Decimator Image Response
This article presents a way to compute and plot the image response of a decimator. I'm defining the image response as the unwanted spectrum of the impulse response after downsampling, relative to the desired passband response.
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.
Digital Envelope Detection: The Good, the Bad, and the Ugly
Recently I've been thinking about the process of envelope detection. Tutorial information on this topic is readily available but that information is spread out over a number of DSP textbooks and many Internet web sites. The purpose of this blog is to summarize various digital envelope detection methods in one place. Here I focus of envelope detection as it is applied to an amplitude-fluctuating sinusoidal signal where the positive-amplitude fluctuations (the sinusoid's envelope) contain some sort of information. Let's begin by looking at the simplest envelope detection method.
Python For Audio Signal Processing
This paper discusses the use of Python for developing audio signal processing applications. Overviews of Python language, NumPy, SciPy and Matplotlib are given, which together form a powerful platform for scientific computing. We then show how SciPy was used to create two audio programming libraries, and describe ways that Python can be integrated with the SndObj library and Pure Data, two existing environments for music composition and signal processing.
Lecture Notes on Elliptic Filter Design
Elliptic 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.
Optimizing the Half-band Filters in Multistage Decimation and Interpolation
This article discusses a not so well-known rule regarding the filtering in multistage decimation and interpolation by an integer power of two.
The DFT Magnitude of a Real-valued Cosine Sequence
This 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.
Sum of Two Equal-Frequency Sinusoids
The sum of two equal-frequency real sinusoids is itself a single real sinusoid. However, the exact equations for all the various forms of that single equivalent sinusoid are difficult to find in the signal processing literature. Here we provide those equations.
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.
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 :-).
Active control of automobile cabin noise with conventional and advanced speakers
Recently much research has focused on the control of enclosed sound fields, particularly in automobiles. Both Active Noise Control (ANC) and Active Structural Acoustic Control (ASAC) techniques are being applied to problems stemming from power train noise and road noise (noise due to the interaction of the tires with the surface of the road). Due to the low frequency characteristics of these noise problems, large acoustic sources are required to obtain efficient control of the sound field. This creates demand in the automobile industry for compact lightweight sources. This work is concerned with the application of active control to power train noise, as well as road noise in the interior cabin of a sport utility vehicle using advanced, compact lightweight piezoelectric acoustic sources. First, a test structure approximately the same size as the automobile was built to study the principles of active noise control in a cavity. A finite element model of the cavity was created in order to optimize the positions of the error sensors and the control sources. Experimental work was performed with the optimized actuator and sensor locations in order to validate the model, and draw conclusions regarding the conditions to obtain global control of the sound field. Second, a broad-band feedforward filtered-X LMS algorithm was used to control power train noise. Preliminary power train noise tests were conducted using arrangements of four microphones and up to four commercially available speakers for control. Attenuation of seven decibel (dB) at the error sensors was measured in the 40-500 Hz frequency band. The dimensions of the zone of quiet generated by the control were measured, and show that noise reductions were obtained for a large volume surrounding the error sensors. Next, advanced speakers were implemented for active control of power train noise. The results obtained with different arrangements of these speakers were very similar to those obtained with the commercially-available speakers. These advanced speakers use piezoelectric devices to induce the displacement of a speaker membrane, which radiates sound. Their lighter weight and compact dimensions are a significant advantage over conventional speakers, for their application in automobile. Third, preliminary results were obtained for active control of road noise. The controller used an optimized set of four reference signals to control the noise at one error sensor using one control source. Two sets of tests were conducted. The first set of tests was performed on a dynamometer, which simulates the effects of the road on the tires. The second set of tests was performed on a rough road. Reduction of two to four decibel of the sound pressure level at the error sensor was obtained between 100 and 200 Hz.
