## 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

●5 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.

## A Quadrature Signals Tutorial: Complex, But Not Complicated

●10 commentsQuadrature signals are based on the notion of complex numbers and perhaps no other topic causes more heartache for newcomers to DSP than these numbers and their strange terminology of j operator, complex, imaginary, real, and orthogonal. If you're a little unsure of the physical meaning of complex numbers and the j = √-1 operator, don't feel bad because you're in good company. Why even Karl Gauss, one the world's greatest mathematicians, called the j operator the "shadow of shadows". Here we'll shine some light on that shadow so you'll never have to call the Quadrature Signal Psychic Hotline for help. Quadrature signal processing is used in many fields of science and engineering, and quadrature signals are necessary to describe the processing and implementation that takes place in modern digital communications systems. In this tutorial we'll review the fundamentals of complex numbers and get comfortable with how they're used to represent quadrature signals. Next we examine the notion of negative frequency as it relates to quadrature signal algebraic notation, and learn to speak the language of quadrature processing. In addition, we'll use three-dimensional time and frequency-domain plots to give some physical meaning to quadrature signals. This tutorial concludes with a brief look at how a quadrature signal can be generated by means of quadrature-sampling.

## 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.

## Hilbert Transform and Applications

●1 commentSection 1: reviews the mathematical deﬁnition of Hilbert transform and various ways to calculate it.

Sections 2 and 3: review applications of Hilbert transform in two major areas: Signal processing and system identiﬁcation.

Section 4: concludes with remarks on the historical development of Hilbert transform

## Voice Activity Detection. Fundamentals and Speech Recognition System Robustness

An important drawback affecting most of the speech processing systems is the environmental noise and its harmful effect on the system performance. Examples of such systems are the new wireless communications voice services or digital hearing aid devices. In speech recognition, there are still technical barriers inhibiting such systems from meeting the demands of modern applications. Numerous noise reduction techniques have been developed to palliate the effect of the noise on the system performance and often require an estimate of the noise statistics obtained by means of a precise voice activity detector (VAD). Speech/non-speech detection is an unsolved problem in speech processing and affects numerous applications including robust speech recognition, discontinuous transmission, real-time speech transmission on the Internet or combined noise reduction and echo cancellation schemes in the context of telephony. The speech/non-speech classification task is not as trivial as it appears, and most of the VAD algorithms fail when the level of background noise increases. During the last decade, numerous researchers have developed different strategies for detecting speech on a noisy signal and have evaluated the influence of the VAD effectiveness on the performance of speech processing systems. Most of the approaches have focussed on the development of robust algorithms with special attention being paid to the derivation and study of noise robust features and decision rules. The different VAD methods include those based on energy thresholds, pitch detection, spectrum analysis, zero-crossing rate, periodicity measure, higher order statistics in the LPC residual domain or combinations of different features. This chapter shows a comprehensive approximation to the main challenges in voice activity detection, the different solutions that have been reported in a complete review of the state of the art and the evaluation frameworks that are normally used. The application of VADs for speech coding, speech enhancement and robust speech recognition systems is shown and discussed. Three different VAD methods are described and compared to standardized and recently reported strategies by assessing the speech/non-speech discrimination accuracy and the robustness of speech recognition systems.

## Introduction to Signal Processing

●1 commentThis 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.

## Design of a Scalable Polyphony-MIDI Synthesizer for a Low Cost DSP

In this thesis, the design of a music synthesizer implementing the Scalable Polyphony-MIDI soundset on a low cost DSP system is presented. First, the SP-MIDI standard and the target DSP platform are presented followed by review of commonly used synthesis techniques and their applicability to systems with limited computational and memory resources. Next, various oscillator and ﬁlter algorithms used in digital subtractive synthesis are reviewed in detail. Special attention is given to the aliasing problem caused by discontinuities in classical waveforms, such as sawtooth and pulse waves and existing methods for bandlimited waveform synthesis are presented. This is followed by review of established structures for computationally efﬁcient time-varying ﬁlters. A novel digital structure is presented that decouples the cutoff and resonance controls. The new structure is based on the analog Korg MS-20 lowpass ﬁlter and is computationally very efﬁcient and well suited for implementation on low bitdepth architectures. Finally, implementation issues are discussed with emphasis on the Differentiated Parabole Wave oscillator and MS-20 ﬁlter structures and the effects of limited computational capability and low bitdepth. This is followed by designs for several example instruments.

## Complex Down-Conversion Amplitude Loss

●2 commentsThis 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.")

## 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.

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

●1 commentI 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.

