The Rise and Fall of the early ʿAbbasid Political and Military Elite

This paper explores the composition and role of the military and political elite of the early ʿAbbāsid caliphate (750 –809) whose support enabled the caliphs to maintain sovereignty over their far-flung domains. It considers the importance of different groups, including members of the ʿAbbāsid family, military commanders from Khurāsān and members of powerful and wealthy families like the Muhallabīs and the Shaybāni tribal chiefs. The paper concludes with a discussion of the reasons for the disappearance and effective extinction of this elite in the years after the great civil war that followed Hārūn al-Rashīd’s death in 809

Lecture notes on the design of low-pass digital filters with wireless-communication applications

The low-pass filter is a fundamental building block from which digital signal-processing systems (e.g. radio and radar) are built. Signals in the electromagnetic spectrum extend over all timescales/frequencies and are used to transmit and receive very long or very short pulses of very narrow or very wide bandwidth. Time/Frequency agility is the key for optimal spectrum utilization (i.e. to suppress interference and enhance propagation) and low-pass filtering is the low-level digital mechanism for manoeuvre in this domain. By increasing and decreasing the bandwidth of a low-pass filter, thus decreasing and increasing its pulse duration, the engineer may shift energy concentration between frequency and time. Simple processes for engineering such components are described and explained below. These lecture notes are part of a short course that is intended to help recent engineering graduates design low-pass digital filters for this purpose, who have had some exposure to the topic during their studies, and who are now interested in the sending and receiving signals over the electromagnetic spectrum, in wireless communication (i.e. radio) and remote sensing (e.g. radar) applications, for instance. The best way to understand the material is to interact with the spectrum using receivers and or transmitters and software-defined radio development-kits provide a convenient platform for experimentation. Fortunately, wireless communication in the radio-frequency spectrum is an ideal application for the illustration of waveform agility in the electromagnetic spectrum. In Parts I and II, the theoretical foundations of digital low-pass filters are presented, i.e. signals-and-systems theory, then in Part III they are applied to the problem of radio communication and used to concentrate energy in time or frequency.Comment: Added Slepian ref. Added arXiv ID to heade

Digital Filters for Instantaneous Frequency Estimation

This technical note is on digital filters for the high-fidelity estimation of a sinusoidal signal's frequency in the presence of additive noise. The complex noise is assumed to be white (i.e. uncorrelated) however it need not be Gaussian. The complex signal is assumed to be of (approximately) constant magnitude and (approximately) polynomial phase such as the chirps emitted by bats, whale songs, pulse-compression radars, and frequency-modulated (FM) radios, over sufficiently short timescales. Such digital signals may be found at the end of a sequence of analogue heterodyning (i.e. mixing and low-pass filtering), down to a bandwidth that is matched to an analogue-to-digital converter (ADC), followed by digital heterodyning and sample rate reduction (optional) to match the clock frequency of the processor. The spacing of the discrete frequency bins (in cycles per sample) produced by the Fast Fourier Transform (FFT) is equal to the reciprocal of the window length (in samples). However, a long FFT (for fine frequency resolution) has a high complexity and a long latency, which may be prohibitive in embedded closed-loop systems, and unnecessary when the channel only contains a single sinusoid. In such cases, and for signals of constant frequency, the conventional approach involves the (weighted) average of instantaneous phase differences. General, naive, optimal, and pragmatic (recursive), filtering solutions are discussed and analysed here using Monte-Carlo (MC) simulations.Comment: Added arXiv ID to header and fixed a few typo

Recursive and non-recursive filters for sequential smoothing and prediction with instantaneous phase and frequency estimation applications (extended version)

A simple procedure for the design of recursive digital filters with an infinite impulse response (IIR) and non-recursive digital filters with a finite impulse response (FIR) is described. The fixed-lag smoothing filters are designed to track an approximately polynomial signal of specified degree without bias at steady state, while minimizing the gain of high-frequency (coloured) noise with a specified power spectral density. For the IIR variant, the procedure determines the optimal lag (i.e. the passband group delay) yielding a recursive low-complexity smoother of low order, with a specified bandwidth, and excellent passband phase linearity. The filters are applied to the problem of instantaneous frequency estimation, e.g. for Doppler-shift measurement, for a complex exponential with polynomial phase progression in additive white noise. For this classical problem, simulations show that the incorporation of a prediction filter (with a one-sample lead) reduces the incidence of (phase or frequency) angle unwrapping errors, particularly for signals with high rates of angle change, which are known to limit the performance of standard FIR estimators at low SNR. This improvement allows the instantaneous phase of low-frequency signals to be estimated, e.g. for time-delay measurement, and/or the instantaneous frequency of frequency-modulated signals, down to a lower SNR. In the absence of unwrapping errors, the error variance of the IIR estimators (with the optimal phase lag) reaches the FIR lower bound, at a significantly lower computational cost. Guidelines for configuring and tuning both FIR and IIR filters are provided.Comment: Reduced page count from 80 down to 50 by removing page breaks between figures and reducing figure size. Added page numbers. Added (extended version) to titl

Improved IIR Low-Pass Smoothers and Differentiators with Tunable Delay

Regression analysis using orthogonal polynomials in the time domain is used to derive closed-form expressions for causal and non-causal filters with an infinite impulse response (IIR) and a maximally-flat magnitude and delay response. The phase response of the resulting low-order smoothers and differentiators, with low-pass characteristics, may be tuned to yield the desired delay in the pass band or for zero gain at the Nyquist frequency. The filter response is improved when the shape of the exponential weighting function is modified and discrete associated Laguerre polynomials are used in the analysis. As an illustrative example, the derivative filters are used to generate an optical-flow field and to detect moving ground targets, in real video data collected from an airborne platform with an electro-optic sensor.Comment: To appear in Proc. International Conference on Digital Image Computing: Techniques and Applications (DICTA), Adelaide, 23rd-25th Nov. 201