A Subspace Based Approach to the Design, Implementation and Validation of Algorithms for Active Vibration Isolation Control
Vibration isolation endeavors to reduce the transmission of vibration energy from one structure (the source) to another (the receiver), to prevent undesirable phenomena such as sound radiation. A well-known method for achieving this is passive vibration isolation (PVI). In the case of PVI, mounts are used - consisting of springs and dampers - to connect the vibrating source to the receiver. The stiffness of the mount determines the fundamental resonance frequency of the mounted system and vibrations with a frequency higher than the fundamental resonance frequency are attenuated. Unfortunately, however, other design requirements (such as static stability) often impose a minimum allowable stiffness, thus limiting the achievable vibration isolation by passive means. A more promising method for vibration isolation is hybrid vibration isolation control. This entails that, in addition to PVI, an active vibration isolation control (AVIC) system is used with sensors, actuators and a control system that compensates for vibrations in the lower frequency range. Here, the use of a special form of AVIC using statically determinate stiff mounts is proposed. The mounts establish a statically determinate system of high stiffness connections in the actuated directions and of low stiffness connections in the unactuated directions. The latter ensures PVI in the unactuated directions. This approach is called statically determinate AVIC (SD-AVIC). The aim of the control system is to produce antidisturbance forces that counteract the disturbance forces stemming from the source. Using this approach, the vibration energy transfer from the source to the receiver is blocked in the mount due to the anti-forces. This thesis deals with the design of controllers generating the anti-forces by applying techniques that are commonly used in the field of signal processing. The control approaches - that are model-based - are both adaptive and fixed gain and feedforward and feedback oriented. The control approaches are validated using two experimental vibration isolation setups: a single reference single actuator single error sensor (SR-SISO) setup and a single reference input multiple actuator input multiple error sensor output (SR-MIMO) setup. Finding a plant model can be a problem. This is solved by using a black-box modelling strategy. The plants are identified using subspace model identification. It is shown that accurate linear models can be found in a straightforward manner by using small batches of recorded (sampled) time-domain data only. Based on the identified models, controllers are designed, implemented and validated. Due to resonance in mechanical structures, adaptive SD-AVIC systems are often hampered by slow convergence of the controller coefficients. In general, it is desirable that the SD-AVIC system yields fast optimum performance after it is switched on. To achieve this result and speed up the convergence of the adaptive controller coefficients, the so-called inverse outer factor model is included in the adaptive control scheme. The inner/outer factorization, that has to be performed to obtain the inverse outer factor model, is completely determined in state space to enable a numerically robust computation. The inverse outer factor model is also incorporated in the control scheme as a state space model. It is found that fast adaptation of the controller coefficients is possible. Controllers are designed, implemented and validated to suppress both narrowband and broadband disturbances. Scalar regularization is used to prevent actuator saturation and an unstable closed loop. In order to reduce the computational load of the controllers, several steps are taken including controller order reduction and implementation of lower order models. It is found that in all experiments the simulation and real-time results correspond closely for both the fixed gain and adaptive control situation. On the SR-SISO setup, reductions up to 5.0 dB are established in real-time for suppressing a broadband disturbance output (0-2 kHz) using feedback-control. On the SR-MIMO vibration isolation setup, using feedforward-control reductions of broadband disturbances (0-1 kHz) of 9.4 dB are established in real-time. Using feedback-control, reductions are established up to 3.5 dB in real-time (0-1 kHz). In case of the SR-MIMO setup, the values for the reduction are obtained by averaging the reductions obtained in all sensor outputs. The results pave the way for the next generation of algorithms for SD-AVIC.
Implementing IS-95, the CDMA Standard, on TMS320C6201 DSP
IS-95 is the present U.S. 2nd generation CDMA standard. Currently, the 2nd generation CDMA phones are produced by Qualcomm. Texas Instruments (TI) has ASIC design for Viterbi Decoder on C54x. Several of the components in the forward link process are also implemented in hardware. However, having to design a specific hardware for a particular application is expensive and time consuming. Thus, the possibility of the alternative implementations is of great interest to both customers and TI itself. This research has achieved in successful implementation of IS-95 entirely in software on TI fixed-point DSP TMS320C6201, and met the real time constraint. IS-95 system, the industrial standard for CDMA, is a very complicated system and extremely computationally demanding. The transmission rate for an IS-95 system is 1.2288 Mcps. This research project includes all the major components of the demodulation process for the forward link system: PN Descrambling, Walsh Despreading, Phase Correction & Maximal Ratio Combining, Deinterleaver, Digital Automatic Gain Control, and Viterbi Deccc:r. The entire demodulation process is done completely in C. That makes it a very attractive alternative implementation in the future applications. It is well known that ASIC design is not only expensive and but also time consuming, programming in assembly is easier and cheaper, but programming in C is a much easier and efficient way out, in particular, for general computer engineers. During the whole process, efforts have been devoted on developing various specific techniques to optimize the design for all the components involved. These developments are successfully achieved by making the best use of the following techniques: to simplify the algorithms first before programming, to look for regularity in the problem, to work toward the Compiler's full efficiency, and to use C intrinsics whenever possible. All these attributes together make the implementation scheme great for DSP applications. The benchmark results compare very well to the TI-internal hand scheduled assembly performance of the same type of decoders. The estimated percentage usage of all the components (excluding PN) is only 21.18% of the total CPU cycles available (4,000 K), which is very efficient and impressive.
