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.
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.
Reducing IIR Filter Computational Workload
This document describes a straightforward method to significantly reduce the number of necessary multiplies per input sample of traditional IIR lowpass and highpass digital filters.
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.")
A Friendly Introduction to Compressed Sensing
Compared to other signal processing techniques, compressed sensing (or sparse sampling) has caught the interest of many mathematicians, electrical engineers, and computer scientists. The field of compressed sensing is still rapidly evolving. As most papers and textbooks about compressed sensing are at graduate level, the purpose of this paper is to offer a gentler exposure to compressed sensing from a mathematical perspective. By synthesizing my study on compressed sensing as an undergraduate, this thesis covers important concepts in CS such as coherence and restricted isometry property. Several key algorithms in compressed sensing will also be introduced with discussions of their stability, robustness, and performance. In the end, we investigate single-pixel camera as an example of real-world application of compressed sensing.
Update To: A Wide-Notch Comb Filter
This article presents alternatives to the wide-notch comb filter described in Reference [1].
Optimization of Synthesis Oversampled Complex Filter Banks
An important issue with oversampled FIR analysis filter banks (FBs) is to determine inverse synthesis FBs, when they exist. Given any complex oversampled FIR analysis FB, we first provide an algorithm to determine whether there exists an inverse FIR synthesis system. We also provide a method to ensure the Hermitian symmetry property on the synthesis side, which is serviceable to processing real-valued signals. As an invertible analysis scheme corresponds to a redundant decomposition, there is no unique inverse FB. Given a particular solution, we parameterize the whole family of inverses through a null space projection. The resulting reduced parameter set simplifies design procedures, since the perfect reconstruction constrained optimization problem is recast as an unconstrained optimization problem. The design of optimized synthesis FBs based on time or frequency localization criteria is then investigated, using a simple yet efficient gradient algorithm.
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.
Use Matlab Function pwelch to Find Power Spectral Density - or Do It Yourself
In this article, I'll present some examples to show how to use pwelch. You can also "do it yourself", i.e. compute spectra using the Matlab fft or other fft function. As examples, the appendix provides two demonstration mfiles; one computes the spectrum without DFT averaging, and the other computes the spectrum with DFT averaging.
Fully Programmable LDPC Decoder Hardware Architectures
In recent years, the amount of digital data which is stored and transmitted for private and public usage has increased considerably. To allow a save transmission and storage of data despite of error-prone transmission media, error correcting codes are used. A large variety of codes has been developed, and in the past decade low-density parity-check (LDPC) codes which have an excellent error correction performance became more and more popular. Today, low-density parity-check codes have been adopted for several standards, and efficient decoder hardware architectures are known for the chosen structured codes. However, the existing decoder designs lack flexibility as only few structured codes can be decoded with one decoder chip. In consequence, different codes require a redesign of the decoder, and few solutions exist for decoding of codes which are not quasi-cyclic or which are unstructured. In this thesis, three different approaches are presented for the implementation of fully programmable LDPC decoders which can decode arbitrary LDPC codes. As a design study, the first programmable decoder which uses a heuristic mapping algorithm is realized on an field-programmable gate array (FPGA), and error correction curves are measured to verify the correct functionality. The main contribution of this thesis lies in the development of the second and the third architecture and an appropriate mapping algorithm. The proposed fully programmable decoder architectures use one-phase message passing and layered decoding and can decode arbitrary LDPC codes using an optimum mapping and scheduling algorithm. The presented programmable architectures are in fact generalized decoder architectures from which the known decoders architectures for structured LDPC codes can be derived.
Implementing Simultaneous Digital Differentiation, Hilbert Transformation, and Half-Band Filtering
Recently 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
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.
Adaptive Algorithms in Digital Signal Processing - Overview, Theory and Applications
Introduction of C Programming for DSP Applications
Appendix C of the book : Real-Time Digital Signal Processing: Implementations, Application and Experiments with the TMS320C55X
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.
Fractional Delay FIR Filters
Consider the following Finite Impulse Response (FIR) coefficients:
b = [b0 b1 b2 b1 b0]
These coefficients form a 5-tap symmetrical FIR filter having constant group delay [1,2] over 0 to fs/2 of:
D = (ntaps - 1)/2 = 2 samples
For a symmetrical filter with an odd number of taps, the group delay is always an integer number of samples, while for one with an even number of taps, the group delay is always an integer + 0.5 samples. Can we design a filter with arbitrary delay, say 9.3 samples? The answer is yes -- It is possible to design a non-symmetrical FIR filter with arbitrary group delay which is approximately constant over a wide band, with approximately flat magnitude response [3,4]. Let the desired group delay be:
D = (ntaps - 1)/2 + u
= D0 + u samples, (1)
where we call u the fractional delay and -0.5 <= u <= 0.5. D0 is the fixed portion of the total delay; it is determined by ntaps. The appendix lists a simple Matlab function frac_delay_fir.m to compute FIR coefficients for a given value of u and ntaps. The function provides coefficients with approximately flat delay and frequency responses over a frequency range approaching 0 to fs/2.
In this post, we'll present a couple of examples using the function, then discuss the theory behind it. Finally, we'll look at an example of a fractional delay lowpass FIR filter with arbitrary cut-off frequency.
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.
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.
Introduction to Digital Signal Processing
Nice slides introducing Digital Signal Processing.
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.
Correcting an Important Goertzel Filter Misconception
Correcting an Important Goertzel Filter Misconception
Hilbert Transform and Applications
Section 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
Digital Signal Processor Fundamentals and System Design
Digital Signal Processors (DSPs) have been used in accelerator systems for more than fifteen years and have largely contributed to the evolution towards digital technology of many accelerator systems, such as machine protection, diagnostics and control of beams, power supply and motors. This paper aims at familiarising the reader with DSP fundamentals, namely DSP characteristics and processing development. Several DSP examples are given, in particular on Texas Instruments DSPs, as they are used in the DSP laboratory companion of the lectures this paper is based upon. The typical system design flow is described; common difficulties, problems and choices faced by DSP developers are outlined; and hints are given on the best solution.
