

## Lecture Notes on Elliptic Filter Design

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.

## The DFT of Finite-Length Time-Reversed Sequences

Recently I've been reading papers on underwater acoustic communications systems and this caused me to investigate the frequency-domain effects of time-reversal of time-domain sequences. I created this article because there is so little coverage of this topic in the literature of DSP.

## Decimator Image Response

This article presents a way to compute and plot the image response of a decimator. I'm defining the image response as the unwanted spectrum of the impulse response after downsampling, relative to the desired passband response.

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

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?

## Fixed-Point Arithmetic: An Introduction

This document presents definitions of signed and unsigned fixed-point binary number representations and develops basic rules and guidelines for the manipulation of these number representations using the common arithmetic and logical operations found in fixed-point DSPs and hardware components.

## Algorithms, Architectures, and Applications for Compressive Video Sensing

The design of conventional sensors is based primarily on the Shannon-Nyquist sampling theorem, which states that a signal of bandwidth W Hz is fully determined by its discrete-time samples provided the sampling rate exceeds 2W samples per second. For discrete-time signals, the Shannon-Nyquist theorem has a very simple interpretation: the number of data samples must be at least as large as the dimensionality of the signal being sampled and recovered. This important result enables signal processing in the discrete-time domain without any loss of information. However, in an increasing number of applications, the Shannon-Nyquist sampling theorem dictates an unnecessary and often prohibitively high sampling rate. (See Box 1 for a derivation of the Nyquist rate of a time-varying scene.) As a motivating example, the high resolution of the image sensor hardware in modern cameras reflects the large amount of data sensed to capture an image. A 10-megapixel camera, in effect, takes 10 million measurements of the scene. Yet, almost immediately after acquisition, redundancies in the image are exploited to compress the acquired data significantly, often at compression ratios of 100:1 for visualization and even higher for detection and classification tasks. This example suggests immense wastage in the overall design of conventional cameras.

## Complex Down-Conversion Amplitude Loss

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.")

## Using the DFT as a Filter: Correcting a Misconception

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.

## Computing Translated Frequencies in Digitizing and Downsampling Analog Bandpass Signals

In digital signal processing (DSP) we're all familiar with the processes of bandpass sampling an analog bandpass signal and downsampling a digital bandpass signal. The overall spectral behavior of those operations are well-documented. However, mathematical expressions for computing the translated frequency of individual spectral components, after bandpass sampling or downsampling, are not available in the standard DSP textbooks. This document explains how to compute the frequencies of translated spectral components and provide the desired equations in the hope that they are of use to you.