## A Pragmatic Introduction to Signal Processing

●8 commentsAn illustrated essay with software available for free download.

## Introduction to Signal Processing

●2 commentsThis book provides an applications-oriented introduction to digital signal processing written primarily for electrical engineering undergraduates. Practicing engineers and graduate students may also ﬁnd it useful as a ﬁrst text on the subject.

## C++ Tutorial

●12 commentsThis 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.

## Introduction to Sound Processing

●5 commentsAudio signal processing with MATLAB and Octave code examples.

## Computing FFT Twiddle Factors

●2 commentsIn 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

●3 commentsThere 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

●2 commentsEarlier 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

●6 commentsThere 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.

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

●2 commentsI 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.

## Multirate Systems and Filter Banks

●2 commentsDuring the last two decades, multirate filter banks have found various applications in many different areas, such as speech coding, scrambling, adaptive signal processing, image compression, signal and image processing applications as well as transmission of several signals through the same channel. The main idea of using multirate filter banks is the ability of the system to separate in the frequency domain the signal under consideration into two or more signals or to compose two or more different signals into a single signal.

## Generating Complex Baseband and Analytic Bandpass Signals

●3 commentsThere 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.

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

●1 commentIn 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.

## Filter a Rectangular Pulse with no Ringing

To filter a rectangular pulse without any ringing, there is only one requirement on the filter coefficients: they must all be positive. However, if we want the leading and trailing edge of the pulse to be symmetrical, then the coefficients must be symmetrical. What we are describing is basically a window function.

## Specifying the Maximum Amplifier Noise When Driving an ADC

●3 commentsI recently learned an interesting rule of thumb regarding the use of an amplifier to drive the input of an analog to digital converter (ADC). The rule of thumb describes how to specify the maximum allowable noise power of the amplifier.

## A DGPS/Radiobeacon Receiver for Minimum Shift Keying with Soft Decision Capabilities

The Global Positioning System (GPS) is now in operation, and many improvements to its performance are being sought. One such improvement is Differential GPS (DGPS), where known errors in the GPS broadcast are identified and the corrections broadcast to the end user. One implementation of DGPS being considered is the use of coastal marine radio direction finding (RDF) radiobeacons in the 285-325kHz band as transmitters for the DGPS broadcast. The normal RDF beacon signal consists of a continuous carrier on a one kilohertz boundary plus a Morse-code identification signal 1025Hz above the carrier. In the DGPS/radiobeacon implementation proposed for the US coastal regions, the differential data link signal uses minimum shift keying (MSK) at a data rate of 25, 50, 100, 200 or 400 baud (the exact baud rat has not yet been decided). This MSK signal is centered between the RDF beacon carrier and identification signal. At the frequencies that these radiobeacons are operated, the prevailing atmospheric noise is both non-Gaussian and very strong. This noise characteristic makes the design of a long-range data link difficult. One solution that has been proposed is the use of forward error correction (FEC) coding of the data. The performance of FEC decoders can be improved by the used of a soft decision receiver, which delivers both bit decisions and information about the validity of the bit decisions. This work describes the design of a radio receiver for DGPS/Radiobeacon servics which is capable of reception of 400 baud MSK in the DGPS/Radiobeacon band. The receiver is designed to be easily augmented to provide soft decisions and easily modified to recieve MSK at data rates of 25 to 400 baud. The radio is a microprocessor controlled dual conversion superheterodyne with an audio frequency of 1kHz. The demodulator runs on the same microprocessor that controls the radio. The weak-signal performance of the demodulator is very good: the Eb/No vs. bit error rate performance of the demodulator is only a couple of dB worse than the theoretical performance of differential phase-shift keying. The radio has a noise floor of -114dBm referenced to it's 500Hz wide audio bandwidth and a 3rd order intermodulation intercept of +7dBm for a dynamic range of 83dB. This work concludes with a thumbnail analysis of the operations needed to implement a soft bit decision estimator, and some suggestions for the implementation of said soft bit decision estimator.

## Real-time Motion Picture Restoration

Through age or misuse, motion picture films can develop damage in the form of dirt or scratches which detract from the quality of the film. Removal of these artifacts is a worthwhile process as it makes the films more visually attractive and extends the life of the material. In this thesis, various methods for detecting and concealing the effects of film damage are described. Appropriate algorithms are selected for implementation of a system, based on a TMS320C80 video processor, which can remove the effects of film defects using digital processing. The restoration process operates in real-time at video frame rates (30 frames per second). Details of the software implementation of this system are presented along with results from processing damaged film material. The effects of damage are significantly reduced after processing.

## A New Approach to Linear Filtering and Prediction Problems

●3 commentsIn 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation.

## How to reduce the bill of material costs with digital signal processing

The need to decrease the bill of material (BOM) costs in embedded products is being driven by the need for high volume, low-cost sensor systems. As IoT devices become more sophisticated, they require developers to utilize digital signal processing to handle more features within the product, such as device provisioning. In this paper, we will examine how digital signal processing (DSP) can be used to reduce a product’s cost.

## Lecture Notes on Elliptic Filter Design

●1 commentElliptic 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.