Biosignal processing challenges in emotion recognition for adaptive learning
User-centered computer based learning is an emerging field of interdisciplinary research. Research in diverse areas such as psychology, computer science, neuroscience and signal processing is making contributions to take this field to the next level. Learning systems built using contributions from these fields could be used in actual training and education instead of just laboratory proof-of-concept. One of the important advances in this research is the detection and assessment of the cognitive and emotional state of the learner using such systems. This capability moves development beyond the use of traditional user performance metrics to include system intelligence measures that are based on current theories in neuroscience. These advances are of paramount importance in the success and wide spread use of learning systems that are automated and intelligent. Emotion is considered an important aspect of how learning occurs, and yet estimating it and making adaptive adjustments are not part of most learning systems. In this research we focus on one specific aspect of constructing an adaptive and intelligent learning system, that is, estimation of the emotion of the learner as he/she is using the automated training system. The challenge starts with the definition of the emotion and the utility of it in human life. The next challenge is to measure the co-varying factors of the emotions in a non-invasive way, and find consistent features from these measures that are valid across wide population. In this research we use four physiological sensors that are non-invasive, and establish a methodology of utilizing the data from these sensors using different signal processing tools. A validated set of visual stimuli used worldwide in the research of emotion and attention, called International Affective Picture System (IAPS), is used. A dataset is collected from the sensors in an experiment designed to elicit emotions from these validated visual stimuli. We describe a novel wavelet method to calculate hemispheric asymmetry metric using electroencephalography data. This method is tested against typically used power spectral density method. We show overall improvement in accuracy in classifying specific emotions using the novel method. We also show distinctions between different discrete emotions from the autonomic nervous system activity using electrocardiography, electrodermal activity and pupil diameter changes. Findings from different features from these sensors are used to give guidelines to use each of the individual sensors in the adaptive learning environment.
Auditory Component Analysis Using Perceptual Pattern Recognition to Identify and Extract Independent Components From an Auditory Scene
The cocktail party effect, our ability to separate a sound source from a multitude of other sources, has been researched in detail over the past few decades, and many investigators have tried to model this on computers. Two of the major research areas currently being evaluated for the so-called sound source separation problem are Auditory Scene Analysis (Bregman 1990) and a class of statistical analysis techniques known as Independent Component Analysis (Hyvärinen 2001). This paper presents a methodology for combining these two techniques. It suggests a framework that first separates sounds by analyzing the incoming audio for patterns and synthesizing or filtering them accordingly, measures features of the resulting tracks, and finally separates sounds statistically by matching feature sets and making the output streams statistically independent. Artificial and acoustical mixes of sounds are used to evaluate the signal-to-noise ratio where the signal is the desired source and the noise is comprised of all other sources. The proposed system is found to successfully separate audio streams. The amount of separation is inversely proportional to the amount of reverberation present.
Design IIR Bandpass Filters
In this post, I present a method to design Butterworth IIR bandpass filters. My previous post [1] covered lowpass IIR filter design, and provided a Matlab function to design them. Here, we'll do the same thing for IIR bandpass filters, with a Matlab function bp_synth.m
Design IIR Butterworth Filters Using 12 Lines of Code
While there are plenty of canned functions to design Butterworth IIR filters [1], it's instructive and not that complicated to design them from scratch. You can do it in 12 lines of Matlab code.
A Simplified Matlab Function for Power Spectral Density
In an earlier post, I showed how to compute power spectral density (PSD) of a discrete-time signal using the Matlab function pwelch. Pwelch is a useful function because it gives the correct output, and it has the option to average multiple Discrete Fourier Transforms (DFTs). However, a typical function call has five arguments, and it can be hard to remember how to set them all and how they default.
In this post, I create a simplified PSD function by putting a wrapper on pwelch that sets some parameters and converts the output units from W/Hz to dBW/bin. The function is named psd_simple.m, and its code is listed in the appendix.
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.
The DFT of Finite-Length Time-Reversed Sequences
Recently I've been reading papers on underwater acoustic communications systems and this caused me to investigate the frequency-domain effects of time-reversal of time-domain sequences. I created this article because there is so little coverage of this topic in the literature of DSP.
