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
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?
Correcting an Important Goertzel Filter Misconception
Correcting an Important Goertzel Filter Misconception
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.")
Specifying the Maximum Amplifier Noise When Driving an ADC
I 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
Automatic 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.
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.
Negative Group Delay
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 :-).
Method to Calculate the Inverse of a Complex Matrix using Real Matrix Inversion
This paper describes a simple method to calculate the invers of a complex matrix. The key element of the method is to use a matrix inversion, which is available and optimised for real numbers. Some actual libraries used for digital signal processing only provide highly optimised methods to calculate the inverse of a real matrix, whereas no solution for complex matrices are available, like in [1]. The presented algorithm is very easy to implement, while still much more efficient than for example the method presented in [2]. [1] Visual DSP++ 4.0 C/C++ Compiler and Library Manual for TigerSHARC Processors; Analog Devices; 2005. [2] W. Press, S.A. Teukolsky, W.T. Vetterling, B.R. Flannery; Numerical Recipes in C++, The art of scientific computing, Second Edition; p52 : “Complex Systems of Equations”;Cambridge University Press 2002.
Gauss-Newton Based Learning for Fully Recurrent Neural Networks
The thesis discusses a novel off-line and on-line learning approach for Fully Recurrent Neural Networks (FRNNs). The most popular algorithm for training FRNNs, the Real Time Recurrent Learning (RTRL) algorithm, employs the gradient descent technique for finding the optimum weight vectors in the recurrent neural network. Within the framework of the research presented, a new off-line and on-line variation of RTRL is presented, that is based on the Gauss-Newton method. The method itself is an approximate Newton’s method tailored to the specific optimization problem, (non-linear least squares), which aims to speed up the process of FRNN training. The new approach stands as a robust and effective compromise between the original gradient-based RTRL (low computational complexity, slow convergence) and Newton-based variants of RTRL (high computational complexity, fast convergence). By gathering information over time in order to form Gauss-Newton search vectors, the new learning algorithm, GN-RTRL, is capable of converging faster to a better quality solution than the original algorithm. Experimental results reflect these qualities of GN-RTRL, as well as the fact that GN-RTRL may have in practice lower computational cost in comparison, again, to the original RTRL.
Fundamentals of the DFT (fft) Algorithms
In this article, a physical explanation of the fundamentals of the DFT (fft) algorithms is presented in terms of waveform decomposition. After reading the article and trying the examples, the reader is expected to gain a clear understanding of the basics of the mysterious DFT (fft) algorithms.
Acoustic Echo Cancellation using Digital Signal Processing
Acoustic echo cancellation is a common occurrence in todays telecommunication systems. It occurs when an audio source and sink operate in full duplex mode, an example of this is a hands-free loudspeaker telephone. In this situation the received signal is output through the telephone loudspeaker (audio source), this audio signal is then reverberated through the physical environment and picked up by the systems microphone (audio sink). The effect is the return to the distant user of time delayed and attenuated images of their original speech signal. The signal interference caused by acoustic echo is distracting to both users and causes a reduction in the quality of the communication. This thesis focuses on the use of adaptive filtering techniques to reduce this unwanted echo, thus increasing communication quality. Adaptive filters are a class of filters that iteratively alter their parameters in order to minimise a function of the difference between a desired target output and their output. In the case of acoustic echo in telecommunications, the optimal output is an echoed signal that accurately emulates the unwanted echo signal. This is then used to negate the echo in the return signal. The better the adaptive filter emulates this echo, the more successful the cancellation will be. This thesis examines various techniques and algorithms of adaptive filtering, employing discrete signal processing in MATLAB. Also a real-time implementation of an adaptive echo cancellation system has been developed using the Texas Instruments TMS320C6711 DSP development kit.
Digital Filtering in the Frequency Domain
Time domain digital filtering, whether implemented using FIR or IIR techniques, has been very well documented in literature and been thoroughly used in many base band processor designs. However, with the advent of software defined radios as well as CPU support in more recent baseband processors, it has become possible and often desirable to filter signals in software rather than digital hardware. Whereas, time domain digital filtering can certainly be implemented in software as well, it becomes highly inefficient as the number of filter taps grows. Frequency domain filtering, using FFT and IFFT operations, is significantly more efficient and surprisingly easy to understand. This document introduces the reader to frequency domain filtering both in theory and in practice via a MatLab script.
A Review of Physical and Perceptual Feature Extraction Techniques for Speech, Music and Environmental Sounds
Endowing 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.
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.
Implementation of Uncoordinated Direct Sequence Spread Spectrum using Software Defined Radios
One of the major threats to wireless communications is jamming. Many anti-jamming techniques have been presented in the past. However most of them are based on the precondition that the communicating devices have a pre-shared secret that can be used to synchronize the anti-jamming scheme. E.g. for frequency hopping the secret could be used to derive the hopping sequence and for direct sequence spread spectrum the secret is used to derive the spreading codes. But how can the devices bootstrap a jamming-resistant communication without having a pre-shared secret? Christina Popper and Mario Strasser propose as scheme for Uncoordinated Frequency Hopping (UFH) and Uncoordinated Direct Sequence Spread Spectrum (UDSSS) in their papers [1] and [2] respectively. The goal of my project was an implementation of Uncoordinated Direct Sequence Spread Spectrum (UDSSS) using Software Dened Radios. The First version should serve as an easy to use and extendable proof of conceptfor the proposed scheme.