## Implementing Simultaneous Digital Differentiation, Hilbert Transformation, and Half-Band Filtering

●2 commentsRecently I've been thinking about digital differentiator and Hilbert transformer implementations and I've developed a processing scheme that may be of interest to the readers here on dsprelated.com.

## 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.

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

●9 commentsThis 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?

## Correcting an Important Goertzel Filter Misconception

Correcting an Important Goertzel Filter Misconception

## 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.")

## 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.

## Towards Efﬁcient and Robust Automatic Speech Recognition: Decoding Techniques and Discriminative Training

●1 commentAutomatic speech recognition has been widely studied and is already being applied in everyday use. Nevertheless, the recognition performance is still a bottleneck in many practical applications of large vocabulary continuous speech recognition. Either the recognition speed is not sufﬁcient, or the errors in the recognition result limit the applications. This thesis studies two aspects of speech recognition, decoding and training of acoustic models, to improve speech recognition performance in different conditions.

## Optimizing the Half-band Filters in Multistage Decimation and Interpolation

●2 commentsThis article discusses a not so well-known rule regarding the filtering in multistage decimation and interpolation by an integer power of two.

## A Review of Physical and Perceptual Feature Extraction Techniques for Speech, Music and Environmental Sounds

●3 commentsEndowing machines with sensing capabilities similar to those of humans is a prevalent quest in engineering and computer science. In the pursuit of making computers sense their surroundings, a huge effort has been conducted to allow machines and computers to acquire, process, analyze and understand their environment in a human-like way. Focusing on the sense of hearing, the ability of computers to sense their acoustic environment as humans do goes by the name of machine hearing. To achieve this ambitious aim, the representation of the audio signal is of paramount importance. In this paper, we present an up-to-date review of the most relevant audio feature extraction techniques developed to analyze the most usual audio signals: speech, music and environmental sounds. Besides revisiting classic approaches for completeness, we include the latest advances in the field based on new domains of analysis together with novel bio-inspired proposals. These approaches are described following a taxonomy that organizes them according to their physical or perceptual basis, being subsequently divided depending on the domain of computation (time, frequency, wavelet, image-based, cepstral, or other domains). The description of the approaches is accompanied with recent examples of their application to machine hearing related problems.

## An Experimental Multichannel Pulse Code Modulation System of Toll Quality + Electron Beam Deflection Tube For Pulse Code Modulation

●1 commentSee this blog post for context. Pulse Code Modulation offers attractive possibilities for multiplex telephony via such media as the microwave radio relay. The various problems involved in its use have been explored in terms of a 96-channel system designed to meet the transmission requirements commonly imposed upon commercial toll circuits. Twenty-four of the 96 channels have been fully equipped in an experimental model of the system. Coding and decoding devices are described, along with other circuit details. The coder is based upon a new electron beam tube, and is characterized by speed and simplicity as well as accuracy of coding. These qualities are matched in the decoder, which employs pulse excitation of a simple reactive network.

## The DFT Magnitude of a Real-valued Cosine Sequence

●5 commentsThis article may seem a bit trivial to some readers here but, then again, it might be of some value to DSP beginners. It presents a mathematical proof of what is the magnitude of an N-point discrete Fourier transform (DFT) when the DFT's input is a real-valued sinusoidal sequence.

## Hybrid Floating Point Technique Yields 1.2 Gigasample Per Second 32 to 2048 point Floating Point FFT in a single FPGA

Hardware Digital Signal Processing, especially hardware targeted to FPGAs, has traditionally been done using fixed point arithmetic, mainly due to the high cost associated with implementing floating point arithmetic. That cost comes in the form of increased circuit complexity. The increase circuit complexity usually also degrades maximum clock performance. Certain applications demand the dynamic range offered by floating point hardware, and yet require the speeds and circuit density usually associated with fixed point hardware. The Fourier transform is one DSP building block that frequently requires floating point dynamic range. Textbook construction of a pipelined floating point FFT engine capable of continuous input entails dozens of floating point adders and multipliers. The complexity of those circuits quickly exceeds the resources available on a single FPGA. This paper describes a technique that is a hybrid of fixed point and floating point operations designed to significantly reduce the overhead for floating point. The results are illustrated with an FFT processor that performs 32, 64, 128, 256, 512, 1024 and 2048 point Fourier transforms with IEEE single precision floating point inputs and outputs. The design achieves sufficient density to realize a continuous complex data rate of 1.2 Gigasamples per second data throughput using a single Virtex4-SX55-10 device.

## Introduction to Sound Processing

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

## Implementation of a Tx/Rx OFDM System in a FPGA

●1 commentThe aim of this project consists in the FPGA design and implementation of a transmitter and receiver (Tx/Rx) multicarrier system such the Orthogonal Frequency Division Multiplexing (OFDM). This Tx/Rx OFDM subsystem is capable to deal with with different M-QAM modulations and is implemented in a digital signal processor (DSP-FPGA). The implementation of the Tx/Rx subsystem has been carried out in a FPGA using both System Generator visual programming running over Matlab/Simulink, and the Xilinx ISE program which uses VHDL language. This project is divided into four chapters, each one with a concrete objective. The first chapter is a brief introduction to the digital signal processor used, a field-programmable gate array (FPGA), and to the VHDL programming language. The second chapter is an overview on OFDM, its main advantages and disadvantages in front of previous systems, and a brief description of the different blocks composing the OFDM system. Chapter three provides the implementation details for each of these blocks, and also there is a brief explanation on the theory behind each of the OFDM blocks to provide a better comprehension on its implementation. The fourth chapter is focused, on the one hand, in showing the results of the Matlab/Simulink simulations for the different simulation schemes used and, on the other hand, to show the experimental results obtained using the FPGA to generate the OFDM signal at baseband and then upconverted at the frequency of 3,5 GHz. Finally the conclusions regarding the whole Tx/Rx design and implementation of the OFDM subsystem are given.

## 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.

## 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.

## A Brief Introduction To Romberg Integration

This article briefly describes a remarkable integration algorithm, called "Romberg integration." The algorithm is used in the field of numerical analysis but it's not so well-known in the world of DSP.