## De-Noising Audio Signals Using MATLAB Wavelets Toolbox

Based on the fact that noise and distortion are the main factors that limit the capacity of data transmission in telecommunications and that they also affect the accuracy of the results in the signal measurement systems, whereas, modeling and removing noise and distortions are at the core of theoretical and practical considerations in communications and signal processing. Another important issue here is that, noise reduction and distortion removal are major problems in applications such as; cellular mobile communication, speech recognition, image processing, medical signal processing, radar, sonar, and any other application where the desired signals cannot be isolated from noise and distortion. The use of wavelets in the field of de-noising audio signals is relatively new, the use of this technique has been increasing over the past 20 years. One way to think about wavelets matches the way how our eyes perceive the world when they are faced to different distances. In the real world, a forest can be seen from many different perspectives; they are, in fact, different scales of resolution. From the window of an airplane, for instance, the forest cover appears as a solid green roof. From the window of a car, the green roof gets transformed into individual trees, and if we leave the car and approach to the forest, we can gradually see details such as the trees branches and leaves. If we had a magnifying glass, we could see a dew drop on the tip of a leaf. As we get closer to even smaller scales, we can discover details that we had not seen before. On the other hand, if we tried to do the same thing with a photograph, we would be completely frustrated. If we enlarged the picture "closer" to a tree, we would only be able to see a blurred tree image; we would not be able to spot neither the branch, nor the leaf, and it would be impossible to spot the dew drop. Although our eyes can see on many scales of resolution, the camera can only display one at a time. In this chapter, we introduce the reader to a way to reduce noise in an audio signal by using wavelet transforms. We developed this technique by using the wavelet tool in MATLAB. A Simulink is used to acquire an audio signal and we use it to convert the signal to a digital format so it can be processed. Finally, a Graphical User Interface Development Environment (GUIDE) is used to create a graphical user interface. The reader can go through this chapter systematically, from the theory to the implementation of the noise reduction technique. We will introduce in the first place the basic theory of an audio signal, the noise treatment fundamentals and principles of the wavelets theory. Then, we will present the development of noise reduction when using wavelet functions in MATLAB. In the foreground, we will demonstrate the usefulness of wavelets to reduce noise in a model system where Gaussian noise is inserted to an audio signal. In the following sections, we will present a practical example of noise reduction in a sinusoidal signal that has been generated in the MATLAB, which it is followed by an example with a real audio signal captured via Simulink. Finally, the graphic noise reduction model using GUIDE will be shown.

## STUDY OF DIGITAL MODULATION TECHNIQUES

●1 commentModulation is the process of facilitating the transfer of information over a medium. Typically the objective of a digital communication system is to transport digital data between two or more nodes. In radio communications this is usually achieved by adjusting a physical characteristic of a sinusoidal carrier, either the frequency, phase, amplitude or a combination thereof . This is performed in real systems with a modulator at the transmitting end to impose the physical change to the carrier and a demodulator at the receiving end to detect the resultant modulation on reception. Hence, modulation can be objectively defined as the process of converting information so that it can be successfully sent through a medium. This thesis deals with the current digital modulation techniques used in industry. Also, the thesis examines the qualitative and quantitative criteria used in selection of one modulation technique over the other. All the experiments, and realted data collected were obtained using MATLAB and SIMULINK

## Interaction with Sound and Pre-Recorded Music: Novel Interfaces and Use Patterns

Computers are changing the way sound and recorded music are listened to and used. The use of computers to playback music makes it possible to change and adapt music to different usage situations in ways that were not possible with analog sound equipment. In this thesis, interaction with pre-recorded music is investigated using prototypes and user studies. First, different interfaces for browsing music on consumer or mobile devices were compared. It was found that the choice of input controller, mapping and auditory feedback influences how the music was searched and how the interfaces were perceived. Search performance was not affected by the tested interfaces. Based on this study, several ideas for the future design of music browsing interfaces were proposed. Indications that search time depends linearly on distance to target were observed and examined in a related study where a movement time model for searching in a text document using scrolling was developed. Second, work practices of professional disc jockeys (DJs) were studied and a new design for digital DJing was proposed and tested. Strong indications were found that the use of beat information could reduce the DJ’s cognitive workload while maintaining flexibility during the musical performance. A system for automatic beat extraction was designed based on an evaluation of a number of perceptually important parameters extracted from audio signals. Finally, auditory feedback in pen-gesture interfaces was investigated through a series of informal and formal experiments. The experiments point to several general rules of auditory feedback in pen-gesture interfaces: a few simple functions are easy to achieve, gaining further performance and learning advantage is difficult, the gesture set and its computerized recognizer can be designed to minimize visual dependence, and positive emotional or aesthetic response can be achieved using musical auditory feedback.

## A New Contender in the Digital Differentiator Race

This blog proposes a novel differentiator worth your consideration. Although simple, the differentiator provides a fairly wide 'frequency range of linear operation' and can be implemented, if need be, without performing numerical multiplications.

## Hilbert Transform and Applications

●1 commentSection 1: reviews the mathematical deﬁnition of Hilbert transform and various ways to calculate it.

Sections 2 and 3: review applications of Hilbert transform in two major areas: Signal processing and system identiﬁcation.

Section 4: concludes with remarks on the historical development of Hilbert transform