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 :-).
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.
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.
Teaching MODEM Concepts and Design Procedure with MATLAB Simulations
MATLAB simulation is used as the primary tool to illustrate concepts, to validate MODEM designs, and to vent' operation of the subsystems employed in DSP based transmitters and receivers presented in a pair of classes on MODEM Design and Digital Receiver Design. The whole gamut of subsystems found in conventional and experimental modem designs are simulated and assembled to form a full end-to-end simulation of an operating MODEM. This paper describes the philosophy used to guide class involvement and assess the experience and the learning value to student participants.
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.
Multirate Systems and Filter Banks
During 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.
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.")
Model Signal Impairments at Complex Baseband
In this article, we develop complex-baseband models for several signal impairments: interfering carrier, multipath, phase noise, and Gaussian noise. To provide concrete examples, we'll apply the impairments to a QAM system. The impairment models are Matlab functions that each use at most seven lines of code. Although our example system is QAM, the models can be used for any complex-baseband signal.
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.
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.
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.
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.
