## Python For Audio Signal Processing

●6 commentsThis 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

●1 commentElliptic 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

●2 commentsThis 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

●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.

## Sum of Two Equal-Frequency Sinusoids

●4 commentsThe 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

●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.

## Negative Group Delay

●2 commentsDispersive 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 :-).

## 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

●8 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?

## Digital PLL's -- Part 1

●4 commentsWe will use Matlab to model the DPLL in the time and frequency domains (Simulink is also a good tool for modeling a DPLL in the time domain). Part 1 discusses the time domain model; the frequency domain model will be covered in Part 2. The frequency domain model will allow us to calculate the loop filter parameters to give the desired bandwidth and damping, but it is a linear model and cannot predict acquisition behavior. The time domain model can be made almost identical to the gate-level system, and as such, is able to model acquisition.

## Two Easy Ways To Test Multistage CIC Decimation Filters

●1 commentThis article presents two very easy ways to test the performance of multistage cascaded integrator-comb (CIC) decimation filters. Anyone implementing CIC filters should take note of the following proposed CIC filter test methods.

## 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.

## The Swiss Army Knife of Digital Networks

●4 commentsThis article describes a general discrete-signal network that appears, in various forms, inside so many DSP applications.

## Algorithms for Efficient Computation of Convolution

●5 commentsConvolution is an important mathematical tool in both ﬁelds of signal and image processing. It is employed in ﬁltering, denoising, edge detection, correlation, compression, deconvolution, simulation, and in many other applications. Although the concept of convolution is not new, the efﬁcient computation of convolution is still an open topic. As the amount of processed data is constantly increasing, there is considerable request for fast manipulation with huge data. Moreover, there is demand for fast algorithms which can exploit computational power of modern parallel architectures.

## Peak-to-Average Power Ratio and CCDF

●1 commentPeak to Average Power Ratio (PAPR) is often used to characterize digitally modulated signals. One example application is setting the level of the signal in a digital modulator. Knowing PAPR allows setting the average power to a level that is just low enough to minimize clipping.

## Digital PLL's - Part 2

In Part 1, we found the time response of a 2nd order PLL with a proportional + integral (lead-lag) loop filter. Now let's look at this PLL in the Z-domain.

## 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.

## 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.

## Negative Group Delay

●2 commentsDispersive 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 :-).